idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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42,401 | Minimum dimension of sufficient statistics | Since sufficiency of fixed dimension only occurs in exponential families (Darmois-Pitman-Koopman lemma), apart from distributions with varying support like the Uniform, let us consider an exponential family with parameter $\theta$ and density [against a fixed dominating measure]
$$f_\theta(x)=\exp\left\{\sum_{i=1}^k a_... | Minimum dimension of sufficient statistics | Since sufficiency of fixed dimension only occurs in exponential families (Darmois-Pitman-Koopman lemma), apart from distributions with varying support like the Uniform, let us consider an exponential | Minimum dimension of sufficient statistics
Since sufficiency of fixed dimension only occurs in exponential families (Darmois-Pitman-Koopman lemma), apart from distributions with varying support like the Uniform, let us consider an exponential family with parameter $\theta$ and density [against a fixed dominating measur... | Minimum dimension of sufficient statistics
Since sufficiency of fixed dimension only occurs in exponential families (Darmois-Pitman-Koopman lemma), apart from distributions with varying support like the Uniform, let us consider an exponential |
42,402 | Expected number of times you spent in a state of an absorbing markov chain, given the eventual absorbing state | Using the Wikipedia notation, the full matrix of transition probabilities is written as
$$P = \left(\begin{array}{cc} Q & R \\ 0 & I \end{array}\right)$$
with the states organized so that the last states are all absorbing. In the OP's example from population genetics, the states would be organized as $1, 2, \ldots, M-... | Expected number of times you spent in a state of an absorbing markov chain, given the eventual absor | Using the Wikipedia notation, the full matrix of transition probabilities is written as
$$P = \left(\begin{array}{cc} Q & R \\ 0 & I \end{array}\right)$$
with the states organized so that the last st | Expected number of times you spent in a state of an absorbing markov chain, given the eventual absorbing state
Using the Wikipedia notation, the full matrix of transition probabilities is written as
$$P = \left(\begin{array}{cc} Q & R \\ 0 & I \end{array}\right)$$
with the states organized so that the last states are ... | Expected number of times you spent in a state of an absorbing markov chain, given the eventual absor
Using the Wikipedia notation, the full matrix of transition probabilities is written as
$$P = \left(\begin{array}{cc} Q & R \\ 0 & I \end{array}\right)$$
with the states organized so that the last st |
42,403 | Are the balls drawn randomly (independently of the number of balls existing in their colours)? | Because your proposed test has no theoretical foundation and does not account for the correlations among the counts, it would not be a good use of our time to evaluate it. Instead, let's develop some tests that will work.
The Likelihood Ratio test is guaranteed to work well when all counts are relatively large. So wi... | Are the balls drawn randomly (independently of the number of balls existing in their colours)? | Because your proposed test has no theoretical foundation and does not account for the correlations among the counts, it would not be a good use of our time to evaluate it. Instead, let's develop some | Are the balls drawn randomly (independently of the number of balls existing in their colours)?
Because your proposed test has no theoretical foundation and does not account for the correlations among the counts, it would not be a good use of our time to evaluate it. Instead, let's develop some tests that will work.
Th... | Are the balls drawn randomly (independently of the number of balls existing in their colours)?
Because your proposed test has no theoretical foundation and does not account for the correlations among the counts, it would not be a good use of our time to evaluate it. Instead, let's develop some |
42,404 | Enlarging a random sample | Correction
I withdraw the previous answer (below) as wrong. @Glen_b is correct, if the second sample is not based on any results in the first, then the overall probability of selection is $\dfrac{n}{N}$, the same as for a SRS (proof below). Further, you can treat the result as a SRS although the size was not fixed in... | Enlarging a random sample | Correction
I withdraw the previous answer (below) as wrong. @Glen_b is correct, if the second sample is not based on any results in the first, then the overall probability of selection is $\dfrac{n}{ | Enlarging a random sample
Correction
I withdraw the previous answer (below) as wrong. @Glen_b is correct, if the second sample is not based on any results in the first, then the overall probability of selection is $\dfrac{n}{N}$, the same as for a SRS (proof below). Further, you can treat the result as a SRS although... | Enlarging a random sample
Correction
I withdraw the previous answer (below) as wrong. @Glen_b is correct, if the second sample is not based on any results in the first, then the overall probability of selection is $\dfrac{n}{ |
42,405 | Enlarging a random sample | It depends on whether an assumption about same distribution between the remaining 900+ after the first sampling process and original 1000+ can be held. If possible you can perform an test about mean or heteroscedasticity of the parameter(s) of interested. | Enlarging a random sample | It depends on whether an assumption about same distribution between the remaining 900+ after the first sampling process and original 1000+ can be held. If possible you can perform an test about mean | Enlarging a random sample
It depends on whether an assumption about same distribution between the remaining 900+ after the first sampling process and original 1000+ can be held. If possible you can perform an test about mean or heteroscedasticity of the parameter(s) of interested. | Enlarging a random sample
It depends on whether an assumption about same distribution between the remaining 900+ after the first sampling process and original 1000+ can be held. If possible you can perform an test about mean |
42,406 | Enlarging a random sample | I am not quite sure how random this sample could be considered. I don't have a great experience of statistics but the method you suggest doesn't sound very good to me. What I would do is put back the sample I took from the entire population, reorder them and take again a random sample from it. Or I would just take a ne... | Enlarging a random sample | I am not quite sure how random this sample could be considered. I don't have a great experience of statistics but the method you suggest doesn't sound very good to me. What I would do is put back the | Enlarging a random sample
I am not quite sure how random this sample could be considered. I don't have a great experience of statistics but the method you suggest doesn't sound very good to me. What I would do is put back the sample I took from the entire population, reorder them and take again a random sample from it.... | Enlarging a random sample
I am not quite sure how random this sample could be considered. I don't have a great experience of statistics but the method you suggest doesn't sound very good to me. What I would do is put back the |
42,407 | LRT for one-sided Bernoulli parameter | You can take the derivative of $\log(\lambda)$ in order to get a rejection region. This is problem 8.3 in (1).
(1) Casella, G., and Berger, R. L. (2002). Statistical inference. Duxbury Press. | LRT for one-sided Bernoulli parameter | You can take the derivative of $\log(\lambda)$ in order to get a rejection region. This is problem 8.3 in (1).
(1) Casella, G., and Berger, R. L. (2002). Statistical inference. Duxbury Press. | LRT for one-sided Bernoulli parameter
You can take the derivative of $\log(\lambda)$ in order to get a rejection region. This is problem 8.3 in (1).
(1) Casella, G., and Berger, R. L. (2002). Statistical inference. Duxbury Press. | LRT for one-sided Bernoulli parameter
You can take the derivative of $\log(\lambda)$ in order to get a rejection region. This is problem 8.3 in (1).
(1) Casella, G., and Berger, R. L. (2002). Statistical inference. Duxbury Press. |
42,408 | LRT for one-sided Bernoulli parameter | Let $k=\sum_ix_i$. The likelihood $L(\theta|X)=\theta^k(1-\theta)^{n-k}$ is unimodal and maximized at $\theta=\frac{k}{n}$. Hence, the likelihood ratio $\lambda(X)$ is given by $$\lambda(X)=\frac{\theta_0^k(1-\theta_0)^{n-k}}{\left(\frac{k}{n}\right)^k\left(1-\frac{k}{n}\right)^{n-k}}$$ when $\theta_0<\frac{k}{n}$ and ... | LRT for one-sided Bernoulli parameter | Let $k=\sum_ix_i$. The likelihood $L(\theta|X)=\theta^k(1-\theta)^{n-k}$ is unimodal and maximized at $\theta=\frac{k}{n}$. Hence, the likelihood ratio $\lambda(X)$ is given by $$\lambda(X)=\frac{\the | LRT for one-sided Bernoulli parameter
Let $k=\sum_ix_i$. The likelihood $L(\theta|X)=\theta^k(1-\theta)^{n-k}$ is unimodal and maximized at $\theta=\frac{k}{n}$. Hence, the likelihood ratio $\lambda(X)$ is given by $$\lambda(X)=\frac{\theta_0^k(1-\theta_0)^{n-k}}{\left(\frac{k}{n}\right)^k\left(1-\frac{k}{n}\right)^{n-... | LRT for one-sided Bernoulli parameter
Let $k=\sum_ix_i$. The likelihood $L(\theta|X)=\theta^k(1-\theta)^{n-k}$ is unimodal and maximized at $\theta=\frac{k}{n}$. Hence, the likelihood ratio $\lambda(X)$ is given by $$\lambda(X)=\frac{\the |
42,409 | A question about the effective sample size in life tables | Observations censored within the interval under consideration are not at risk of death for the whole period.
They don't count as a whole person-period of exposure, but only the fraction to which they were exposed. Under the uniformity assumption, on average they're exposed half a period. So on average each of the $c_j... | A question about the effective sample size in life tables | Observations censored within the interval under consideration are not at risk of death for the whole period.
They don't count as a whole person-period of exposure, but only the fraction to which they | A question about the effective sample size in life tables
Observations censored within the interval under consideration are not at risk of death for the whole period.
They don't count as a whole person-period of exposure, but only the fraction to which they were exposed. Under the uniformity assumption, on average the... | A question about the effective sample size in life tables
Observations censored within the interval under consideration are not at risk of death for the whole period.
They don't count as a whole person-period of exposure, but only the fraction to which they |
42,410 | A question about the effective sample size in life tables | thank you for this discussion, I'm also dubitative regarding this denominator correction. When you estimate a rate you have to consider the total time spent by subject during a given period of time, so one usually assumes that censored (as well as dying) people have lived half of the period on average. But this is not ... | A question about the effective sample size in life tables | thank you for this discussion, I'm also dubitative regarding this denominator correction. When you estimate a rate you have to consider the total time spent by subject during a given period of time, s | A question about the effective sample size in life tables
thank you for this discussion, I'm also dubitative regarding this denominator correction. When you estimate a rate you have to consider the total time spent by subject during a given period of time, so one usually assumes that censored (as well as dying) people ... | A question about the effective sample size in life tables
thank you for this discussion, I'm also dubitative regarding this denominator correction. When you estimate a rate you have to consider the total time spent by subject during a given period of time, s |
42,411 | Making sense of the first difference regression model | Actually, the two procedures are the same. The difference between
$$
\Delta Y_t = B\Delta X_t + \Delta \epsilon_t
$$
and
$$
\Delta Y_t = B\Delta X_t + v_t
$$
is that you can estimate the second but not the first because you don't observe $\epsilon_t$. So the first equation is rather a theoretical model whilst the sec... | Making sense of the first difference regression model | Actually, the two procedures are the same. The difference between
$$
\Delta Y_t = B\Delta X_t + \Delta \epsilon_t
$$
and
$$
\Delta Y_t = B\Delta X_t + v_t
$$
is that you can estimate the second but | Making sense of the first difference regression model
Actually, the two procedures are the same. The difference between
$$
\Delta Y_t = B\Delta X_t + \Delta \epsilon_t
$$
and
$$
\Delta Y_t = B\Delta X_t + v_t
$$
is that you can estimate the second but not the first because you don't observe $\epsilon_t$. So the first... | Making sense of the first difference regression model
Actually, the two procedures are the same. The difference between
$$
\Delta Y_t = B\Delta X_t + \Delta \epsilon_t
$$
and
$$
\Delta Y_t = B\Delta X_t + v_t
$$
is that you can estimate the second but |
42,412 | Markov decision process in R for a song suggestion software? | This question is months old now but it's still interesting. To me this sounds like a massive contingency table or sparse data, tensor problem. This doesn't make any of the MDP or reinforcement learning issues moot, it just realigns the statistical framework within which they are modeled.
The decision or dependent varia... | Markov decision process in R for a song suggestion software? | This question is months old now but it's still interesting. To me this sounds like a massive contingency table or sparse data, tensor problem. This doesn't make any of the MDP or reinforcement learnin | Markov decision process in R for a song suggestion software?
This question is months old now but it's still interesting. To me this sounds like a massive contingency table or sparse data, tensor problem. This doesn't make any of the MDP or reinforcement learning issues moot, it just realigns the statistical framework w... | Markov decision process in R for a song suggestion software?
This question is months old now but it's still interesting. To me this sounds like a massive contingency table or sparse data, tensor problem. This doesn't make any of the MDP or reinforcement learnin |
42,413 | Markov decision process in R for a song suggestion software? | The problem can be modeled as Markov Decision problem. I have tried to fit the problem in MDP framework, let me know if this is of any help.
Assuming that there exists a method to select a song within a playlist 'cluster', the states would act as such clusters for MDP.
Defining a transition probability matrix between c... | Markov decision process in R for a song suggestion software? | The problem can be modeled as Markov Decision problem. I have tried to fit the problem in MDP framework, let me know if this is of any help.
Assuming that there exists a method to select a song within | Markov decision process in R for a song suggestion software?
The problem can be modeled as Markov Decision problem. I have tried to fit the problem in MDP framework, let me know if this is of any help.
Assuming that there exists a method to select a song within a playlist 'cluster', the states would act as such cluster... | Markov decision process in R for a song suggestion software?
The problem can be modeled as Markov Decision problem. I have tried to fit the problem in MDP framework, let me know if this is of any help.
Assuming that there exists a method to select a song within |
42,414 | Markov decision process in R for a song suggestion software? | It is right that there is a Reinforcement Learning problem here. The negative reinforcement would be when the person skips the song, and positive when he/she doesn't. The action in this case would be choosing the song, and you wanted the state to be a playlist. I don't think this is a good idea. First, you'd have a var... | Markov decision process in R for a song suggestion software? | It is right that there is a Reinforcement Learning problem here. The negative reinforcement would be when the person skips the song, and positive when he/she doesn't. The action in this case would be | Markov decision process in R for a song suggestion software?
It is right that there is a Reinforcement Learning problem here. The negative reinforcement would be when the person skips the song, and positive when he/she doesn't. The action in this case would be choosing the song, and you wanted the state to be a playlis... | Markov decision process in R for a song suggestion software?
It is right that there is a Reinforcement Learning problem here. The negative reinforcement would be when the person skips the song, and positive when he/she doesn't. The action in this case would be |
42,415 | Linear regression scaling independent variables | Using logs of the inputs will make your model nonlinear but that may be what you want. With financial data, natural log usually makes models more predictable.
Typically if you what to have the coefficients have the same scale, you normalize the inputs by: x=(x-mean(x))/stdev(x)
That being said, it actually doesn't real... | Linear regression scaling independent variables | Using logs of the inputs will make your model nonlinear but that may be what you want. With financial data, natural log usually makes models more predictable.
Typically if you what to have the coeffic | Linear regression scaling independent variables
Using logs of the inputs will make your model nonlinear but that may be what you want. With financial data, natural log usually makes models more predictable.
Typically if you what to have the coefficients have the same scale, you normalize the inputs by: x=(x-mean(x))/st... | Linear regression scaling independent variables
Using logs of the inputs will make your model nonlinear but that may be what you want. With financial data, natural log usually makes models more predictable.
Typically if you what to have the coeffic |
42,416 | Linear regression scaling independent variables | Values of independent variables $x$ are very high compare to dependent $y$, $\beta$-value would be very small, there will be many errors like.......sampling error, rounding error.
Yes! you really need to rebase $x$, The best way is to take logs
$$\ln{\hat y}=\beta\ln{\hat x}+\alpha$$
$$\ln{y}=\beta\ln{x}+\alpha+\epsilo... | Linear regression scaling independent variables | Values of independent variables $x$ are very high compare to dependent $y$, $\beta$-value would be very small, there will be many errors like.......sampling error, rounding error.
Yes! you really need | Linear regression scaling independent variables
Values of independent variables $x$ are very high compare to dependent $y$, $\beta$-value would be very small, there will be many errors like.......sampling error, rounding error.
Yes! you really need to rebase $x$, The best way is to take logs
$$\ln{\hat y}=\beta\ln{\hat... | Linear regression scaling independent variables
Values of independent variables $x$ are very high compare to dependent $y$, $\beta$-value would be very small, there will be many errors like.......sampling error, rounding error.
Yes! you really need |
42,417 | How do I do a classification problem with autoencoders (AEs) | Yes, once you've trained the network as an autoencoder, if you're only interested in classification you can just ignore the decoding part of the network and just feed the output of the deepest hidden layer into the classifier layer.
This page might be informative. | How do I do a classification problem with autoencoders (AEs) | Yes, once you've trained the network as an autoencoder, if you're only interested in classification you can just ignore the decoding part of the network and just feed the output of the deepest hidden | How do I do a classification problem with autoencoders (AEs)
Yes, once you've trained the network as an autoencoder, if you're only interested in classification you can just ignore the decoding part of the network and just feed the output of the deepest hidden layer into the classifier layer.
This page might be informa... | How do I do a classification problem with autoencoders (AEs)
Yes, once you've trained the network as an autoencoder, if you're only interested in classification you can just ignore the decoding part of the network and just feed the output of the deepest hidden |
42,418 | sample from a von Mises distribution by transforming a RV? | Simulation for the von Mises distribution is generally done via some form of rejection sampling. There is no method available to transform a random variate from a different distribution to a von Mises random variate in the way you describe. A natural way would have been some form of inversion sampling, but the CDF of t... | sample from a von Mises distribution by transforming a RV? | Simulation for the von Mises distribution is generally done via some form of rejection sampling. There is no method available to transform a random variate from a different distribution to a von Mises | sample from a von Mises distribution by transforming a RV?
Simulation for the von Mises distribution is generally done via some form of rejection sampling. There is no method available to transform a random variate from a different distribution to a von Mises random variate in the way you describe. A natural way would ... | sample from a von Mises distribution by transforming a RV?
Simulation for the von Mises distribution is generally done via some form of rejection sampling. There is no method available to transform a random variate from a different distribution to a von Mises |
42,419 | What does cluster size mean (in context of k-means)? | The area of the original (occupied) data space, and to a lesser extend the area of the clusters convex hull, volume, spread. Not the cardinality.
Counterexample in 1 dimension, k=2: 1,2,3,4,5,6,7,8,9,10,100. Both kmeans clusters will cover a "similar" area of the data range (out of 1..100, values in 1..52.75 will be as... | What does cluster size mean (in context of k-means)? | The area of the original (occupied) data space, and to a lesser extend the area of the clusters convex hull, volume, spread. Not the cardinality.
Counterexample in 1 dimension, k=2: 1,2,3,4,5,6,7,8,9, | What does cluster size mean (in context of k-means)?
The area of the original (occupied) data space, and to a lesser extend the area of the clusters convex hull, volume, spread. Not the cardinality.
Counterexample in 1 dimension, k=2: 1,2,3,4,5,6,7,8,9,10,100. Both kmeans clusters will cover a "similar" area of the dat... | What does cluster size mean (in context of k-means)?
The area of the original (occupied) data space, and to a lesser extend the area of the clusters convex hull, volume, spread. Not the cardinality.
Counterexample in 1 dimension, k=2: 1,2,3,4,5,6,7,8,9, |
42,420 | Is there any package in R that's commonly used for semi-supervised learning? [closed] | You can try for example the upclass package
http://cran.r-project.org/web/packages/upclass/index.html
There you will find the standard pdf reference and a vignette explaining it all along with examples. I think the function upclassify() would match your requirements. | Is there any package in R that's commonly used for semi-supervised learning? [closed] | You can try for example the upclass package
http://cran.r-project.org/web/packages/upclass/index.html
There you will find the standard pdf reference and a vignette explaining it all along with exampl | Is there any package in R that's commonly used for semi-supervised learning? [closed]
You can try for example the upclass package
http://cran.r-project.org/web/packages/upclass/index.html
There you will find the standard pdf reference and a vignette explaining it all along with examples. I think the function upclassif... | Is there any package in R that's commonly used for semi-supervised learning? [closed]
You can try for example the upclass package
http://cran.r-project.org/web/packages/upclass/index.html
There you will find the standard pdf reference and a vignette explaining it all along with exampl |
42,421 | Is there any package in R that's commonly used for semi-supervised learning? [closed] | Probably irrelevant now, but it might make the answer more complete to also mention the spa package as well. It uses a graph-based technique to learn a model. Basically it uses information from both the data point features and how similar data points are to each other. If you have a distance matrix for the data points,... | Is there any package in R that's commonly used for semi-supervised learning? [closed] | Probably irrelevant now, but it might make the answer more complete to also mention the spa package as well. It uses a graph-based technique to learn a model. Basically it uses information from both t | Is there any package in R that's commonly used for semi-supervised learning? [closed]
Probably irrelevant now, but it might make the answer more complete to also mention the spa package as well. It uses a graph-based technique to learn a model. Basically it uses information from both the data point features and how sim... | Is there any package in R that's commonly used for semi-supervised learning? [closed]
Probably irrelevant now, but it might make the answer more complete to also mention the spa package as well. It uses a graph-based technique to learn a model. Basically it uses information from both t |
42,422 | How can increasing the dimension increase the variance without increasing the bias in kNN? | First of all, the bias of a classifier is the discrepancy between its averaged
estimated and true function, wheras the variance of a classifier is the expected divergence of the estimated prediction function from its average value (i.e. how dependent the classifier is on the random sampling made in the training set).
... | How can increasing the dimension increase the variance without increasing the bias in kNN? | First of all, the bias of a classifier is the discrepancy between its averaged
estimated and true function, wheras the variance of a classifier is the expected divergence of the estimated prediction f | How can increasing the dimension increase the variance without increasing the bias in kNN?
First of all, the bias of a classifier is the discrepancy between its averaged
estimated and true function, wheras the variance of a classifier is the expected divergence of the estimated prediction function from its average valu... | How can increasing the dimension increase the variance without increasing the bias in kNN?
First of all, the bias of a classifier is the discrepancy between its averaged
estimated and true function, wheras the variance of a classifier is the expected divergence of the estimated prediction f |
42,423 | How can increasing the dimension increase the variance without increasing the bias in kNN? | Well, I don't know whether it's appropriate to answer a question asked by myself... But I think I have a relatively intuitive answer and I just wanna share it.
First let me add the true function in Figure 2.7 for comparison:
$$Y=f_1(X)=e^{-8||X||^2}$$
and the one in Figure 2.8 is
$$Y=f_2(X)=\frac12(X_1+1)^3$$
As @st... | How can increasing the dimension increase the variance without increasing the bias in kNN? | Well, I don't know whether it's appropriate to answer a question asked by myself... But I think I have a relatively intuitive answer and I just wanna share it.
First let me add the true function in F | How can increasing the dimension increase the variance without increasing the bias in kNN?
Well, I don't know whether it's appropriate to answer a question asked by myself... But I think I have a relatively intuitive answer and I just wanna share it.
First let me add the true function in Figure 2.7 for comparison:
$$... | How can increasing the dimension increase the variance without increasing the bias in kNN?
Well, I don't know whether it's appropriate to answer a question asked by myself... But I think I have a relatively intuitive answer and I just wanna share it.
First let me add the true function in F |
42,424 | Motivation for gradient descent method over canonical method (for OLS/MLE) for simple linear regression? | For ordinary linear regression, maximum likelihood and least squares are the same, i.e., give the same answer (the maximum likelihood solution is the least squares solution, if you derive the so called ``normal equations'' you'll see this, also see the book The Elements of Statistical Learning which discusses this).
B... | Motivation for gradient descent method over canonical method (for OLS/MLE) for simple linear regress | For ordinary linear regression, maximum likelihood and least squares are the same, i.e., give the same answer (the maximum likelihood solution is the least squares solution, if you derive the so call | Motivation for gradient descent method over canonical method (for OLS/MLE) for simple linear regression?
For ordinary linear regression, maximum likelihood and least squares are the same, i.e., give the same answer (the maximum likelihood solution is the least squares solution, if you derive the so called ``normal equ... | Motivation for gradient descent method over canonical method (for OLS/MLE) for simple linear regress
For ordinary linear regression, maximum likelihood and least squares are the same, i.e., give the same answer (the maximum likelihood solution is the least squares solution, if you derive the so call |
42,425 | non-normal residuals in ARIMA | Your QQplots could indicate $t$-distributed error terms might fit better. You could try to fit an ARIMA-model with $t$-distributed innovation terms, and see if the fit is very different from the fit you have now. I have done such things with the bugs software, there are certainly other options. | non-normal residuals in ARIMA | Your QQplots could indicate $t$-distributed error terms might fit better. You could try to fit an ARIMA-model with $t$-distributed innovation terms, and see if the fit is very different from the fit y | non-normal residuals in ARIMA
Your QQplots could indicate $t$-distributed error terms might fit better. You could try to fit an ARIMA-model with $t$-distributed innovation terms, and see if the fit is very different from the fit you have now. I have done such things with the bugs software, there are certainly other opt... | non-normal residuals in ARIMA
Your QQplots could indicate $t$-distributed error terms might fit better. You could try to fit an ARIMA-model with $t$-distributed innovation terms, and see if the fit is very different from the fit y |
42,426 | non-normal residuals in ARIMA | Before you do an ARIMA model you have to check if the data is be stationary and if any seasonality should be defined using autocorrelation (ACF) and partial correlation functions(PACF). The auto correlation should follow the 95% confidence bands. Stationary data is detected using a run sequence plot or auto correlation... | non-normal residuals in ARIMA | Before you do an ARIMA model you have to check if the data is be stationary and if any seasonality should be defined using autocorrelation (ACF) and partial correlation functions(PACF). The auto corre | non-normal residuals in ARIMA
Before you do an ARIMA model you have to check if the data is be stationary and if any seasonality should be defined using autocorrelation (ACF) and partial correlation functions(PACF). The auto correlation should follow the 95% confidence bands. Stationary data is detected using a run seq... | non-normal residuals in ARIMA
Before you do an ARIMA model you have to check if the data is be stationary and if any seasonality should be defined using autocorrelation (ACF) and partial correlation functions(PACF). The auto corre |
42,427 | non-normal residuals in ARIMA | If the residuals contain pulses or level shifts this can lead to "non-normality" . Try detecting Interventions and add them as necessary. Another way residuals can exhibit non-normality is if there is a deterministic change in error variance suggesting Weighted Least Squares OR if the model's parameters are not constan... | non-normal residuals in ARIMA | If the residuals contain pulses or level shifts this can lead to "non-normality" . Try detecting Interventions and add them as necessary. Another way residuals can exhibit non-normality is if there is | non-normal residuals in ARIMA
If the residuals contain pulses or level shifts this can lead to "non-normality" . Try detecting Interventions and add them as necessary. Another way residuals can exhibit non-normality is if there is a deterministic change in error variance suggesting Weighted Least Squares OR if the mode... | non-normal residuals in ARIMA
If the residuals contain pulses or level shifts this can lead to "non-normality" . Try detecting Interventions and add them as necessary. Another way residuals can exhibit non-normality is if there is |
42,428 | Geometry of robust linear model | Yes! Robust regression has a clear geometric interpretation.
One can think about the geometry of an estimator by looking at the group of equivariance to which it belongs. Quick example;
Example scale estimator $S(x)$ (the usual variance, $\sigma^2(x)$, and the median absolute deviation, $\mbox{mad}(x)$, are two cart... | Geometry of robust linear model | Yes! Robust regression has a clear geometric interpretation.
One can think about the geometry of an estimator by looking at the group of equivariance to which it belongs. Quick example;
Example sca | Geometry of robust linear model
Yes! Robust regression has a clear geometric interpretation.
One can think about the geometry of an estimator by looking at the group of equivariance to which it belongs. Quick example;
Example scale estimator $S(x)$ (the usual variance, $\sigma^2(x)$, and the median absolute deviatio... | Geometry of robust linear model
Yes! Robust regression has a clear geometric interpretation.
One can think about the geometry of an estimator by looking at the group of equivariance to which it belongs. Quick example;
Example sca |
42,429 | How to pretrain Convolution filter | As far as I know, pre-training is not so popular nowadays.
Try to use proper initialisation like this or this.
Use Batch Normalisation (it will make the previous point less important, though). You will get more in terms of accuracy, but with some computational overhead.
P.S.
Now when I wrote this, I found a great a... | How to pretrain Convolution filter | As far as I know, pre-training is not so popular nowadays.
Try to use proper initialisation like this or this.
Use Batch Normalisation (it will make the previous point less important, though). You w | How to pretrain Convolution filter
As far as I know, pre-training is not so popular nowadays.
Try to use proper initialisation like this or this.
Use Batch Normalisation (it will make the previous point less important, though). You will get more in terms of accuracy, but with some computational overhead.
P.S.
Now w... | How to pretrain Convolution filter
As far as I know, pre-training is not so popular nowadays.
Try to use proper initialisation like this or this.
Use Batch Normalisation (it will make the previous point less important, though). You w |
42,430 | Interpretation of Cramér's V | The quote is correct. If you have two categorical variables and you recode them into two sets of dummy variables and then perform canonical correlation analysis (CCA) on these two sets (leaving out any one dummy from each set as redundant) - you will get canonical correlations (see CCA algorithm, to compute) the averag... | Interpretation of Cramér's V | The quote is correct. If you have two categorical variables and you recode them into two sets of dummy variables and then perform canonical correlation analysis (CCA) on these two sets (leaving out an | Interpretation of Cramér's V
The quote is correct. If you have two categorical variables and you recode them into two sets of dummy variables and then perform canonical correlation analysis (CCA) on these two sets (leaving out any one dummy from each set as redundant) - you will get canonical correlations (see CCA algo... | Interpretation of Cramér's V
The quote is correct. If you have two categorical variables and you recode them into two sets of dummy variables and then perform canonical correlation analysis (CCA) on these two sets (leaving out an |
42,431 | What do these decision boundaries indicate in random forest and svm? | The images you present are the same as those here: link.
The following is some code, translated to R with some adjustments, to work through this. The RF selected (2 trees) is not acceptable. This is not apples-to-apples, so any of the authors' assertions about "entropy" can be mis-informative.
First we get the data:
... | What do these decision boundaries indicate in random forest and svm? | The images you present are the same as those here: link.
The following is some code, translated to R with some adjustments, to work through this. The RF selected (2 trees) is not acceptable. This is | What do these decision boundaries indicate in random forest and svm?
The images you present are the same as those here: link.
The following is some code, translated to R with some adjustments, to work through this. The RF selected (2 trees) is not acceptable. This is not apples-to-apples, so any of the authors' asser... | What do these decision boundaries indicate in random forest and svm?
The images you present are the same as those here: link.
The following is some code, translated to R with some adjustments, to work through this. The RF selected (2 trees) is not acceptable. This is |
42,432 | Understanding the effect of hyperparameters in machine learning experiments | Many dedicated optimization methods exist for hyperparameter tuning. Sequential model based optimization (a Bayesian inspired method) is a particularly popular research topic, for instance here. Metaheuristic approaches like genetic algorithms, particle swarm optimization and simulated annealing are also common, see fo... | Understanding the effect of hyperparameters in machine learning experiments | Many dedicated optimization methods exist for hyperparameter tuning. Sequential model based optimization (a Bayesian inspired method) is a particularly popular research topic, for instance here. Metah | Understanding the effect of hyperparameters in machine learning experiments
Many dedicated optimization methods exist for hyperparameter tuning. Sequential model based optimization (a Bayesian inspired method) is a particularly popular research topic, for instance here. Metaheuristic approaches like genetic algorithms,... | Understanding the effect of hyperparameters in machine learning experiments
Many dedicated optimization methods exist for hyperparameter tuning. Sequential model based optimization (a Bayesian inspired method) is a particularly popular research topic, for instance here. Metah |
42,433 | Understanding the effect of hyperparameters in machine learning experiments | Design of Experiments on Wikipedia might be a good place for additional reading. At its most general, it covers how to make progress in problems where there is so much complexity that the intuitive approach is no longer constructive. | Understanding the effect of hyperparameters in machine learning experiments | Design of Experiments on Wikipedia might be a good place for additional reading. At its most general, it covers how to make progress in problems where there is so much complexity that the intuitive ap | Understanding the effect of hyperparameters in machine learning experiments
Design of Experiments on Wikipedia might be a good place for additional reading. At its most general, it covers how to make progress in problems where there is so much complexity that the intuitive approach is no longer constructive. | Understanding the effect of hyperparameters in machine learning experiments
Design of Experiments on Wikipedia might be a good place for additional reading. At its most general, it covers how to make progress in problems where there is so much complexity that the intuitive ap |
42,434 | Real motivation for using mixed effect models, and when to use them and when not to | There are many reasons for using mixed or random effects models, but I'll highlight one due to my time constraints. Let's say you have 1500 subjects with 10 measurements taken on each subject, along with many covariates. You could model the response measurements $Y$ using fixed subject terms as $Y=X\beta+\epsilon.$ ... | Real motivation for using mixed effect models, and when to use them and when not to | There are many reasons for using mixed or random effects models, but I'll highlight one due to my time constraints. Let's say you have 1500 subjects with 10 measurements taken on each subject, along | Real motivation for using mixed effect models, and when to use them and when not to
There are many reasons for using mixed or random effects models, but I'll highlight one due to my time constraints. Let's say you have 1500 subjects with 10 measurements taken on each subject, along with many covariates. You could mo... | Real motivation for using mixed effect models, and when to use them and when not to
There are many reasons for using mixed or random effects models, but I'll highlight one due to my time constraints. Let's say you have 1500 subjects with 10 measurements taken on each subject, along |
42,435 | Hierarchical Gamma-Poisson CDF? | If you integrate the other way, you get a closed form expression:
\begin{align*}
P(X \leq x|r,\nu) &= \int_0^\infty P(X \leq x| \lambda)P(\lambda|r,v) \text{d}\lambda\\
&= \int_0^\infty \sum_{k=0}^x \frac{\lambda^k\exp(-\lambda)}{k!} \frac{\lambda^{r-1}e^{-\lambda/v}}{\Gamma(r)v^r} \text{d}\lambda\\
&= \frac{1}{\Gamma... | Hierarchical Gamma-Poisson CDF? | If you integrate the other way, you get a closed form expression:
\begin{align*}
P(X \leq x|r,\nu) &= \int_0^\infty P(X \leq x| \lambda)P(\lambda|r,v) \text{d}\lambda\\
&= \int_0^\infty \sum_{k=0}^x \ | Hierarchical Gamma-Poisson CDF?
If you integrate the other way, you get a closed form expression:
\begin{align*}
P(X \leq x|r,\nu) &= \int_0^\infty P(X \leq x| \lambda)P(\lambda|r,v) \text{d}\lambda\\
&= \int_0^\infty \sum_{k=0}^x \frac{\lambda^k\exp(-\lambda)}{k!} \frac{\lambda^{r-1}e^{-\lambda/v}}{\Gamma(r)v^r} \tex... | Hierarchical Gamma-Poisson CDF?
If you integrate the other way, you get a closed form expression:
\begin{align*}
P(X \leq x|r,\nu) &= \int_0^\infty P(X \leq x| \lambda)P(\lambda|r,v) \text{d}\lambda\\
&= \int_0^\infty \sum_{k=0}^x \ |
42,436 | Hierarchical Gamma-Poisson CDF? | Yes when there is no closed form of the PDF you can use the Metropolis-Hastings Algorithm. Once you understand the algorithm you can easily program it yourself but upon a google search many have done so in python. Here
http://www.nehalemlabs.net/prototype/blog/2014/02/24/an-introduction-to-the-metropolis-method-with-p... | Hierarchical Gamma-Poisson CDF? | Yes when there is no closed form of the PDF you can use the Metropolis-Hastings Algorithm. Once you understand the algorithm you can easily program it yourself but upon a google search many have done | Hierarchical Gamma-Poisson CDF?
Yes when there is no closed form of the PDF you can use the Metropolis-Hastings Algorithm. Once you understand the algorithm you can easily program it yourself but upon a google search many have done so in python. Here
http://www.nehalemlabs.net/prototype/blog/2014/02/24/an-introduction... | Hierarchical Gamma-Poisson CDF?
Yes when there is no closed form of the PDF you can use the Metropolis-Hastings Algorithm. Once you understand the algorithm you can easily program it yourself but upon a google search many have done |
42,437 | Test for trend (ordinal predictor, continuous outcome)? | Very late answer but you might find this question, and this post helpful. Personally, I would just run a linear model with the categories represented as (ordered) integers, and examine the coefficient.
There is also some nice guidance in the BMJ stats series. | Test for trend (ordinal predictor, continuous outcome)? | Very late answer but you might find this question, and this post helpful. Personally, I would just run a linear model with the categories represented as (ordered) integers, and examine the coefficient | Test for trend (ordinal predictor, continuous outcome)?
Very late answer but you might find this question, and this post helpful. Personally, I would just run a linear model with the categories represented as (ordered) integers, and examine the coefficient.
There is also some nice guidance in the BMJ stats series. | Test for trend (ordinal predictor, continuous outcome)?
Very late answer but you might find this question, and this post helpful. Personally, I would just run a linear model with the categories represented as (ordered) integers, and examine the coefficient |
42,438 | Test for trend (ordinal predictor, continuous outcome)? | The first step is to plot the three histograms and see how much they overlap. If there is enough data to make a histogram (40+ samples) that can be used to identify if the distribution in each category is normally distributed or not, and they are normally distributed then doing t-test for paired means and Levene's tes... | Test for trend (ordinal predictor, continuous outcome)? | The first step is to plot the three histograms and see how much they overlap. If there is enough data to make a histogram (40+ samples) that can be used to identify if the distribution in each catego | Test for trend (ordinal predictor, continuous outcome)?
The first step is to plot the three histograms and see how much they overlap. If there is enough data to make a histogram (40+ samples) that can be used to identify if the distribution in each category is normally distributed or not, and they are normally distrib... | Test for trend (ordinal predictor, continuous outcome)?
The first step is to plot the three histograms and see how much they overlap. If there is enough data to make a histogram (40+ samples) that can be used to identify if the distribution in each catego |
42,439 | Test for trend (ordinal predictor, continuous outcome)? | Jonckheere-Terpstra test is the tool you was probably looking for. | Test for trend (ordinal predictor, continuous outcome)? | Jonckheere-Terpstra test is the tool you was probably looking for. | Test for trend (ordinal predictor, continuous outcome)?
Jonckheere-Terpstra test is the tool you was probably looking for. | Test for trend (ordinal predictor, continuous outcome)?
Jonckheere-Terpstra test is the tool you was probably looking for. |
42,440 | Test for trend (ordinal predictor, continuous outcome)? | The R package brms (Bayesian regression models using Stan) can use Bayesian estimation to fit models with ordinal predictors. brms can handle a wide range of designs (e.g. multivariate and/or longitudinal and/or hierarchical) and a wide range of distributions (counts, ordinal outcomes, continuous outcomes, censored, et... | Test for trend (ordinal predictor, continuous outcome)? | The R package brms (Bayesian regression models using Stan) can use Bayesian estimation to fit models with ordinal predictors. brms can handle a wide range of designs (e.g. multivariate and/or longitud | Test for trend (ordinal predictor, continuous outcome)?
The R package brms (Bayesian regression models using Stan) can use Bayesian estimation to fit models with ordinal predictors. brms can handle a wide range of designs (e.g. multivariate and/or longitudinal and/or hierarchical) and a wide range of distributions (cou... | Test for trend (ordinal predictor, continuous outcome)?
The R package brms (Bayesian regression models using Stan) can use Bayesian estimation to fit models with ordinal predictors. brms can handle a wide range of designs (e.g. multivariate and/or longitud |
42,441 | How to prove that Asymptotic Variance-Covariance matrix of OLS estimator is Positive Definite? | Applying the Law of Iterated Expectations,
$$E[(\mathbf{x}_i\cdot \epsilon_i)(\mathbf{x}_i\cdot \epsilon_i)'] = E[\epsilon_i^2\mathbf{x}_i\mathbf{x}_i']=E\Big(E[\epsilon_i^2\mid \mathbf{x}_i]\mathbf{x}_i\mathbf{x}_i'\Big) $$
For exposition purposes, assume that the regressors are two, $X_1$ and $X_2$. Set also $E[\epsi... | How to prove that Asymptotic Variance-Covariance matrix of OLS estimator is Positive Definite? | Applying the Law of Iterated Expectations,
$$E[(\mathbf{x}_i\cdot \epsilon_i)(\mathbf{x}_i\cdot \epsilon_i)'] = E[\epsilon_i^2\mathbf{x}_i\mathbf{x}_i']=E\Big(E[\epsilon_i^2\mid \mathbf{x}_i]\mathbf{x | How to prove that Asymptotic Variance-Covariance matrix of OLS estimator is Positive Definite?
Applying the Law of Iterated Expectations,
$$E[(\mathbf{x}_i\cdot \epsilon_i)(\mathbf{x}_i\cdot \epsilon_i)'] = E[\epsilon_i^2\mathbf{x}_i\mathbf{x}_i']=E\Big(E[\epsilon_i^2\mid \mathbf{x}_i]\mathbf{x}_i\mathbf{x}_i'\Big) $$
... | How to prove that Asymptotic Variance-Covariance matrix of OLS estimator is Positive Definite?
Applying the Law of Iterated Expectations,
$$E[(\mathbf{x}_i\cdot \epsilon_i)(\mathbf{x}_i\cdot \epsilon_i)'] = E[\epsilon_i^2\mathbf{x}_i\mathbf{x}_i']=E\Big(E[\epsilon_i^2\mid \mathbf{x}_i]\mathbf{x |
42,442 | Time Series Stationarity | Since you have put the tag "augmented-dickey-fuller", I will assume you did the ADF test with a trend.
So in that case, if you think your series do have a deterministic trend, then the result of the test is indeed correct, because it is trend stationary. That is, once you account for the deterministic trend (as you do... | Time Series Stationarity | Since you have put the tag "augmented-dickey-fuller", I will assume you did the ADF test with a trend.
So in that case, if you think your series do have a deterministic trend, then the result of the | Time Series Stationarity
Since you have put the tag "augmented-dickey-fuller", I will assume you did the ADF test with a trend.
So in that case, if you think your series do have a deterministic trend, then the result of the test is indeed correct, because it is trend stationary. That is, once you account for the deter... | Time Series Stationarity
Since you have put the tag "augmented-dickey-fuller", I will assume you did the ADF test with a trend.
So in that case, if you think your series do have a deterministic trend, then the result of the |
42,443 | Mean of predictive distribution | While writing$$p(x_{N+1}|D)=\mathbb{E}_{\mu|D}[p(x_{N+1}|\mu)]$$is formally correct, this leads to confusion when applying the Law of Total Expectation, in that the formula $$\mathbb{E}_{x_{N+1}|D} \Big[\mathbb{E}_{\mu|D}\Big[p(x_{N+1}|\mu)\Big]\Big]$$ does not make sense.
What you want to find is $\mathbb{E}_{x_{N+1}|... | Mean of predictive distribution | While writing$$p(x_{N+1}|D)=\mathbb{E}_{\mu|D}[p(x_{N+1}|\mu)]$$is formally correct, this leads to confusion when applying the Law of Total Expectation, in that the formula $$\mathbb{E}_{x_{N+1}|D} \B | Mean of predictive distribution
While writing$$p(x_{N+1}|D)=\mathbb{E}_{\mu|D}[p(x_{N+1}|\mu)]$$is formally correct, this leads to confusion when applying the Law of Total Expectation, in that the formula $$\mathbb{E}_{x_{N+1}|D} \Big[\mathbb{E}_{\mu|D}\Big[p(x_{N+1}|\mu)\Big]\Big]$$ does not make sense.
What you want ... | Mean of predictive distribution
While writing$$p(x_{N+1}|D)=\mathbb{E}_{\mu|D}[p(x_{N+1}|\mu)]$$is formally correct, this leads to confusion when applying the Law of Total Expectation, in that the formula $$\mathbb{E}_{x_{N+1}|D} \B |
42,444 | Should I take the Shapiro Wilk test with a pinch of salt here? | With a sample size that large, I'd just ignore the normality assumptions, not least because normality statistics--including SW--are sensitive to sample size. You could inspect the QQ plot (which as you say, looks fine) or the histogram, but I find it difficult to trust my own eyes (or others' for that matter). You coul... | Should I take the Shapiro Wilk test with a pinch of salt here? | With a sample size that large, I'd just ignore the normality assumptions, not least because normality statistics--including SW--are sensitive to sample size. You could inspect the QQ plot (which as yo | Should I take the Shapiro Wilk test with a pinch of salt here?
With a sample size that large, I'd just ignore the normality assumptions, not least because normality statistics--including SW--are sensitive to sample size. You could inspect the QQ plot (which as you say, looks fine) or the histogram, but I find it diffic... | Should I take the Shapiro Wilk test with a pinch of salt here?
With a sample size that large, I'd just ignore the normality assumptions, not least because normality statistics--including SW--are sensitive to sample size. You could inspect the QQ plot (which as yo |
42,445 | Where is the correlation parameter in the linear mixed-effect model equation? | Maybe this will help you: in lme4 you can specify correlated intercept and slope:
y ~ x + (x | g) that translates to: y ~ 1 + x + (1 + x | g)
where y is a response variable and x is a predictor, while g is some grouping variable for random effects. lme4 by default assumes that the terms could be correlated, but you can... | Where is the correlation parameter in the linear mixed-effect model equation? | Maybe this will help you: in lme4 you can specify correlated intercept and slope:
y ~ x + (x | g) that translates to: y ~ 1 + x + (1 + x | g)
where y is a response variable and x is a predictor, while | Where is the correlation parameter in the linear mixed-effect model equation?
Maybe this will help you: in lme4 you can specify correlated intercept and slope:
y ~ x + (x | g) that translates to: y ~ 1 + x + (1 + x | g)
where y is a response variable and x is a predictor, while g is some grouping variable for random ef... | Where is the correlation parameter in the linear mixed-effect model equation?
Maybe this will help you: in lme4 you can specify correlated intercept and slope:
y ~ x + (x | g) that translates to: y ~ 1 + x + (1 + x | g)
where y is a response variable and x is a predictor, while |
42,446 | Where is the correlation parameter in the linear mixed-effect model equation? | A model of type LMM/GLMM is defined by two equations: An equation including the linear combination of fixed and random effect predictors (as for example Eq. 12 in Moscatelli et al. (2012)) and a second equation for the variance-covariance matrix of the error term. The cross-correlation parameter is in the variance-cova... | Where is the correlation parameter in the linear mixed-effect model equation? | A model of type LMM/GLMM is defined by two equations: An equation including the linear combination of fixed and random effect predictors (as for example Eq. 12 in Moscatelli et al. (2012)) and a secon | Where is the correlation parameter in the linear mixed-effect model equation?
A model of type LMM/GLMM is defined by two equations: An equation including the linear combination of fixed and random effect predictors (as for example Eq. 12 in Moscatelli et al. (2012)) and a second equation for the variance-covariance mat... | Where is the correlation parameter in the linear mixed-effect model equation?
A model of type LMM/GLMM is defined by two equations: An equation including the linear combination of fixed and random effect predictors (as for example Eq. 12 in Moscatelli et al. (2012)) and a secon |
42,447 | Zero-inflated negative binomial models: why not use two separate models? | Zero-inflated negative binomial models don't assume that all the zeroes come from the Bernoulli process; some may come from the negative binomial process. Toss a coin & write down zero if it's tails. If it's heads then start tossing again & write down the number of tails until you have three, say, heads. There are two ... | Zero-inflated negative binomial models: why not use two separate models? | Zero-inflated negative binomial models don't assume that all the zeroes come from the Bernoulli process; some may come from the negative binomial process. Toss a coin & write down zero if it's tails. | Zero-inflated negative binomial models: why not use two separate models?
Zero-inflated negative binomial models don't assume that all the zeroes come from the Bernoulli process; some may come from the negative binomial process. Toss a coin & write down zero if it's tails. If it's heads then start tossing again & write ... | Zero-inflated negative binomial models: why not use two separate models?
Zero-inflated negative binomial models don't assume that all the zeroes come from the Bernoulli process; some may come from the negative binomial process. Toss a coin & write down zero if it's tails. |
42,448 | Beginner learning resources : Pdf and likelihood function for non-Gaussian time series model | Let $\Phi=(\phi_1,...,\phi_p)$ and $\mathbf{y}_{t-1} = (y_{t-1},...,y_{t-p})$
So your equations become $y_t = \Phi^{T}\mathbf{y}_{t-1} + \eta(t)$ and $z_{t} = y_{t} + v(t)$
thus
$$
z_t - \Phi^{T}\mathbf{y}_{t-1} = \eta(t) + v(t)
$$
Where $p$ is the parameter of the Bernoulli distributed variable $\eta$; note that
$$E[... | Beginner learning resources : Pdf and likelihood function for non-Gaussian time series model | Let $\Phi=(\phi_1,...,\phi_p)$ and $\mathbf{y}_{t-1} = (y_{t-1},...,y_{t-p})$
So your equations become $y_t = \Phi^{T}\mathbf{y}_{t-1} + \eta(t)$ and $z_{t} = y_{t} + v(t)$
thus
$$
z_t - \Phi^{T}\math | Beginner learning resources : Pdf and likelihood function for non-Gaussian time series model
Let $\Phi=(\phi_1,...,\phi_p)$ and $\mathbf{y}_{t-1} = (y_{t-1},...,y_{t-p})$
So your equations become $y_t = \Phi^{T}\mathbf{y}_{t-1} + \eta(t)$ and $z_{t} = y_{t} + v(t)$
thus
$$
z_t - \Phi^{T}\mathbf{y}_{t-1} = \eta(t) + v(t... | Beginner learning resources : Pdf and likelihood function for non-Gaussian time series model
Let $\Phi=(\phi_1,...,\phi_p)$ and $\mathbf{y}_{t-1} = (y_{t-1},...,y_{t-p})$
So your equations become $y_t = \Phi^{T}\mathbf{y}_{t-1} + \eta(t)$ and $z_{t} = y_{t} + v(t)$
thus
$$
z_t - \Phi^{T}\math |
42,449 | "...if the data is linearly separable" | You can use the tour to look at the data. This is a movie of linear projections of the data, so that if the data is linearly separable you should see the groups separate somewhere. Tours are available in ggobi, and the tourr package in R. Video examples can be viewed at the Cook & Swayne "Interactive and Dynamic Graphi... | "...if the data is linearly separable" | You can use the tour to look at the data. This is a movie of linear projections of the data, so that if the data is linearly separable you should see the groups separate somewhere. Tours are available | "...if the data is linearly separable"
You can use the tour to look at the data. This is a movie of linear projections of the data, so that if the data is linearly separable you should see the groups separate somewhere. Tours are available in ggobi, and the tourr package in R. Video examples can be viewed at the Cook &... | "...if the data is linearly separable"
You can use the tour to look at the data. This is a movie of linear projections of the data, so that if the data is linearly separable you should see the groups separate somewhere. Tours are available |
42,450 | How to choose a kernel for KDE | This is not really a data visualization question. The information is fairly readily available online, eg http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0405/MISHRA/kde.html
mentions using AMISE to select bandwidth, same approach for kernels could be used. But for EDA, you would want to work like the recommen... | How to choose a kernel for KDE | This is not really a data visualization question. The information is fairly readily available online, eg http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0405/MISHRA/kde.html
mentions using A | How to choose a kernel for KDE
This is not really a data visualization question. The information is fairly readily available online, eg http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0405/MISHRA/kde.html
mentions using AMISE to select bandwidth, same approach for kernels could be used. But for EDA, you would... | How to choose a kernel for KDE
This is not really a data visualization question. The information is fairly readily available online, eg http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0405/MISHRA/kde.html
mentions using A |
42,451 | How to choose a kernel for KDE | The framework of regularization theory (see Regularization Theory and Neural Networks Architectures by Girosi et. al) allows to tackle the problem of looking for a good kernel in a systematic way.
The idea is that the kernel is determined by a smoothness stabilizer which is analogous to controlling the complexity in th... | How to choose a kernel for KDE | The framework of regularization theory (see Regularization Theory and Neural Networks Architectures by Girosi et. al) allows to tackle the problem of looking for a good kernel in a systematic way.
The | How to choose a kernel for KDE
The framework of regularization theory (see Regularization Theory and Neural Networks Architectures by Girosi et. al) allows to tackle the problem of looking for a good kernel in a systematic way.
The idea is that the kernel is determined by a smoothness stabilizer which is analogous to c... | How to choose a kernel for KDE
The framework of regularization theory (see Regularization Theory and Neural Networks Architectures by Girosi et. al) allows to tackle the problem of looking for a good kernel in a systematic way.
The |
42,452 | What are some good examples of exploratory data analysis today? | One example I enjoy (and is a simple illustration) is the work by Michael Maltz on analyzing the uniform crime reports that police agencies supply to the FBI. See:
Maltz, M. D. (2010). Look before you analyze: Visualizing data in criminal justice. In Piquero, A. . and Weisburd, D., editors, Handbook of Quantitative Cr... | What are some good examples of exploratory data analysis today? | One example I enjoy (and is a simple illustration) is the work by Michael Maltz on analyzing the uniform crime reports that police agencies supply to the FBI. See:
Maltz, M. D. (2010). Look before yo | What are some good examples of exploratory data analysis today?
One example I enjoy (and is a simple illustration) is the work by Michael Maltz on analyzing the uniform crime reports that police agencies supply to the FBI. See:
Maltz, M. D. (2010). Look before you analyze: Visualizing data in criminal justice. In Piqu... | What are some good examples of exploratory data analysis today?
One example I enjoy (and is a simple illustration) is the work by Michael Maltz on analyzing the uniform crime reports that police agencies supply to the FBI. See:
Maltz, M. D. (2010). Look before yo |
42,453 | What are some good examples of exploratory data analysis today? | Our neuroscientist and colleage Dr. Trejo had a successful experience with exploratory data analysis applied to adult neurogenesis in his work "Involvement of specific adult hippocampal neurogenic subpopulations on behavior acquisition and persistence abilities" (under peer-review so details cannot be provided still).
... | What are some good examples of exploratory data analysis today? | Our neuroscientist and colleage Dr. Trejo had a successful experience with exploratory data analysis applied to adult neurogenesis in his work "Involvement of specific adult hippocampal neurogenic sub | What are some good examples of exploratory data analysis today?
Our neuroscientist and colleage Dr. Trejo had a successful experience with exploratory data analysis applied to adult neurogenesis in his work "Involvement of specific adult hippocampal neurogenic subpopulations on behavior acquisition and persistence abil... | What are some good examples of exploratory data analysis today?
Our neuroscientist and colleage Dr. Trejo had a successful experience with exploratory data analysis applied to adult neurogenesis in his work "Involvement of specific adult hippocampal neurogenic sub |
42,454 | Does the log likelihood become unimodal when the sample size goes to infinity? | Regarding "I would expect that the number and depth of the local minima would decrease as the sample size increases", this is not true in general.
For example, let $X_1,\dots,X_n$ be a random sample from the $k$-component mixture
$$
w_1\cdot\mathrm{N}(\mu_1,\sigma_1^2) + \dots + w_k\cdot\mathrm{N}(\mu_k,\sigma_k^2) \... | Does the log likelihood become unimodal when the sample size goes to infinity? | Regarding "I would expect that the number and depth of the local minima would decrease as the sample size increases", this is not true in general.
For example, let $X_1,\dots,X_n$ be a random sample f | Does the log likelihood become unimodal when the sample size goes to infinity?
Regarding "I would expect that the number and depth of the local minima would decrease as the sample size increases", this is not true in general.
For example, let $X_1,\dots,X_n$ be a random sample from the $k$-component mixture
$$
w_1\cd... | Does the log likelihood become unimodal when the sample size goes to infinity?
Regarding "I would expect that the number and depth of the local minima would decrease as the sample size increases", this is not true in general.
For example, let $X_1,\dots,X_n$ be a random sample f |
42,455 | Presenting results of a meta-analysis with multiple moderators? | In essence, there are 6 different combinations of those two moderators. So, you could just compute and present the estimated/predicted effects for each of those combinations. Here is an example using a dataset from the metafor package that also happens to include two categorical moderators with 2 and 3 levels, respecti... | Presenting results of a meta-analysis with multiple moderators? | In essence, there are 6 different combinations of those two moderators. So, you could just compute and present the estimated/predicted effects for each of those combinations. Here is an example using | Presenting results of a meta-analysis with multiple moderators?
In essence, there are 6 different combinations of those two moderators. So, you could just compute and present the estimated/predicted effects for each of those combinations. Here is an example using a dataset from the metafor package that also happens to ... | Presenting results of a meta-analysis with multiple moderators?
In essence, there are 6 different combinations of those two moderators. So, you could just compute and present the estimated/predicted effects for each of those combinations. Here is an example using |
42,456 | Low explained variance in Random Forest (R randomForest) | edited response*
Some few changes which may drive forward a little signal...
Scaling:
RF is only scaling invariant to the features not to the responses. RFreg uses mean square error as loss function and CV squared residuals to assess performance. Try to take the logarithm or sqaure root to your responses to lower lever... | Low explained variance in Random Forest (R randomForest) | edited response*
Some few changes which may drive forward a little signal...
Scaling:
RF is only scaling invariant to the features not to the responses. RFreg uses mean square error as loss function a | Low explained variance in Random Forest (R randomForest)
edited response*
Some few changes which may drive forward a little signal...
Scaling:
RF is only scaling invariant to the features not to the responses. RFreg uses mean square error as loss function and CV squared residuals to assess performance. Try to take the ... | Low explained variance in Random Forest (R randomForest)
edited response*
Some few changes which may drive forward a little signal...
Scaling:
RF is only scaling invariant to the features not to the responses. RFreg uses mean square error as loss function a |
42,457 | Birthday "Paradox" -- with a different perspective | When in doubt, simulate. (I'm sure that you can actually put together a formula, but it will likely be painful to look at.) I'll work with the criterion being "at least one triple birthday" and "at least eleven double birthdays" -- changing the code below to checking for exactly so many birthdays is not hard.
n.sims <-... | Birthday "Paradox" -- with a different perspective | When in doubt, simulate. (I'm sure that you can actually put together a formula, but it will likely be painful to look at.) I'll work with the criterion being "at least one triple birthday" and "at le | Birthday "Paradox" -- with a different perspective
When in doubt, simulate. (I'm sure that you can actually put together a formula, but it will likely be painful to look at.) I'll work with the criterion being "at least one triple birthday" and "at least eleven double birthdays" -- changing the code below to checking f... | Birthday "Paradox" -- with a different perspective
When in doubt, simulate. (I'm sure that you can actually put together a formula, but it will likely be painful to look at.) I'll work with the criterion being "at least one triple birthday" and "at le |
42,458 | Birthday "Paradox" -- with a different perspective | Assuming you aim for the case that exactly (so not at least) 11 double birthdays and 1 triple birthdays occur:
$$\begin{align}p(60,n_2=11,n_3=1) &= \frac{\text{possibilities with 11 double birthdays and 1 triple birthdays}}{\text{all possibilities}}\\
&= \frac{\frac{60!}{35!22!3!} 21!! \,\cdot \,365 \cdot 364 \cdot \,... | Birthday "Paradox" -- with a different perspective | Assuming you aim for the case that exactly (so not at least) 11 double birthdays and 1 triple birthdays occur:
$$\begin{align}p(60,n_2=11,n_3=1) &= \frac{\text{possibilities with 11 double birthdays a | Birthday "Paradox" -- with a different perspective
Assuming you aim for the case that exactly (so not at least) 11 double birthdays and 1 triple birthdays occur:
$$\begin{align}p(60,n_2=11,n_3=1) &= \frac{\text{possibilities with 11 double birthdays and 1 triple birthdays}}{\text{all possibilities}}\\
&= \frac{\frac{6... | Birthday "Paradox" -- with a different perspective
Assuming you aim for the case that exactly (so not at least) 11 double birthdays and 1 triple birthdays occur:
$$\begin{align}p(60,n_2=11,n_3=1) &= \frac{\text{possibilities with 11 double birthdays a |
42,459 | How to evaluate fit of a logistic regression | Standard univariate logistic regression of $y$ on $x$ finds the coefficients $\alpha$, $\beta$ that best fit your training data $\{(x_i, y_i), i \in [1, N]\}$ in the following equation:
(model 1): $y_i = (1 + exp(-(\alpha + \beta x_i)))^{-1}$
Note that the fit will be bad if the $y$ in your data are not in $(0,1)$, s... | How to evaluate fit of a logistic regression | Standard univariate logistic regression of $y$ on $x$ finds the coefficients $\alpha$, $\beta$ that best fit your training data $\{(x_i, y_i), i \in [1, N]\}$ in the following equation:
(model 1): $y | How to evaluate fit of a logistic regression
Standard univariate logistic regression of $y$ on $x$ finds the coefficients $\alpha$, $\beta$ that best fit your training data $\{(x_i, y_i), i \in [1, N]\}$ in the following equation:
(model 1): $y_i = (1 + exp(-(\alpha + \beta x_i)))^{-1}$
Note that the fit will be bad ... | How to evaluate fit of a logistic regression
Standard univariate logistic regression of $y$ on $x$ finds the coefficients $\alpha$, $\beta$ that best fit your training data $\{(x_i, y_i), i \in [1, N]\}$ in the following equation:
(model 1): $y |
42,460 | How to decide which penalty measure to use ? any general guidelines or thumb rules out of textbook | There can be many considerations to this matter.
To name a few:
Inference: the distribution of ridge estimates is fairly simple to derive. Lasso, and basically any other penalty that performs variable selection, has only limited probabilistic results.
Sparsity: If you desire a model with only a few predictors (say, f... | How to decide which penalty measure to use ? any general guidelines or thumb rules out of textbook | There can be many considerations to this matter.
To name a few:
Inference: the distribution of ridge estimates is fairly simple to derive. Lasso, and basically any other penalty that performs variab | How to decide which penalty measure to use ? any general guidelines or thumb rules out of textbook
There can be many considerations to this matter.
To name a few:
Inference: the distribution of ridge estimates is fairly simple to derive. Lasso, and basically any other penalty that performs variable selection, has onl... | How to decide which penalty measure to use ? any general guidelines or thumb rules out of textbook
There can be many considerations to this matter.
To name a few:
Inference: the distribution of ridge estimates is fairly simple to derive. Lasso, and basically any other penalty that performs variab |
42,461 | re-arrange elements in two vectors to minimize the elementwise difference between them | Sort the two vectors and match them in order.
The question seeks a permutation $\sigma$ of the indexes $\{1,2,\ldots, n\}$ that minimizes
$$f_{X,Y}(\sigma) = \sum_{i=1}^n |X_i - Y_{\sigma(i)}|.$$
Let $X_{[1]} \le X_{[2]} \le \cdots \le X_{[n]}$ be the order statistics for $X$. Use similar notation for the order stati... | re-arrange elements in two vectors to minimize the elementwise difference between them | Sort the two vectors and match them in order.
The question seeks a permutation $\sigma$ of the indexes $\{1,2,\ldots, n\}$ that minimizes
$$f_{X,Y}(\sigma) = \sum_{i=1}^n |X_i - Y_{\sigma(i)}|.$$
Let | re-arrange elements in two vectors to minimize the elementwise difference between them
Sort the two vectors and match them in order.
The question seeks a permutation $\sigma$ of the indexes $\{1,2,\ldots, n\}$ that minimizes
$$f_{X,Y}(\sigma) = \sum_{i=1}^n |X_i - Y_{\sigma(i)}|.$$
Let $X_{[1]} \le X_{[2]} \le \cdots ... | re-arrange elements in two vectors to minimize the elementwise difference between them
Sort the two vectors and match them in order.
The question seeks a permutation $\sigma$ of the indexes $\{1,2,\ldots, n\}$ that minimizes
$$f_{X,Y}(\sigma) = \sum_{i=1}^n |X_i - Y_{\sigma(i)}|.$$
Let |
42,462 | Boundary or threshold test for regression-type scatter plot | Such a pattern would often occur when no "boundary" actually exists.
Here I generate X and Y as independent right-skew random variates, yet such a pattern occurs:
The impression of any sense of a boundary in my plot is completely bogus, yet it looks very similar to yours. (There's an actual vertical boundary in this b... | Boundary or threshold test for regression-type scatter plot | Such a pattern would often occur when no "boundary" actually exists.
Here I generate X and Y as independent right-skew random variates, yet such a pattern occurs:
The impression of any sense of a bou | Boundary or threshold test for regression-type scatter plot
Such a pattern would often occur when no "boundary" actually exists.
Here I generate X and Y as independent right-skew random variates, yet such a pattern occurs:
The impression of any sense of a boundary in my plot is completely bogus, yet it looks very simi... | Boundary or threshold test for regression-type scatter plot
Such a pattern would often occur when no "boundary" actually exists.
Here I generate X and Y as independent right-skew random variates, yet such a pattern occurs:
The impression of any sense of a bou |
42,463 | Boundary or threshold test for regression-type scatter plot | You can use a permutation based test for such threshold.
Permutation-based test
It tests the hypothesis whether a "data-sparse" region above the threshold line is due to a random chance or not.
In brief:
The basic idea behind is to calculate the area of the "data-sparse" region and use it as a statistic. The next step... | Boundary or threshold test for regression-type scatter plot | You can use a permutation based test for such threshold.
Permutation-based test
It tests the hypothesis whether a "data-sparse" region above the threshold line is due to a random chance or not.
In br | Boundary or threshold test for regression-type scatter plot
You can use a permutation based test for such threshold.
Permutation-based test
It tests the hypothesis whether a "data-sparse" region above the threshold line is due to a random chance or not.
In brief:
The basic idea behind is to calculate the area of the "... | Boundary or threshold test for regression-type scatter plot
You can use a permutation based test for such threshold.
Permutation-based test
It tests the hypothesis whether a "data-sparse" region above the threshold line is due to a random chance or not.
In br |
42,464 | Boundary or threshold test for regression-type scatter plot | I would start by finding the "upper envelope" of your data and then representing the "envelope" as a straight line or piece-wise linear function.
For starters, you could estimate the "envelope" as a piece-wise constant function f(x) =max(yk, given abs(x-xk) is below delta), where delta is a parameter, say 3 and ... | Boundary or threshold test for regression-type scatter plot | I would start by finding the "upper envelope" of your data and then representing the "envelope" as a straight line or piece-wise linear function.
For starters, you could estimate the "envelope" as | Boundary or threshold test for regression-type scatter plot
I would start by finding the "upper envelope" of your data and then representing the "envelope" as a straight line or piece-wise linear function.
For starters, you could estimate the "envelope" as a piece-wise constant function f(x) =max(yk, given abs(x-x... | Boundary or threshold test for regression-type scatter plot
I would start by finding the "upper envelope" of your data and then representing the "envelope" as a straight line or piece-wise linear function.
For starters, you could estimate the "envelope" as |
42,465 | Boundary or threshold test for regression-type scatter plot | My intention on how this problem might be solved is:
Calculate linear model to receive the regression line $r$.
Calculate the normal vector $v$ to the resulting regression line.
Shift $r$ by $v$ till all data points are under $r$.
To optimize $r$, you might rotate it by some angle $\alpha$ and stop for the best $\alp... | Boundary or threshold test for regression-type scatter plot | My intention on how this problem might be solved is:
Calculate linear model to receive the regression line $r$.
Calculate the normal vector $v$ to the resulting regression line.
Shift $r$ by $v$ till | Boundary or threshold test for regression-type scatter plot
My intention on how this problem might be solved is:
Calculate linear model to receive the regression line $r$.
Calculate the normal vector $v$ to the resulting regression line.
Shift $r$ by $v$ till all data points are under $r$.
To optimize $r$, you might ... | Boundary or threshold test for regression-type scatter plot
My intention on how this problem might be solved is:
Calculate linear model to receive the regression line $r$.
Calculate the normal vector $v$ to the resulting regression line.
Shift $r$ by $v$ till |
42,466 | Boundary or threshold test for regression-type scatter plot | This is potentially not the most robust solution. But you may be able to seriously improve the quality of the envelope using something along these lines:
break down your data into n intervals (where the number of intervals depends on the density of your data)
find the max of you data within each interval
Pass linear r... | Boundary or threshold test for regression-type scatter plot | This is potentially not the most robust solution. But you may be able to seriously improve the quality of the envelope using something along these lines:
break down your data into n intervals (where | Boundary or threshold test for regression-type scatter plot
This is potentially not the most robust solution. But you may be able to seriously improve the quality of the envelope using something along these lines:
break down your data into n intervals (where the number of intervals depends on the density of your data)... | Boundary or threshold test for regression-type scatter plot
This is potentially not the most robust solution. But you may be able to seriously improve the quality of the envelope using something along these lines:
break down your data into n intervals (where |
42,467 | Random Forest checklist | Scaling is not required; RF training is invariant to all combinations of monotonic transformations of predictors.
classwt is not reliable; RF and unbalanced data is long story, try browsing the site or ask a more detailed question.
RF shouldn't have any problems with correlated predictors (provided that you have enoug... | Random Forest checklist | Scaling is not required; RF training is invariant to all combinations of monotonic transformations of predictors.
classwt is not reliable; RF and unbalanced data is long story, try browsing the site | Random Forest checklist
Scaling is not required; RF training is invariant to all combinations of monotonic transformations of predictors.
classwt is not reliable; RF and unbalanced data is long story, try browsing the site or ask a more detailed question.
RF shouldn't have any problems with correlated predictors (prov... | Random Forest checklist
Scaling is not required; RF training is invariant to all combinations of monotonic transformations of predictors.
classwt is not reliable; RF and unbalanced data is long story, try browsing the site |
42,468 | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts? | What you are talking about is using a "direct" forecasting strategy rather than the more popular "recursive" forecasting strategy.
In a recursive strategy, one model is fitted, usually based on minimizing the one-step forecast mean squared error, and the forecasts for all future horizons are estimated by iterating the ... | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts? | What you are talking about is using a "direct" forecasting strategy rather than the more popular "recursive" forecasting strategy.
In a recursive strategy, one model is fitted, usually based on minimi | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?
What you are talking about is using a "direct" forecasting strategy rather than the more popular "recursive" forecasting strategy.
In a recursive strategy, one model is fitted, usually based on minimizing the one-step forecast mean squared error, and... | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?
What you are talking about is using a "direct" forecasting strategy rather than the more popular "recursive" forecasting strategy.
In a recursive strategy, one model is fitted, usually based on minimi |
42,469 | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts? | This is a very common issue in business forecasting, where we want sensible forecasts for the short term without sacrificing long term performance.
You can test your data to see this by going back over multiple lags and holdout periods to see which models work best at different lags-- maybe one model does well 1-3 per... | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts? | This is a very common issue in business forecasting, where we want sensible forecasts for the short term without sacrificing long term performance.
You can test your data to see this by going back ov | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?
This is a very common issue in business forecasting, where we want sensible forecasts for the short term without sacrificing long term performance.
You can test your data to see this by going back over multiple lags and holdout periods to see which ... | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?
This is a very common issue in business forecasting, where we want sensible forecasts for the short term without sacrificing long term performance.
You can test your data to see this by going back ov |
42,470 | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts? | John,
I am not sure who is feeding you these theories about model parameters being optimal for periods out, but it just isn't right. Please share the source of your comments(books, web pages, software, etc.) I would like to read more about this. You want a model to describe the historical variations and also the peri... | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts? | John,
I am not sure who is feeding you these theories about model parameters being optimal for periods out, but it just isn't right. Please share the source of your comments(books, web pages, software | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?
John,
I am not sure who is feeding you these theories about model parameters being optimal for periods out, but it just isn't right. Please share the source of your comments(books, web pages, software, etc.) I would like to read more about this. Yo... | Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?
John,
I am not sure who is feeding you these theories about model parameters being optimal for periods out, but it just isn't right. Please share the source of your comments(books, web pages, software |
42,471 | Feature selection: permutation test Vs deleting a variable | I think the result might be very similar, unless the classification algorithm you are using is biased.
Permuting a single variable does not chance the characteristics of your dataset. If your dataset has $n$ records and $m$ features it will still have $n$ records and $m$ features if you permute one of them. If you del... | Feature selection: permutation test Vs deleting a variable | I think the result might be very similar, unless the classification algorithm you are using is biased.
Permuting a single variable does not chance the characteristics of your dataset. If your dataset | Feature selection: permutation test Vs deleting a variable
I think the result might be very similar, unless the classification algorithm you are using is biased.
Permuting a single variable does not chance the characteristics of your dataset. If your dataset has $n$ records and $m$ features it will still have $n$ reco... | Feature selection: permutation test Vs deleting a variable
I think the result might be very similar, unless the classification algorithm you are using is biased.
Permuting a single variable does not chance the characteristics of your dataset. If your dataset |
42,472 | Naive Bayes with unbalanced classes | Tackling the Poor Assumptions of Naive Bayes Text Classiffiers suggests some modifications to Naive Bayes in order to correct for biased sample sets.
Also have a look at this (and similar) CV posts on class imbalance, unbalanced class labels, etc. | Naive Bayes with unbalanced classes | Tackling the Poor Assumptions of Naive Bayes Text Classiffiers suggests some modifications to Naive Bayes in order to correct for biased sample sets.
Also have a look at this (and similar) CV posts on | Naive Bayes with unbalanced classes
Tackling the Poor Assumptions of Naive Bayes Text Classiffiers suggests some modifications to Naive Bayes in order to correct for biased sample sets.
Also have a look at this (and similar) CV posts on class imbalance, unbalanced class labels, etc. | Naive Bayes with unbalanced classes
Tackling the Poor Assumptions of Naive Bayes Text Classiffiers suggests some modifications to Naive Bayes in order to correct for biased sample sets.
Also have a look at this (and similar) CV posts on |
42,473 | Naive Bayes with unbalanced classes | I know an answer has already been accepted. i thought the following could help future reader.Try implementing this to handle unbalanced classes, This worked pretty good for me.
Naive Bayes for Text Classification with Unbalanced Classes | Naive Bayes with unbalanced classes | I know an answer has already been accepted. i thought the following could help future reader.Try implementing this to handle unbalanced classes, This worked pretty good for me.
Naive Bayes for Text Cl | Naive Bayes with unbalanced classes
I know an answer has already been accepted. i thought the following could help future reader.Try implementing this to handle unbalanced classes, This worked pretty good for me.
Naive Bayes for Text Classification with Unbalanced Classes | Naive Bayes with unbalanced classes
I know an answer has already been accepted. i thought the following could help future reader.Try implementing this to handle unbalanced classes, This worked pretty good for me.
Naive Bayes for Text Cl |
42,474 | Benefits of CART over ID3 algorithm | CART does binary splits. ID3, C45 and the family exhaust one attribute once it is used. This makes sometimes a difference which means that in CART the decisions on how to split values based on an attribute are delayed. Which means that there are pretty good chances that a CART might catch better splits than C45.
The d... | Benefits of CART over ID3 algorithm | CART does binary splits. ID3, C45 and the family exhaust one attribute once it is used. This makes sometimes a difference which means that in CART the decisions on how to split values based on an attr | Benefits of CART over ID3 algorithm
CART does binary splits. ID3, C45 and the family exhaust one attribute once it is used. This makes sometimes a difference which means that in CART the decisions on how to split values based on an attribute are delayed. Which means that there are pretty good chances that a CART might ... | Benefits of CART over ID3 algorithm
CART does binary splits. ID3, C45 and the family exhaust one attribute once it is used. This makes sometimes a difference which means that in CART the decisions on how to split values based on an attr |
42,475 | Error term interpretation in the Cox PH model | This is a very old question, but still doens't have an answer.
The simple answer to the question is that in its original formulation (both in discrete time and later in continuous time) the Cox model does not have an error term.
This implies that all sources of individual heterogeneity are captured by the vector of obs... | Error term interpretation in the Cox PH model | This is a very old question, but still doens't have an answer.
The simple answer to the question is that in its original formulation (both in discrete time and later in continuous time) the Cox model | Error term interpretation in the Cox PH model
This is a very old question, but still doens't have an answer.
The simple answer to the question is that in its original formulation (both in discrete time and later in continuous time) the Cox model does not have an error term.
This implies that all sources of individual h... | Error term interpretation in the Cox PH model
This is a very old question, but still doens't have an answer.
The simple answer to the question is that in its original formulation (both in discrete time and later in continuous time) the Cox model |
42,476 | Error term interpretation in the Cox PH model | You seem to be confusing the Cox proportional hazards model with a linear Gaussian model. The Cox model has no need for an error term. A consequence of this is that an omitted variable can destroy $\beta$s that are in the model, unlike normal regression when a terms is omitted that is orthogonal to other terms. | Error term interpretation in the Cox PH model | You seem to be confusing the Cox proportional hazards model with a linear Gaussian model. The Cox model has no need for an error term. A consequence of this is that an omitted variable can destroy $ | Error term interpretation in the Cox PH model
You seem to be confusing the Cox proportional hazards model with a linear Gaussian model. The Cox model has no need for an error term. A consequence of this is that an omitted variable can destroy $\beta$s that are in the model, unlike normal regression when a terms is om... | Error term interpretation in the Cox PH model
You seem to be confusing the Cox proportional hazards model with a linear Gaussian model. The Cox model has no need for an error term. A consequence of this is that an omitted variable can destroy $ |
42,477 | Appropriate GLM when response variable is proportion, but not binomial | Before venturing into the territory of GLMs it might be worth fitting a regression model on an appropriately transformed version of the response variable. If we let $0<Y_i<1$ be the area-proportion (and assuming you don't have any proportions that are exactly zero or one) then a reasonable regression model would be:
$... | Appropriate GLM when response variable is proportion, but not binomial | Before venturing into the territory of GLMs it might be worth fitting a regression model on an appropriately transformed version of the response variable. If we let $0<Y_i<1$ be the area-proportion ( | Appropriate GLM when response variable is proportion, but not binomial
Before venturing into the territory of GLMs it might be worth fitting a regression model on an appropriately transformed version of the response variable. If we let $0<Y_i<1$ be the area-proportion (and assuming you don't have any proportions that ... | Appropriate GLM when response variable is proportion, but not binomial
Before venturing into the territory of GLMs it might be worth fitting a regression model on an appropriately transformed version of the response variable. If we let $0<Y_i<1$ be the area-proportion ( |
42,478 | Appropriate GLM when response variable is proportion, but not binomial | Beta-regression comes to mind, as you mentioned. Look around the site and the respective tag, beta-regression.
R has a package, betareg as well. | Appropriate GLM when response variable is proportion, but not binomial | Beta-regression comes to mind, as you mentioned. Look around the site and the respective tag, beta-regression.
R has a package, betareg as well. | Appropriate GLM when response variable is proportion, but not binomial
Beta-regression comes to mind, as you mentioned. Look around the site and the respective tag, beta-regression.
R has a package, betareg as well. | Appropriate GLM when response variable is proportion, but not binomial
Beta-regression comes to mind, as you mentioned. Look around the site and the respective tag, beta-regression.
R has a package, betareg as well. |
42,479 | How can we evaluate the predicted values using Scikit-Learn | In order to get the accuracy of the predication you can do:
print accuracy_score(expected, y_1)
If you want a few metrics, such as, precision, recall, f1-score you can get a classification report:
print classification_report(expected, y_1)
A confusion matrix will tell how many of the samples that were classified are ... | How can we evaluate the predicted values using Scikit-Learn | In order to get the accuracy of the predication you can do:
print accuracy_score(expected, y_1)
If you want a few metrics, such as, precision, recall, f1-score you can get a classification report:
pr | How can we evaluate the predicted values using Scikit-Learn
In order to get the accuracy of the predication you can do:
print accuracy_score(expected, y_1)
If you want a few metrics, such as, precision, recall, f1-score you can get a classification report:
print classification_report(expected, y_1)
A confusion matrix... | How can we evaluate the predicted values using Scikit-Learn
In order to get the accuracy of the predication you can do:
print accuracy_score(expected, y_1)
If you want a few metrics, such as, precision, recall, f1-score you can get a classification report:
pr |
42,480 | If the level of a test is decreased, would the power of the test be expected to increase? | The likelihood of making a type 1 error v. a type 2 error is inversely proportional. Thus, if you make your rejection of the null less stringent, all else being equal, the power of your test should increase.
From Wikipedia on Statistical Power: “One easy way to increase the power of a test is to carry out a less conser... | If the level of a test is decreased, would the power of the test be expected to increase? | The likelihood of making a type 1 error v. a type 2 error is inversely proportional. Thus, if you make your rejection of the null less stringent, all else being equal, the power of your test should in | If the level of a test is decreased, would the power of the test be expected to increase?
The likelihood of making a type 1 error v. a type 2 error is inversely proportional. Thus, if you make your rejection of the null less stringent, all else being equal, the power of your test should increase.
From Wikipedia on Stat... | If the level of a test is decreased, would the power of the test be expected to increase?
The likelihood of making a type 1 error v. a type 2 error is inversely proportional. Thus, if you make your rejection of the null less stringent, all else being equal, the power of your test should in |
42,481 | If the level of a test is decreased, would the power of the test be expected to increase? | The level is of a test is its significance level, $\alpha$. Decreasing the level means making $\alpha$ smaller.
If you make $\alpha$ smaller, you make $\beta$ larger* ... and power is $1-\beta$.
What you're doing when you lower $\alpha$ is moving the critical value further out into the tail, so you make it harder to re... | If the level of a test is decreased, would the power of the test be expected to increase? | The level is of a test is its significance level, $\alpha$. Decreasing the level means making $\alpha$ smaller.
If you make $\alpha$ smaller, you make $\beta$ larger* ... and power is $1-\beta$.
What | If the level of a test is decreased, would the power of the test be expected to increase?
The level is of a test is its significance level, $\alpha$. Decreasing the level means making $\alpha$ smaller.
If you make $\alpha$ smaller, you make $\beta$ larger* ... and power is $1-\beta$.
What you're doing when you lower $\... | If the level of a test is decreased, would the power of the test be expected to increase?
The level is of a test is its significance level, $\alpha$. Decreasing the level means making $\alpha$ smaller.
If you make $\alpha$ smaller, you make $\beta$ larger* ... and power is $1-\beta$.
What |
42,482 | If the level of a test is decreased, would the power of the test be expected to increase? | Ceteris paribus, when you decrease the significance level $\alpha$ in a classical hypothesis test, you are increasing the amount of evidence required to reject the null hypothesis. This means that you are less likely to reject the null hypothesis, which lowers the probability of a Type I error, but also reduces the po... | If the level of a test is decreased, would the power of the test be expected to increase? | Ceteris paribus, when you decrease the significance level $\alpha$ in a classical hypothesis test, you are increasing the amount of evidence required to reject the null hypothesis. This means that yo | If the level of a test is decreased, would the power of the test be expected to increase?
Ceteris paribus, when you decrease the significance level $\alpha$ in a classical hypothesis test, you are increasing the amount of evidence required to reject the null hypothesis. This means that you are less likely to reject th... | If the level of a test is decreased, would the power of the test be expected to increase?
Ceteris paribus, when you decrease the significance level $\alpha$ in a classical hypothesis test, you are increasing the amount of evidence required to reject the null hypothesis. This means that yo |
42,483 | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test | Radmacher and colleagues (J. Comput. Biol. 9:505-511) describe a process for computing the significance of an error rate. We permute the class labels (a few thousand times) and repeat the entire cross-validation procedure to assess the probability of producing a cross-validated error rate as small as the observed one. ... | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test | Radmacher and colleagues (J. Comput. Biol. 9:505-511) describe a process for computing the significance of an error rate. We permute the class labels (a few thousand times) and repeat the entire cross | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test
Radmacher and colleagues (J. Comput. Biol. 9:505-511) describe a process for computing the significance of an error rate. We permute the class labels (a few thousand times) and repeat the entire cross-validation procedure to as... | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test
Radmacher and colleagues (J. Comput. Biol. 9:505-511) describe a process for computing the significance of an error rate. We permute the class labels (a few thousand times) and repeat the entire cross |
42,484 | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test | This is not really an answer to my question, but I would like to provide an explicit and very simple simulation demonstrating the symptoms I described, and I don't want to clutter the question too much.
Let's consider the absolutely simplest case possible. I will take 400 one-dimensional samples: 200 are equal to -1 an... | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test | This is not really an answer to my question, but I would like to provide an explicit and very simple simulation demonstrating the symptoms I described, and I don't want to clutter the question too muc | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test
This is not really an answer to my question, but I would like to provide an explicit and very simple simulation demonstrating the symptoms I described, and I don't want to clutter the question too much.
Let's consider the absol... | Significance testing of cross-validated classification accuracy: shuffling vs. binomial test
This is not really an answer to my question, but I would like to provide an explicit and very simple simulation demonstrating the symptoms I described, and I don't want to clutter the question too muc |
42,485 | How to find the Fisher Information of a function of the MLE of a Geometric (p) distribution? | By the formula for the MLE, I understand that you are dealing with the variant of the Geometric distribution where the random variables can take the value $0$. In this case we have
$$E(X_1) = \frac {1-p}{p},\,\,\, \text {Var}(X_1) = \frac {1-p}{p^2}$$
The Fisher Information of a single observation can be derived by ap... | How to find the Fisher Information of a function of the MLE of a Geometric (p) distribution? | By the formula for the MLE, I understand that you are dealing with the variant of the Geometric distribution where the random variables can take the value $0$. In this case we have
$$E(X_1) = \frac {1 | How to find the Fisher Information of a function of the MLE of a Geometric (p) distribution?
By the formula for the MLE, I understand that you are dealing with the variant of the Geometric distribution where the random variables can take the value $0$. In this case we have
$$E(X_1) = \frac {1-p}{p},\,\,\, \text {Var}(... | How to find the Fisher Information of a function of the MLE of a Geometric (p) distribution?
By the formula for the MLE, I understand that you are dealing with the variant of the Geometric distribution where the random variables can take the value $0$. In this case we have
$$E(X_1) = \frac {1 |
42,486 | When is the inverse of the Fisher Information exact? (MLE) | Sometimes, when doing MLE problems, I see that the variance expression gotten from the inverse of the Fisher Information is exactly like what it should be and sometimes it isn't.
All depends on what 'exactly like it should be' means ;)
At any rate, I think you need to take a look at the Cramer-Rao bound again. The inv... | When is the inverse of the Fisher Information exact? (MLE) | Sometimes, when doing MLE problems, I see that the variance expression gotten from the inverse of the Fisher Information is exactly like what it should be and sometimes it isn't.
All depends on what | When is the inverse of the Fisher Information exact? (MLE)
Sometimes, when doing MLE problems, I see that the variance expression gotten from the inverse of the Fisher Information is exactly like what it should be and sometimes it isn't.
All depends on what 'exactly like it should be' means ;)
At any rate, I think you... | When is the inverse of the Fisher Information exact? (MLE)
Sometimes, when doing MLE problems, I see that the variance expression gotten from the inverse of the Fisher Information is exactly like what it should be and sometimes it isn't.
All depends on what |
42,487 | Is it possible for a bayesian model to "forget" about some points? | You can remove their contribution from the likelihood or log-likelihood by division or subtraction, exactly reversing their contribution when they were multiplied or added in in the first place.
It's like saying "There's a long multiplication I've done: $3\times 4\times 2\times 5\times 6\times 6\times 2 \times x$. I ha... | Is it possible for a bayesian model to "forget" about some points? | You can remove their contribution from the likelihood or log-likelihood by division or subtraction, exactly reversing their contribution when they were multiplied or added in in the first place.
It's | Is it possible for a bayesian model to "forget" about some points?
You can remove their contribution from the likelihood or log-likelihood by division or subtraction, exactly reversing their contribution when they were multiplied or added in in the first place.
It's like saying "There's a long multiplication I've done:... | Is it possible for a bayesian model to "forget" about some points?
You can remove their contribution from the likelihood or log-likelihood by division or subtraction, exactly reversing their contribution when they were multiplied or added in in the first place.
It's |
42,488 | Help in understanding how to apply correctly False Discovery Rate adjustment | Note that Benjamini-Hochberg controls the false discovery rate to be less than or equal to the specified level, which has been satisfied by all of your scenarios.
In terms of the procedure you have followed, there are no faults there. However, it is worth pointing out that for real gene expression data you may get bett... | Help in understanding how to apply correctly False Discovery Rate adjustment | Note that Benjamini-Hochberg controls the false discovery rate to be less than or equal to the specified level, which has been satisfied by all of your scenarios.
In terms of the procedure you have fo | Help in understanding how to apply correctly False Discovery Rate adjustment
Note that Benjamini-Hochberg controls the false discovery rate to be less than or equal to the specified level, which has been satisfied by all of your scenarios.
In terms of the procedure you have followed, there are no faults there. However,... | Help in understanding how to apply correctly False Discovery Rate adjustment
Note that Benjamini-Hochberg controls the false discovery rate to be less than or equal to the specified level, which has been satisfied by all of your scenarios.
In terms of the procedure you have fo |
42,489 | Comparing AIC and adjusted $R^2$ | (I assume your homework has been turned in by now ;-). I'll answer this so that it doesn't stay officially unanswered.)
@user12202013 is right you don't compare an AIC to an $R^2_{\rm adj}$. You can compare the AICs from two different models, and you can compare the $R^2_{\rm adj}$s from two different models, as way... | Comparing AIC and adjusted $R^2$ | (I assume your homework has been turned in by now ;-). I'll answer this so that it doesn't stay officially unanswered.)
@user12202013 is right you don't compare an AIC to an $R^2_{\rm adj}$. You ca | Comparing AIC and adjusted $R^2$
(I assume your homework has been turned in by now ;-). I'll answer this so that it doesn't stay officially unanswered.)
@user12202013 is right you don't compare an AIC to an $R^2_{\rm adj}$. You can compare the AICs from two different models, and you can compare the $R^2_{\rm adj}$s ... | Comparing AIC and adjusted $R^2$
(I assume your homework has been turned in by now ;-). I'll answer this so that it doesn't stay officially unanswered.)
@user12202013 is right you don't compare an AIC to an $R^2_{\rm adj}$. You ca |
42,490 | R neural network model with target vector as output containing survival predictions | Why not just put binary indicator for event as a target variable and length of time period as a explanatory variable (plus other covariates)? If event happens then target is 1 and time period is calculated as time until event happens - start time. For some observations where target is 0 this time period is 36, if measu... | R neural network model with target vector as output containing survival predictions | Why not just put binary indicator for event as a target variable and length of time period as a explanatory variable (plus other covariates)? If event happens then target is 1 and time period is calcu | R neural network model with target vector as output containing survival predictions
Why not just put binary indicator for event as a target variable and length of time period as a explanatory variable (plus other covariates)? If event happens then target is 1 and time period is calculated as time until event happens - ... | R neural network model with target vector as output containing survival predictions
Why not just put binary indicator for event as a target variable and length of time period as a explanatory variable (plus other covariates)? If event happens then target is 1 and time period is calcu |
42,491 | Is it possible to do a test of significance for a string occurrence in two datasets | Note: This answer is now deprecated in light of the new information added by the OP. This answer is of related interest in the context, hence not deleted.
You can do a z-test of equality of proportions if the word appears in both the the dictionaries.
There are two steps to this process -- a combination of Python and s... | Is it possible to do a test of significance for a string occurrence in two datasets | Note: This answer is now deprecated in light of the new information added by the OP. This answer is of related interest in the context, hence not deleted.
You can do a z-test of equality of proportion | Is it possible to do a test of significance for a string occurrence in two datasets
Note: This answer is now deprecated in light of the new information added by the OP. This answer is of related interest in the context, hence not deleted.
You can do a z-test of equality of proportions if the word appears in both the th... | Is it possible to do a test of significance for a string occurrence in two datasets
Note: This answer is now deprecated in light of the new information added by the OP. This answer is of related interest in the context, hence not deleted.
You can do a z-test of equality of proportion |
42,492 | Is it possible to do a test of significance for a string occurrence in two datasets | You want to know when the difference between counts (a Gap) of the same word in different groups is unexpectedly large. It sounds like you are assuming that the Gap between different groups generally speaking should be small. You also only have 2 groups of counts - you only give 2 datasets - which would make testing ... | Is it possible to do a test of significance for a string occurrence in two datasets | You want to know when the difference between counts (a Gap) of the same word in different groups is unexpectedly large. It sounds like you are assuming that the Gap between different groups generally | Is it possible to do a test of significance for a string occurrence in two datasets
You want to know when the difference between counts (a Gap) of the same word in different groups is unexpectedly large. It sounds like you are assuming that the Gap between different groups generally speaking should be small. You also... | Is it possible to do a test of significance for a string occurrence in two datasets
You want to know when the difference between counts (a Gap) of the same word in different groups is unexpectedly large. It sounds like you are assuming that the Gap between different groups generally |
42,493 | Trying to understand unbiased estimator | I'm not 100% sure about this either, as the post you link to mentions a lot of subtleties that I haven't considered or studied much yet...but here's an attempt to answer nevertheless.
As you've stated it, $h(x)$ is your estimator, because you're using it to approximate $f$. "The process of choosing the linear regressi... | Trying to understand unbiased estimator | I'm not 100% sure about this either, as the post you link to mentions a lot of subtleties that I haven't considered or studied much yet...but here's an attempt to answer nevertheless.
As you've state | Trying to understand unbiased estimator
I'm not 100% sure about this either, as the post you link to mentions a lot of subtleties that I haven't considered or studied much yet...but here's an attempt to answer nevertheless.
As you've stated it, $h(x)$ is your estimator, because you're using it to approximate $f$. "The... | Trying to understand unbiased estimator
I'm not 100% sure about this either, as the post you link to mentions a lot of subtleties that I haven't considered or studied much yet...but here's an attempt to answer nevertheless.
As you've state |
42,494 | Trying to understand unbiased estimator | On looking at those lecture notes, the sample size is only two - so you can hardly do better without knowing anything about f than simply averaging the two values.
The notions of "bias" and "variance" can be defined only relative to some kind of model structure. This is clearly encapsulated by the $ E_x[.] $ and $ E... | Trying to understand unbiased estimator | On looking at those lecture notes, the sample size is only two - so you can hardly do better without knowing anything about f than simply averaging the two values.
The notions of "bias" and "varianc | Trying to understand unbiased estimator
On looking at those lecture notes, the sample size is only two - so you can hardly do better without knowing anything about f than simply averaging the two values.
The notions of "bias" and "variance" can be defined only relative to some kind of model structure. This is clearl... | Trying to understand unbiased estimator
On looking at those lecture notes, the sample size is only two - so you can hardly do better without knowing anything about f than simply averaging the two values.
The notions of "bias" and "varianc |
42,495 | Model selection criterion produces non-normal residuals | We use the Akaike or Schwarz information criteria to compare a set of "Candidate Models". The candidates means that you have already fitted your regression models and did the model adequacy checking including the normality assumption of your residuals. You are just not sure about the balance between the number of param... | Model selection criterion produces non-normal residuals | We use the Akaike or Schwarz information criteria to compare a set of "Candidate Models". The candidates means that you have already fitted your regression models and did the model adequacy checking i | Model selection criterion produces non-normal residuals
We use the Akaike or Schwarz information criteria to compare a set of "Candidate Models". The candidates means that you have already fitted your regression models and did the model adequacy checking including the normality assumption of your residuals. You are jus... | Model selection criterion produces non-normal residuals
We use the Akaike or Schwarz information criteria to compare a set of "Candidate Models". The candidates means that you have already fitted your regression models and did the model adequacy checking i |
42,496 | Model selection criterion produces non-normal residuals | AIC and BIC both have consist of two elements: the likelihood and the penalty for the number of parameters. The likelihood need not be normal likelihood, it can be whatever you find reasonable.
However, if you assume the likelihood to be normal (and use it in AIC or BIC), you need normal residuals, too. In other words... | Model selection criterion produces non-normal residuals | AIC and BIC both have consist of two elements: the likelihood and the penalty for the number of parameters. The likelihood need not be normal likelihood, it can be whatever you find reasonable.
Howev | Model selection criterion produces non-normal residuals
AIC and BIC both have consist of two elements: the likelihood and the penalty for the number of parameters. The likelihood need not be normal likelihood, it can be whatever you find reasonable.
However, if you assume the likelihood to be normal (and use it in AIC... | Model selection criterion produces non-normal residuals
AIC and BIC both have consist of two elements: the likelihood and the penalty for the number of parameters. The likelihood need not be normal likelihood, it can be whatever you find reasonable.
Howev |
42,497 | What can I do with these two time series? | For forecasting low frequency variables with high frequency you can use MIDAS regression. The idea behind this regression is quite simple, average the high-frequency variable and then use it as a regressor. The key is to use custom weights. Suppose we have $Y_t$ which is sampled monthly and $X_\tau$, which is sampled d... | What can I do with these two time series? | For forecasting low frequency variables with high frequency you can use MIDAS regression. The idea behind this regression is quite simple, average the high-frequency variable and then use it as a regr | What can I do with these two time series?
For forecasting low frequency variables with high frequency you can use MIDAS regression. The idea behind this regression is quite simple, average the high-frequency variable and then use it as a regressor. The key is to use custom weights. Suppose we have $Y_t$ which is sample... | What can I do with these two time series?
For forecasting low frequency variables with high frequency you can use MIDAS regression. The idea behind this regression is quite simple, average the high-frequency variable and then use it as a regr |
42,498 | What can I do with these two time series? | For starters, I would check if the draws from list A are two standard deviations outside of the draws from list B.
Secondly, I would check if a 1 month moving average of list A is significantly different from the more slowly sampled list B. | What can I do with these two time series? | For starters, I would check if the draws from list A are two standard deviations outside of the draws from list B.
Secondly, I would check if a 1 month moving average of list A is significantly differ | What can I do with these two time series?
For starters, I would check if the draws from list A are two standard deviations outside of the draws from list B.
Secondly, I would check if a 1 month moving average of list A is significantly different from the more slowly sampled list B. | What can I do with these two time series?
For starters, I would check if the draws from list A are two standard deviations outside of the draws from list B.
Secondly, I would check if a 1 month moving average of list A is significantly differ |
42,499 | What can I do with these two time series? | Fit seasonal time series models to both and then compare the seasonality.
The TBATS model can handle daily data. It is available in the forecast package in R. | What can I do with these two time series? | Fit seasonal time series models to both and then compare the seasonality.
The TBATS model can handle daily data. It is available in the forecast package in R. | What can I do with these two time series?
Fit seasonal time series models to both and then compare the seasonality.
The TBATS model can handle daily data. It is available in the forecast package in R. | What can I do with these two time series?
Fit seasonal time series models to both and then compare the seasonality.
The TBATS model can handle daily data. It is available in the forecast package in R. |
42,500 | Estimate single ARIMA for multiple timeseries | That can happen when the model is not suitable for the data.
stepwise=FALSE makes auto.arima work harder to find the best model. So of course, sometimes it finds a different model than when stepwise=TRUE.
It is impossible to say with the information provided. You should be aware that comparing AIC values with different... | Estimate single ARIMA for multiple timeseries | That can happen when the model is not suitable for the data.
stepwise=FALSE makes auto.arima work harder to find the best model. So of course, sometimes it finds a different model than when stepwise=T | Estimate single ARIMA for multiple timeseries
That can happen when the model is not suitable for the data.
stepwise=FALSE makes auto.arima work harder to find the best model. So of course, sometimes it finds a different model than when stepwise=TRUE.
It is impossible to say with the information provided. You should be ... | Estimate single ARIMA for multiple timeseries
That can happen when the model is not suitable for the data.
stepwise=FALSE makes auto.arima work harder to find the best model. So of course, sometimes it finds a different model than when stepwise=T |
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