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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38,501 | Can you use a percentage as an independent variable in multiple linear regression? | Percentages can be considered continuous on the interval [0,1]. There is no reason why percentages can't be independent variables in linear regression. In fact, there is no requirement that independent variables need to be continuous. Indicator variables are often used as independent variables in regressions. | Can you use a percentage as an independent variable in multiple linear regression? | Percentages can be considered continuous on the interval [0,1]. There is no reason why percentages can't be independent variables in linear regression. In fact, there is no requirement that independ | Can you use a percentage as an independent variable in multiple linear regression?
Percentages can be considered continuous on the interval [0,1]. There is no reason why percentages can't be independent variables in linear regression. In fact, there is no requirement that independent variables need to be continuous. ... | Can you use a percentage as an independent variable in multiple linear regression?
Percentages can be considered continuous on the interval [0,1]. There is no reason why percentages can't be independent variables in linear regression. In fact, there is no requirement that independ |
38,502 | Can you use a percentage as an independent variable in multiple linear regression? | The assumption of normality to which you refer does not apply to any of the predictors (after all how could a binary predictor be normal?) nor does it apply to the outcome. What it applies to is the residuals from your model. So at this stage before you have fitted the model you do not know whether it holds or not. Sim... | Can you use a percentage as an independent variable in multiple linear regression? | The assumption of normality to which you refer does not apply to any of the predictors (after all how could a binary predictor be normal?) nor does it apply to the outcome. What it applies to is the r | Can you use a percentage as an independent variable in multiple linear regression?
The assumption of normality to which you refer does not apply to any of the predictors (after all how could a binary predictor be normal?) nor does it apply to the outcome. What it applies to is the residuals from your model. So at this ... | Can you use a percentage as an independent variable in multiple linear regression?
The assumption of normality to which you refer does not apply to any of the predictors (after all how could a binary predictor be normal?) nor does it apply to the outcome. What it applies to is the r |
38,503 | Can you use a percentage as an independent variable in multiple linear regression? | Suppose you have a model
$$Y = B_1 X_1 + B_2 X_2 + E,$$
where $E \sim Nor(0,1)$
Let $X_3$, $X_4$ be the percentages and $S_1$, $S_2$ be the total of $X_1$, $X_2$ respectively
then, $X_3 = X_1/S_1*100$ and $X_4 = X_2/S_2*100$.
Then the model with percentage will be,
$Y = B_3 X_3 + B_4 X_4 + E'$
The estimates will be $B ... | Can you use a percentage as an independent variable in multiple linear regression? | Suppose you have a model
$$Y = B_1 X_1 + B_2 X_2 + E,$$
where $E \sim Nor(0,1)$
Let $X_3$, $X_4$ be the percentages and $S_1$, $S_2$ be the total of $X_1$, $X_2$ respectively
then, $X_3 = X_1/S_1*100$ | Can you use a percentage as an independent variable in multiple linear regression?
Suppose you have a model
$$Y = B_1 X_1 + B_2 X_2 + E,$$
where $E \sim Nor(0,1)$
Let $X_3$, $X_4$ be the percentages and $S_1$, $S_2$ be the total of $X_1$, $X_2$ respectively
then, $X_3 = X_1/S_1*100$ and $X_4 = X_2/S_2*100$.
Then the mo... | Can you use a percentage as an independent variable in multiple linear regression?
Suppose you have a model
$$Y = B_1 X_1 + B_2 X_2 + E,$$
where $E \sim Nor(0,1)$
Let $X_3$, $X_4$ be the percentages and $S_1$, $S_2$ be the total of $X_1$, $X_2$ respectively
then, $X_3 = X_1/S_1*100$ |
38,504 | Fitting exponential (regression) model by MLE? | This has been answered on the R help list by Adelchi Azzalini: the important point is that the dispersion parameter (which is what distinguishes an exponential distribution from the more general Gamma distribution) does not affect the parameter estimates in a generalized linear model, only the standard errors of the pa... | Fitting exponential (regression) model by MLE? | This has been answered on the R help list by Adelchi Azzalini: the important point is that the dispersion parameter (which is what distinguishes an exponential distribution from the more general Gamma | Fitting exponential (regression) model by MLE?
This has been answered on the R help list by Adelchi Azzalini: the important point is that the dispersion parameter (which is what distinguishes an exponential distribution from the more general Gamma distribution) does not affect the parameter estimates in a generalized l... | Fitting exponential (regression) model by MLE?
This has been answered on the R help list by Adelchi Azzalini: the important point is that the dispersion parameter (which is what distinguishes an exponential distribution from the more general Gamma |
38,505 | Fitting exponential (regression) model by MLE? | Using a GLM call as you suggest there is the easiest correct approach, but to actually make the Gamma into an exponential you can specify the dispersion to be 1. It will not change the fitted mean / coefficients, but it impacts the standard errors.
[i.e. Your suggested call of summary(glm(y~x,family=Gamma(link="log")))... | Fitting exponential (regression) model by MLE? | Using a GLM call as you suggest there is the easiest correct approach, but to actually make the Gamma into an exponential you can specify the dispersion to be 1. It will not change the fitted mean / c | Fitting exponential (regression) model by MLE?
Using a GLM call as you suggest there is the easiest correct approach, but to actually make the Gamma into an exponential you can specify the dispersion to be 1. It will not change the fitted mean / coefficients, but it impacts the standard errors.
[i.e. Your suggested cal... | Fitting exponential (regression) model by MLE?
Using a GLM call as you suggest there is the easiest correct approach, but to actually make the Gamma into an exponential you can specify the dispersion to be 1. It will not change the fitted mean / c |
38,506 | Book recommendations for probability | I suggest you a couple of books that I admit I never had the
occasion to study. These would have been my reference
if I specialized in probability:
Ash, Dade - "Probability and Measure Theory"
Billingsley - "Probability and Measure"
I think (2) is more popular. | Book recommendations for probability | I suggest you a couple of books that I admit I never had the
occasion to study. These would have been my reference
if I specialized in probability:
Ash, Dade - "Probability and Measure Theory"
Billi | Book recommendations for probability
I suggest you a couple of books that I admit I never had the
occasion to study. These would have been my reference
if I specialized in probability:
Ash, Dade - "Probability and Measure Theory"
Billingsley - "Probability and Measure"
I think (2) is more popular. | Book recommendations for probability
I suggest you a couple of books that I admit I never had the
occasion to study. These would have been my reference
if I specialized in probability:
Ash, Dade - "Probability and Measure Theory"
Billi |
38,507 | Book recommendations for probability | Foundations of Modern Probability by Olav Kallenberg meets all your criteria. It is quite concise and mathematically rigorous and as one reviewer puts it "without any non-mathematical distractions". | Book recommendations for probability | Foundations of Modern Probability by Olav Kallenberg meets all your criteria. It is quite concise and mathematically rigorous and as one reviewer puts it "without any non-mathematical distractions". | Book recommendations for probability
Foundations of Modern Probability by Olav Kallenberg meets all your criteria. It is quite concise and mathematically rigorous and as one reviewer puts it "without any non-mathematical distractions". | Book recommendations for probability
Foundations of Modern Probability by Olav Kallenberg meets all your criteria. It is quite concise and mathematically rigorous and as one reviewer puts it "without any non-mathematical distractions". |
38,508 | Book recommendations for probability | I think Amir Dembo's notes are pretty stellar. He updates them each time he teaches the course, but even then they have really good proofs and exercises. He also has notes on stochastic processes. William's Probability with Martingales is also good... but only the parts on martingales are good. Durrett's book is decent... | Book recommendations for probability | I think Amir Dembo's notes are pretty stellar. He updates them each time he teaches the course, but even then they have really good proofs and exercises. He also has notes on stochastic processes. Wil | Book recommendations for probability
I think Amir Dembo's notes are pretty stellar. He updates them each time he teaches the course, but even then they have really good proofs and exercises. He also has notes on stochastic processes. William's Probability with Martingales is also good... but only the parts on martingal... | Book recommendations for probability
I think Amir Dembo's notes are pretty stellar. He updates them each time he teaches the course, but even then they have really good proofs and exercises. He also has notes on stochastic processes. Wil |
38,509 | Book recommendations for probability | I know these are no books, but nonetheless I think these materials are quite useful:
At MIT they offer various courses for free. Some of these courses might also contain books.
Overview of free probability and statistics courses at MIT
This is the best online course of advanced Theory of probability. It is made by Scot... | Book recommendations for probability | I know these are no books, but nonetheless I think these materials are quite useful:
At MIT they offer various courses for free. Some of these courses might also contain books.
Overview of free probab | Book recommendations for probability
I know these are no books, but nonetheless I think these materials are quite useful:
At MIT they offer various courses for free. Some of these courses might also contain books.
Overview of free probability and statistics courses at MIT
This is the best online course of advanced Theo... | Book recommendations for probability
I know these are no books, but nonetheless I think these materials are quite useful:
At MIT they offer various courses for free. Some of these courses might also contain books.
Overview of free probab |
38,510 | Book recommendations for probability | Weiss, A Course in Probability covers at least nearly all of these topics. It's also very readable.
There's a strange problem with probability and stats textbooks where the notation of explanation is exceptionally shoddy and non-rigorous. This book usually doesn't suffer from that deficiency. But occasionally it punts ... | Book recommendations for probability | Weiss, A Course in Probability covers at least nearly all of these topics. It's also very readable.
There's a strange problem with probability and stats textbooks where the notation of explanation is | Book recommendations for probability
Weiss, A Course in Probability covers at least nearly all of these topics. It's also very readable.
There's a strange problem with probability and stats textbooks where the notation of explanation is exceptionally shoddy and non-rigorous. This book usually doesn't suffer from that d... | Book recommendations for probability
Weiss, A Course in Probability covers at least nearly all of these topics. It's also very readable.
There's a strange problem with probability and stats textbooks where the notation of explanation is |
38,511 | Book recommendations for probability | I wholeheartedly recommend Parzen's Modern Probability Theory and its Applications. This is a classic written by someone who has made enormous contributions to statistics, in e.g. non-parametric density estimation, and is very easy to read. Moreover, it covers almost all of your required topics (I only can't remember i... | Book recommendations for probability | I wholeheartedly recommend Parzen's Modern Probability Theory and its Applications. This is a classic written by someone who has made enormous contributions to statistics, in e.g. non-parametric densi | Book recommendations for probability
I wholeheartedly recommend Parzen's Modern Probability Theory and its Applications. This is a classic written by someone who has made enormous contributions to statistics, in e.g. non-parametric density estimation, and is very easy to read. Moreover, it covers almost all of your req... | Book recommendations for probability
I wholeheartedly recommend Parzen's Modern Probability Theory and its Applications. This is a classic written by someone who has made enormous contributions to statistics, in e.g. non-parametric densi |
38,512 | Book recommendations for probability | Probability Theory: The Logic of Science
by E. T. Jaynes
Its a classic for a reason. I only can recommend it since it takes a more practical approach. Also contains a bunch of exercises. PDF of older versions should be available (amazon link) | Book recommendations for probability | Probability Theory: The Logic of Science
by E. T. Jaynes
Its a classic for a reason. I only can recommend it since it takes a more practical approach. Also contains a bunch of exercises. PDF of older | Book recommendations for probability
Probability Theory: The Logic of Science
by E. T. Jaynes
Its a classic for a reason. I only can recommend it since it takes a more practical approach. Also contains a bunch of exercises. PDF of older versions should be available (amazon link) | Book recommendations for probability
Probability Theory: The Logic of Science
by E. T. Jaynes
Its a classic for a reason. I only can recommend it since it takes a more practical approach. Also contains a bunch of exercises. PDF of older |
38,513 | Ground-truth definition | The term "ground truth" was coined in the geological/earth sciences to describe validation of data by going out in the field and checking "on the ground". It has been adopted in other fields to express the notion of data that is "known" to be correct. In my personal experience it is widely used in biometrics and comp... | Ground-truth definition | The term "ground truth" was coined in the geological/earth sciences to describe validation of data by going out in the field and checking "on the ground". It has been adopted in other fields to expre | Ground-truth definition
The term "ground truth" was coined in the geological/earth sciences to describe validation of data by going out in the field and checking "on the ground". It has been adopted in other fields to express the notion of data that is "known" to be correct. In my personal experience it is widely use... | Ground-truth definition
The term "ground truth" was coined in the geological/earth sciences to describe validation of data by going out in the field and checking "on the ground". It has been adopted in other fields to expre |
38,514 | Ground-truth definition | In most cases it is used as 'real true' e.g. scikit in Python, with specific examples such as image recognition eg Nunez-Iglesias et al. PLOS One, character recognition Luis von Ahn et al. Science.
But how close is the 'real true' to a fixed value can depend on the complexity of input and whether "reference data can ... | Ground-truth definition | In most cases it is used as 'real true' e.g. scikit in Python, with specific examples such as image recognition eg Nunez-Iglesias et al. PLOS One, character recognition Luis von Ahn et al. Science.
| Ground-truth definition
In most cases it is used as 'real true' e.g. scikit in Python, with specific examples such as image recognition eg Nunez-Iglesias et al. PLOS One, character recognition Luis von Ahn et al. Science.
But how close is the 'real true' to a fixed value can depend on the complexity of input and whet... | Ground-truth definition
In most cases it is used as 'real true' e.g. scikit in Python, with specific examples such as image recognition eg Nunez-Iglesias et al. PLOS One, character recognition Luis von Ahn et al. Science.
|
38,515 | Ground-truth definition | This is not exactly a definition, but a brief, nuanced description of ground truth in machine learning by James Kobielus at IBM: http://www.ibmbigdatahub.com/blog/ground-truth-agile-machine-learning
Within machine learning, I would call ground truth a human-defined truth or an external truth rather than an epistemologi... | Ground-truth definition | This is not exactly a definition, but a brief, nuanced description of ground truth in machine learning by James Kobielus at IBM: http://www.ibmbigdatahub.com/blog/ground-truth-agile-machine-learning
W | Ground-truth definition
This is not exactly a definition, but a brief, nuanced description of ground truth in machine learning by James Kobielus at IBM: http://www.ibmbigdatahub.com/blog/ground-truth-agile-machine-learning
Within machine learning, I would call ground truth a human-defined truth or an external truth rat... | Ground-truth definition
This is not exactly a definition, but a brief, nuanced description of ground truth in machine learning by James Kobielus at IBM: http://www.ibmbigdatahub.com/blog/ground-truth-agile-machine-learning
W |
38,516 | Ground-truth definition | Meaning “according to the “assumed””. The assumed is the ground, as taken the only referral voltage in electrical systems. The term was adopted by computer scientists working in machine learning who were inherited from electrical engineers. | Ground-truth definition | Meaning “according to the “assumed””. The assumed is the ground, as taken the only referral voltage in electrical systems. The term was adopted by computer scientists working in machine learning who w | Ground-truth definition
Meaning “according to the “assumed””. The assumed is the ground, as taken the only referral voltage in electrical systems. The term was adopted by computer scientists working in machine learning who were inherited from electrical engineers. | Ground-truth definition
Meaning “according to the “assumed””. The assumed is the ground, as taken the only referral voltage in electrical systems. The term was adopted by computer scientists working in machine learning who w |
38,517 | How to interpret this QQ plot? | This QQ plot has the following salient features:
The stairstep pattern, in which only specific, separated heights ("sample quantiles") are attained, shows the data values are discrete. Almost all are whole numbers from $3$ through $21$. A few half-integers appear. Evidently some form of rounding has occurred.
Becaus... | How to interpret this QQ plot? | This QQ plot has the following salient features:
The stairstep pattern, in which only specific, separated heights ("sample quantiles") are attained, shows the data values are discrete. Almost all ar | How to interpret this QQ plot?
This QQ plot has the following salient features:
The stairstep pattern, in which only specific, separated heights ("sample quantiles") are attained, shows the data values are discrete. Almost all are whole numbers from $3$ through $21$. A few half-integers appear. Evidently some form o... | How to interpret this QQ plot?
This QQ plot has the following salient features:
The stairstep pattern, in which only specific, separated heights ("sample quantiles") are attained, shows the data values are discrete. Almost all ar |
38,518 | How to interpret this QQ plot? | (As Nick Cox also suggests) the distribution is right skew and discrete, but to the right of the spike at 3, is roughly similar to a standard normal truncated below -1 (which is right skew), but with a shorter right tail.
I've made some additional comments on the diagram below:
Here's a frequency plot (a sample pmf) t... | How to interpret this QQ plot? | (As Nick Cox also suggests) the distribution is right skew and discrete, but to the right of the spike at 3, is roughly similar to a standard normal truncated below -1 (which is right skew), but with | How to interpret this QQ plot?
(As Nick Cox also suggests) the distribution is right skew and discrete, but to the right of the spike at 3, is roughly similar to a standard normal truncated below -1 (which is right skew), but with a shorter right tail.
I've made some additional comments on the diagram below:
Here's a ... | How to interpret this QQ plot?
(As Nick Cox also suggests) the distribution is right skew and discrete, but to the right of the spike at 3, is roughly similar to a standard normal truncated below -1 (which is right skew), but with |
38,519 | How to interpret this QQ plot? | Your data are positively skewed, meaning skewed to the right. "Right" or "left" is a matter of the longer, more stretched out, tail in the distribution. The terminology presupposes that you are (imagining) looking at a conventional histogram with a horizontal magnitude scale.
But clearly you have integer values betw... | How to interpret this QQ plot? | Your data are positively skewed, meaning skewed to the right. "Right" or "left" is a matter of the longer, more stretched out, tail in the distribution. The terminology presupposes that you are (imag | How to interpret this QQ plot?
Your data are positively skewed, meaning skewed to the right. "Right" or "left" is a matter of the longer, more stretched out, tail in the distribution. The terminology presupposes that you are (imagining) looking at a conventional histogram with a horizontal magnitude scale.
But clear... | How to interpret this QQ plot?
Your data are positively skewed, meaning skewed to the right. "Right" or "left" is a matter of the longer, more stretched out, tail in the distribution. The terminology presupposes that you are (imag |
38,520 | Why convolutional neural networks belong to deep learning? | First, mind that deep learning is a buzz term. There is not even a consensus of a formal definition in the research community. A discussion of the term does not lead anywhere, really. It's just a word.
That being said, convolutional nets are deep because they rely on multiple layers of feature extraction, as you said.... | Why convolutional neural networks belong to deep learning? | First, mind that deep learning is a buzz term. There is not even a consensus of a formal definition in the research community. A discussion of the term does not lead anywhere, really. It's just a wor | Why convolutional neural networks belong to deep learning?
First, mind that deep learning is a buzz term. There is not even a consensus of a formal definition in the research community. A discussion of the term does not lead anywhere, really. It's just a word.
That being said, convolutional nets are deep because they ... | Why convolutional neural networks belong to deep learning?
First, mind that deep learning is a buzz term. There is not even a consensus of a formal definition in the research community. A discussion of the term does not lead anywhere, really. It's just a wor |
38,521 | Why convolutional neural networks belong to deep learning? | The deep learning is an approach where you have a lot of relatively simple layers. You increase learning capabilities by increasing the number of layers, as opposed to increased complexity of layers. You could for instance come up with very fancy output functions, maybe nonlinear functions of inputs or complicated conn... | Why convolutional neural networks belong to deep learning? | The deep learning is an approach where you have a lot of relatively simple layers. You increase learning capabilities by increasing the number of layers, as opposed to increased complexity of layers. | Why convolutional neural networks belong to deep learning?
The deep learning is an approach where you have a lot of relatively simple layers. You increase learning capabilities by increasing the number of layers, as opposed to increased complexity of layers. You could for instance come up with very fancy output functio... | Why convolutional neural networks belong to deep learning?
The deep learning is an approach where you have a lot of relatively simple layers. You increase learning capabilities by increasing the number of layers, as opposed to increased complexity of layers. |
38,522 | Why convolutional neural networks belong to deep learning? | Deep learning is a generic term that refers to the fact that a deep neural network has at least one hidden layer. | Why convolutional neural networks belong to deep learning? | Deep learning is a generic term that refers to the fact that a deep neural network has at least one hidden layer. | Why convolutional neural networks belong to deep learning?
Deep learning is a generic term that refers to the fact that a deep neural network has at least one hidden layer. | Why convolutional neural networks belong to deep learning?
Deep learning is a generic term that refers to the fact that a deep neural network has at least one hidden layer. |
38,523 | Why convolutional neural networks belong to deep learning? | Very late but I think the real answer is more historical. Historically, deep learning refers to networks that use backpropagation in contrast to a lot of other types of neural network (Kohonen, mono-layer perceptron, oscillatory network, chaotic network, etc., etc.) that are a lot of research branches.
When deep learni... | Why convolutional neural networks belong to deep learning? | Very late but I think the real answer is more historical. Historically, deep learning refers to networks that use backpropagation in contrast to a lot of other types of neural network (Kohonen, mono-l | Why convolutional neural networks belong to deep learning?
Very late but I think the real answer is more historical. Historically, deep learning refers to networks that use backpropagation in contrast to a lot of other types of neural network (Kohonen, mono-layer perceptron, oscillatory network, chaotic network, etc., ... | Why convolutional neural networks belong to deep learning?
Very late but I think the real answer is more historical. Historically, deep learning refers to networks that use backpropagation in contrast to a lot of other types of neural network (Kohonen, mono-l |
38,524 | How is the first column of the matrix orthogonal to all the others | The test of orthogonality is the dot product. The column of ones doesn't change any of the values in the other columns. So you are left with the summation of the distance of every point in any of the remaining columns to the mean of the column, which is zero by definition.
$$\begin{bmatrix}1&1\cdots&1\end{bmatrix} \beg... | How is the first column of the matrix orthogonal to all the others | The test of orthogonality is the dot product. The column of ones doesn't change any of the values in the other columns. So you are left with the summation of the distance of every point in any of the | How is the first column of the matrix orthogonal to all the others
The test of orthogonality is the dot product. The column of ones doesn't change any of the values in the other columns. So you are left with the summation of the distance of every point in any of the remaining columns to the mean of the column, which is... | How is the first column of the matrix orthogonal to all the others
The test of orthogonality is the dot product. The column of ones doesn't change any of the values in the other columns. So you are left with the summation of the distance of every point in any of the |
38,525 | How is the first column of the matrix orthogonal to all the others | Two vectors $\mathbf{u}, \mathbf{v}$ are said to be orthogonal iff
$$ \langle \mathbf{u}, \mathbf{v} \rangle = 0 $$
If you do this inner product $r$ times with $\mathbf{v}$ being column 1, and $\mathbf{u}$ being columns $2, ..., r+1 $ respectively, you just have to add the column elements.
The orthogonality follows fro... | How is the first column of the matrix orthogonal to all the others | Two vectors $\mathbf{u}, \mathbf{v}$ are said to be orthogonal iff
$$ \langle \mathbf{u}, \mathbf{v} \rangle = 0 $$
If you do this inner product $r$ times with $\mathbf{v}$ being column 1, and $\mathb | How is the first column of the matrix orthogonal to all the others
Two vectors $\mathbf{u}, \mathbf{v}$ are said to be orthogonal iff
$$ \langle \mathbf{u}, \mathbf{v} \rangle = 0 $$
If you do this inner product $r$ times with $\mathbf{v}$ being column 1, and $\mathbf{u}$ being columns $2, ..., r+1 $ respectively, you ... | How is the first column of the matrix orthogonal to all the others
Two vectors $\mathbf{u}, \mathbf{v}$ are said to be orthogonal iff
$$ \langle \mathbf{u}, \mathbf{v} \rangle = 0 $$
If you do this inner product $r$ times with $\mathbf{v}$ being column 1, and $\mathb |
38,526 | Visualizing variability from graph | The point is presumably elementary, namely that cases with CHD occur at almost any age, but this seems banal even to non-medical people. But statistically, variability means much more than "variation exists"; it is something to be quantified.
With no context and nothing else said, the main problem with the graph seems... | Visualizing variability from graph | The point is presumably elementary, namely that cases with CHD occur at almost any age, but this seems banal even to non-medical people. But statistically, variability means much more than "variation | Visualizing variability from graph
The point is presumably elementary, namely that cases with CHD occur at almost any age, but this seems banal even to non-medical people. But statistically, variability means much more than "variation exists"; it is something to be quantified.
With no context and nothing else said, th... | Visualizing variability from graph
The point is presumably elementary, namely that cases with CHD occur at almost any age, but this seems banal even to non-medical people. But statistically, variability means much more than "variation |
38,527 | Visualizing variability from graph | By "variability," the authors mean any reasonable measure of the dispersion of CHD conditional on age.
Study this by slicing the data into narrow age groups (as shown by different colors in the right hand scatterplot), computing the dispersion of the CHD values within each age group, and plotting those dispersions aga... | Visualizing variability from graph | By "variability," the authors mean any reasonable measure of the dispersion of CHD conditional on age.
Study this by slicing the data into narrow age groups (as shown by different colors in the right | Visualizing variability from graph
By "variability," the authors mean any reasonable measure of the dispersion of CHD conditional on age.
Study this by slicing the data into narrow age groups (as shown by different colors in the right hand scatterplot), computing the dispersion of the CHD values within each age group,... | Visualizing variability from graph
By "variability," the authors mean any reasonable measure of the dispersion of CHD conditional on age.
Study this by slicing the data into narrow age groups (as shown by different colors in the right |
38,528 | Visualizing variability from graph | I believe the point they are trying to make is that, for any given age bin (say 40-45) there are about equal numbers of CHD=0 and CHD=1. This indicates that CHD is not very predictable from age, so it has a high variability. If you wanted to quantify this, you could use something like binary entropy - the closer that p... | Visualizing variability from graph | I believe the point they are trying to make is that, for any given age bin (say 40-45) there are about equal numbers of CHD=0 and CHD=1. This indicates that CHD is not very predictable from age, so it | Visualizing variability from graph
I believe the point they are trying to make is that, for any given age bin (say 40-45) there are about equal numbers of CHD=0 and CHD=1. This indicates that CHD is not very predictable from age, so it has a high variability. If you wanted to quantify this, you could use something like... | Visualizing variability from graph
I believe the point they are trying to make is that, for any given age bin (say 40-45) there are about equal numbers of CHD=0 and CHD=1. This indicates that CHD is not very predictable from age, so it |
38,529 | forecast using arima models [closed] | In the future please provide a reproducible example for a question such as yours, as I don't have any idea on the characteristics of your data set. As @Irishstat mentions your data might not have a trend/pattern and could have a level shift.
Expanding my comment:
arima(0,1,1) is a simple exponential smoothing. The leve... | forecast using arima models [closed] | In the future please provide a reproducible example for a question such as yours, as I don't have any idea on the characteristics of your data set. As @Irishstat mentions your data might not have a tr | forecast using arima models [closed]
In the future please provide a reproducible example for a question such as yours, as I don't have any idea on the characteristics of your data set. As @Irishstat mentions your data might not have a trend/pattern and could have a level shift.
Expanding my comment:
arima(0,1,1) is a s... | forecast using arima models [closed]
In the future please provide a reproducible example for a question such as yours, as I don't have any idea on the characteristics of your data set. As @Irishstat mentions your data might not have a tr |
38,530 | forecast using arima models [closed] | As you note, the forecasts for your $\text{ARIMA}(0,1,1)$ are constant. Nothing is amiss.
Let's begin by considering the differenced series. This is the simple case of an $\text{MA}(1)$ model with $0$ mean: $y(t) = \varepsilon(t) + θ\, \varepsilon(t-1)$.
If we're at time $T$, we have for the forecast of the observation... | forecast using arima models [closed] | As you note, the forecasts for your $\text{ARIMA}(0,1,1)$ are constant. Nothing is amiss.
Let's begin by considering the differenced series. This is the simple case of an $\text{MA}(1)$ model with $0$ | forecast using arima models [closed]
As you note, the forecasts for your $\text{ARIMA}(0,1,1)$ are constant. Nothing is amiss.
Let's begin by considering the differenced series. This is the simple case of an $\text{MA}(1)$ model with $0$ mean: $y(t) = \varepsilon(t) + θ\, \varepsilon(t-1)$.
If we're at time $T$, we hav... | forecast using arima models [closed]
As you note, the forecasts for your $\text{ARIMA}(0,1,1)$ are constant. Nothing is amiss.
Let's begin by considering the differenced series. This is the simple case of an $\text{MA}(1)$ model with $0$ |
38,531 | forecast using arima models [closed] | A characteristic of the model (simple exponential smoothing) that you are using is that forecasts are identical for every period in the future irrespective of the particular value of the ma(1) coefficient. This would also be true for a model that simply had a constant (mean model) or a recent level shift (last local me... | forecast using arima models [closed] | A characteristic of the model (simple exponential smoothing) that you are using is that forecasts are identical for every period in the future irrespective of the particular value of the ma(1) coeffic | forecast using arima models [closed]
A characteristic of the model (simple exponential smoothing) that you are using is that forecasts are identical for every period in the future irrespective of the particular value of the ma(1) coefficient. This would also be true for a model that simply had a constant (mean model) o... | forecast using arima models [closed]
A characteristic of the model (simple exponential smoothing) that you are using is that forecasts are identical for every period in the future irrespective of the particular value of the ma(1) coeffic |
38,532 | forecast using arima models [closed] | I think you need to convert the data to time-series format. The forecast is flat because the model is not able to know the forecast is for which month/year/time period and the patterns in it to learn from. | forecast using arima models [closed] | I think you need to convert the data to time-series format. The forecast is flat because the model is not able to know the forecast is for which month/year/time period and the patterns in it to learn | forecast using arima models [closed]
I think you need to convert the data to time-series format. The forecast is flat because the model is not able to know the forecast is for which month/year/time period and the patterns in it to learn from. | forecast using arima models [closed]
I think you need to convert the data to time-series format. The forecast is flat because the model is not able to know the forecast is for which month/year/time period and the patterns in it to learn |
38,533 | Regression that creates $x \log(x)$ functions? | It's quite straightforward.
Simply create a new variable, $x_1 = x\ln(x)$ then fit a linear regression $E(y)=b+cx_1$.
Here's an example (the code is in R but I'll give the data I generate so you can try it in your favourite line-fitting routine):
#generate some data:
set.seed(29384702)
x = runif(20,.05,6)
y = 11.-0.5*x... | Regression that creates $x \log(x)$ functions? | It's quite straightforward.
Simply create a new variable, $x_1 = x\ln(x)$ then fit a linear regression $E(y)=b+cx_1$.
Here's an example (the code is in R but I'll give the data I generate so you can t | Regression that creates $x \log(x)$ functions?
It's quite straightforward.
Simply create a new variable, $x_1 = x\ln(x)$ then fit a linear regression $E(y)=b+cx_1$.
Here's an example (the code is in R but I'll give the data I generate so you can try it in your favourite line-fitting routine):
#generate some data:
set.s... | Regression that creates $x \log(x)$ functions?
It's quite straightforward.
Simply create a new variable, $x_1 = x\ln(x)$ then fit a linear regression $E(y)=b+cx_1$.
Here's an example (the code is in R but I'll give the data I generate so you can t |
38,534 | Kalman filter equation derivation | There is a simple, straightforward derivation that starts with the assumptions of the Kalman filter and requires a little Algebra to arrive at the update and extrapolation equations as well as some properties regarding the measurement residuals (difference between the predicted state and the measurement). To start, the... | Kalman filter equation derivation | There is a simple, straightforward derivation that starts with the assumptions of the Kalman filter and requires a little Algebra to arrive at the update and extrapolation equations as well as some pr | Kalman filter equation derivation
There is a simple, straightforward derivation that starts with the assumptions of the Kalman filter and requires a little Algebra to arrive at the update and extrapolation equations as well as some properties regarding the measurement residuals (difference between the predicted state a... | Kalman filter equation derivation
There is a simple, straightforward derivation that starts with the assumptions of the Kalman filter and requires a little Algebra to arrive at the update and extrapolation equations as well as some pr |
38,535 | Kalman filter equation derivation | A derivation is given here
https://missingueverymoment.wordpress.com/2019/12/02/derivation-of-kalman-filter/
Basically it assumes the linearly dependent relations, and it minimize the square of prediction error to obtain the form of Kalman gain. Matrix derivation identities are also given in the site. | Kalman filter equation derivation | A derivation is given here
https://missingueverymoment.wordpress.com/2019/12/02/derivation-of-kalman-filter/
Basically it assumes the linearly dependent relations, and it minimize the square of predic | Kalman filter equation derivation
A derivation is given here
https://missingueverymoment.wordpress.com/2019/12/02/derivation-of-kalman-filter/
Basically it assumes the linearly dependent relations, and it minimize the square of prediction error to obtain the form of Kalman gain. Matrix derivation identities are also gi... | Kalman filter equation derivation
A derivation is given here
https://missingueverymoment.wordpress.com/2019/12/02/derivation-of-kalman-filter/
Basically it assumes the linearly dependent relations, and it minimize the square of predic |
38,536 | Kalman filter equation derivation | I think you want $p(\boldsymbol{X}_t|\boldsymbol{X}_{t-1} = N(A\boldsymbol{X}_{t-1} + \mu_p,\ldots)$ in your second equation. Regarding easy-to-follow derivations of the filter, there are many in textbooks such as
Durbin & Koopman or Anderson-Moore. You might also look the Kalman filter at the Wikipedia. | Kalman filter equation derivation | I think you want $p(\boldsymbol{X}_t|\boldsymbol{X}_{t-1} = N(A\boldsymbol{X}_{t-1} + \mu_p,\ldots)$ in your second equation. Regarding easy-to-follow derivations of the filter, there are many in text | Kalman filter equation derivation
I think you want $p(\boldsymbol{X}_t|\boldsymbol{X}_{t-1} = N(A\boldsymbol{X}_{t-1} + \mu_p,\ldots)$ in your second equation. Regarding easy-to-follow derivations of the filter, there are many in textbooks such as
Durbin & Koopman or Anderson-Moore. You might also look the Kalman filt... | Kalman filter equation derivation
I think you want $p(\boldsymbol{X}_t|\boldsymbol{X}_{t-1} = N(A\boldsymbol{X}_{t-1} + \mu_p,\ldots)$ in your second equation. Regarding easy-to-follow derivations of the filter, there are many in text |
38,537 | Kalman filter equation derivation | I would like to add some intuition towards the Kalman gain
The Kalman gain is given by $$K = \Sigma_pH^T(H\Sigma_pH^T + \Sigma_m)^{-1}$$
A useful way to look at this is $$K = \frac{\Sigma_pH^T}{H\Sigma_pH^T + \Sigma_m}$$
The intuition behind this is that if $\Sigma_m$ was infinitely large, i.e. $\lim\limits_{\Sigma_m \... | Kalman filter equation derivation | I would like to add some intuition towards the Kalman gain
The Kalman gain is given by $$K = \Sigma_pH^T(H\Sigma_pH^T + \Sigma_m)^{-1}$$
A useful way to look at this is $$K = \frac{\Sigma_pH^T}{H\Sigm | Kalman filter equation derivation
I would like to add some intuition towards the Kalman gain
The Kalman gain is given by $$K = \Sigma_pH^T(H\Sigma_pH^T + \Sigma_m)^{-1}$$
A useful way to look at this is $$K = \frac{\Sigma_pH^T}{H\Sigma_pH^T + \Sigma_m}$$
The intuition behind this is that if $\Sigma_m$ was infinitely la... | Kalman filter equation derivation
I would like to add some intuition towards the Kalman gain
The Kalman gain is given by $$K = \Sigma_pH^T(H\Sigma_pH^T + \Sigma_m)^{-1}$$
A useful way to look at this is $$K = \frac{\Sigma_pH^T}{H\Sigm |
38,538 | Kalman filter equation derivation | Just a small correction to the excellent answer above. The residual vector can be assessed either before the Kalman correction or after. The pre-fit residual vector is
\begin{equation} {\eta}_{k|k-1} = H_k (x_k - \hat{x}_{k|k-1}) + w_k = H_k \tilde{x}_{k|k-1} + w_k \end{equation}
and equivalently the post-fit residua... | Kalman filter equation derivation | Just a small correction to the excellent answer above. The residual vector can be assessed either before the Kalman correction or after. The pre-fit residual vector is
\begin{equation} {\eta}_{k|k-1} | Kalman filter equation derivation
Just a small correction to the excellent answer above. The residual vector can be assessed either before the Kalman correction or after. The pre-fit residual vector is
\begin{equation} {\eta}_{k|k-1} = H_k (x_k - \hat{x}_{k|k-1}) + w_k = H_k \tilde{x}_{k|k-1} + w_k \end{equation}
and... | Kalman filter equation derivation
Just a small correction to the excellent answer above. The residual vector can be assessed either before the Kalman correction or after. The pre-fit residual vector is
\begin{equation} {\eta}_{k|k-1} |
38,539 | Usable estimators for parameters in Gumbel distribution | The Gumbel distribution
The Gumbel distribution is often used to model the distribution of extreme values. It is one of the three particular cases of the more generalized extreme value distribution (GEV), namely when the parameter of the GEV $\xi$ equals $0$ (that's why the Gumbel distribution is sometimes called "type... | Usable estimators for parameters in Gumbel distribution | The Gumbel distribution
The Gumbel distribution is often used to model the distribution of extreme values. It is one of the three particular cases of the more generalized extreme value distribution (G | Usable estimators for parameters in Gumbel distribution
The Gumbel distribution
The Gumbel distribution is often used to model the distribution of extreme values. It is one of the three particular cases of the more generalized extreme value distribution (GEV), namely when the parameter of the GEV $\xi$ equals $0$ (that... | Usable estimators for parameters in Gumbel distribution
The Gumbel distribution
The Gumbel distribution is often used to model the distribution of extreme values. It is one of the three particular cases of the more generalized extreme value distribution (G |
38,540 | Expert forecasting software evaluation | The last review of SCA and AUTOBOX was done in 1995 (see here). We had approached Prof. Len Tashman the editor of Foresight for a head-to-head review of AUTOBOX vs SAS but SAS's representative replied in the negative in July 2010:
ARIMA modeling is an interesting subject, but not one I would want to
focus on, or on... | Expert forecasting software evaluation | The last review of SCA and AUTOBOX was done in 1995 (see here). We had approached Prof. Len Tashman the editor of Foresight for a head-to-head review of AUTOBOX vs SAS but SAS's representative replied | Expert forecasting software evaluation
The last review of SCA and AUTOBOX was done in 1995 (see here). We had approached Prof. Len Tashman the editor of Foresight for a head-to-head review of AUTOBOX vs SAS but SAS's representative replied in the negative in July 2010:
ARIMA modeling is an interesting subject, but no... | Expert forecasting software evaluation
The last review of SCA and AUTOBOX was done in 1995 (see here). We had approached Prof. Len Tashman the editor of Foresight for a head-to-head review of AUTOBOX vs SAS but SAS's representative replied |
38,541 | Expert forecasting software evaluation | The only proper evaluation of automatic forecasting software is in head-to-head competition on real data. The last large-scale competition like that was done in 2000 in the M3 competition. The results are publicly available: http://www.forecastingprinciples.com/paperpdf/Makridakia-The%20M3%20Competition.pdf. Draw your ... | Expert forecasting software evaluation | The only proper evaluation of automatic forecasting software is in head-to-head competition on real data. The last large-scale competition like that was done in 2000 in the M3 competition. The results | Expert forecasting software evaluation
The only proper evaluation of automatic forecasting software is in head-to-head competition on real data. The last large-scale competition like that was done in 2000 in the M3 competition. The results are publicly available: http://www.forecastingprinciples.com/paperpdf/Makridakia... | Expert forecasting software evaluation
The only proper evaluation of automatic forecasting software is in head-to-head competition on real data. The last large-scale competition like that was done in 2000 in the M3 competition. The results |
38,542 | Expert forecasting software evaluation | This is not an answer but rather a comment to @Irishstat. This is a lengthy comment so I'm writing this as an answer.
@Irishstat, I'm really surprised why an editor of a reputable journal like Foresight need to get permission from a SAS representative to do a comparison between two software. I would consider that this ... | Expert forecasting software evaluation | This is not an answer but rather a comment to @Irishstat. This is a lengthy comment so I'm writing this as an answer.
@Irishstat, I'm really surprised why an editor of a reputable journal like Foresig | Expert forecasting software evaluation
This is not an answer but rather a comment to @Irishstat. This is a lengthy comment so I'm writing this as an answer.
@Irishstat, I'm really surprised why an editor of a reputable journal like Foresight need to get permission from a SAS representative to do a comparison between tw... | Expert forecasting software evaluation
This is not an answer but rather a comment to @Irishstat. This is a lengthy comment so I'm writing this as an answer.
@Irishstat, I'm really surprised why an editor of a reputable journal like Foresig |
38,543 | Why Normalization (Standardization) values should be smaller than $1$? | Rescaling the input features is just a linear transformation. There's no right or wrong way of rescaling outside a problem context. If you want to map the range 1 - 100 to the range 1 - 10 linearly you should do:
$$
x \leftarrow \frac{x - 1}{99} \times 9 + 1
$$
This maps 1 to 1 and 100 to 10 and it will make the durati... | Why Normalization (Standardization) values should be smaller than $1$? | Rescaling the input features is just a linear transformation. There's no right or wrong way of rescaling outside a problem context. If you want to map the range 1 - 100 to the range 1 - 10 linearly yo | Why Normalization (Standardization) values should be smaller than $1$?
Rescaling the input features is just a linear transformation. There's no right or wrong way of rescaling outside a problem context. If you want to map the range 1 - 100 to the range 1 - 10 linearly you should do:
$$
x \leftarrow \frac{x - 1}{99} \ti... | Why Normalization (Standardization) values should be smaller than $1$?
Rescaling the input features is just a linear transformation. There's no right or wrong way of rescaling outside a problem context. If you want to map the range 1 - 100 to the range 1 - 10 linearly yo |
38,544 | Why Normalization (Standardization) values should be smaller than $1$? | One way of standardizing variables is to turn each value into a z-score, by taking
$\frac{x - \bar{x}}{sd}$
Doing this, you would only have to do it once; however, this will not result in a range of -1 to 1, the result can be any number. But most values will be between -1 and 1. | Why Normalization (Standardization) values should be smaller than $1$? | One way of standardizing variables is to turn each value into a z-score, by taking
$\frac{x - \bar{x}}{sd}$
Doing this, you would only have to do it once; however, this will not result in a range of | Why Normalization (Standardization) values should be smaller than $1$?
One way of standardizing variables is to turn each value into a z-score, by taking
$\frac{x - \bar{x}}{sd}$
Doing this, you would only have to do it once; however, this will not result in a range of -1 to 1, the result can be any number. But most v... | Why Normalization (Standardization) values should be smaller than $1$?
One way of standardizing variables is to turn each value into a z-score, by taking
$\frac{x - \bar{x}}{sd}$
Doing this, you would only have to do it once; however, this will not result in a range of |
38,545 | Comparing two vectors from negative binomial distribution in R | Your dependent variable is a count ("number of dots counted on the image of a cell"). Asking whether the distribution of counts is similar in two groups is conceptually the same as asking whether group membership matters for the distribution of counts.
I suggest a Poisson regression as a first step where you model the ... | Comparing two vectors from negative binomial distribution in R | Your dependent variable is a count ("number of dots counted on the image of a cell"). Asking whether the distribution of counts is similar in two groups is conceptually the same as asking whether grou | Comparing two vectors from negative binomial distribution in R
Your dependent variable is a count ("number of dots counted on the image of a cell"). Asking whether the distribution of counts is similar in two groups is conceptually the same as asking whether group membership matters for the distribution of counts.
I su... | Comparing two vectors from negative binomial distribution in R
Your dependent variable is a count ("number of dots counted on the image of a cell"). Asking whether the distribution of counts is similar in two groups is conceptually the same as asking whether grou |
38,546 | Comparing two vectors from negative binomial distribution in R | First of all, +1 for @caracal's answer.
One other possibility would be as follows: fit a negbin distribution to both datasets (e.g., using fitdistr in the MASS package). The parameter estimates are (asymptotically) normally distributed, and we can get the covariance estimates this way:
vcov(fitdistr(w.dots,densfun="neg... | Comparing two vectors from negative binomial distribution in R | First of all, +1 for @caracal's answer.
One other possibility would be as follows: fit a negbin distribution to both datasets (e.g., using fitdistr in the MASS package). The parameter estimates are (a | Comparing two vectors from negative binomial distribution in R
First of all, +1 for @caracal's answer.
One other possibility would be as follows: fit a negbin distribution to both datasets (e.g., using fitdistr in the MASS package). The parameter estimates are (asymptotically) normally distributed, and we can get the c... | Comparing two vectors from negative binomial distribution in R
First of all, +1 for @caracal's answer.
One other possibility would be as follows: fit a negbin distribution to both datasets (e.g., using fitdistr in the MASS package). The parameter estimates are (a |
38,547 | Comparing two vectors from negative binomial distribution in R | The present answer assumes that both distributions are actually Negative Binomial (NB), and also assumes the two samples to be independent.
In this framework, you have a model with four parameters, two for each distribution, and want to test a restriction with two constraints on the parameters. This can be done by stan... | Comparing two vectors from negative binomial distribution in R | The present answer assumes that both distributions are actually Negative Binomial (NB), and also assumes the two samples to be independent.
In this framework, you have a model with four parameters, tw | Comparing two vectors from negative binomial distribution in R
The present answer assumes that both distributions are actually Negative Binomial (NB), and also assumes the two samples to be independent.
In this framework, you have a model with four parameters, two for each distribution, and want to test a restriction w... | Comparing two vectors from negative binomial distribution in R
The present answer assumes that both distributions are actually Negative Binomial (NB), and also assumes the two samples to be independent.
In this framework, you have a model with four parameters, tw |
38,548 | Comparing two vectors from negative binomial distribution in R | You can use a Bayesian technique. http://www.indiana.edu/~kruschke/BEST/
This gives you the posterior distribution of the sample means for comparison.
x<-c(rep(1,200),rep(2,200))
y<-c(c.dots,w.dots)
require(R2jags) #open jags console.
dataList<-list(x=x,y=y, Ntotal=length(y))
modelstring = "
model {
for ( i in 1:Nto... | Comparing two vectors from negative binomial distribution in R | You can use a Bayesian technique. http://www.indiana.edu/~kruschke/BEST/
This gives you the posterior distribution of the sample means for comparison.
x<-c(rep(1,200),rep(2,200))
y<-c(c.dots,w.dots)
| Comparing two vectors from negative binomial distribution in R
You can use a Bayesian technique. http://www.indiana.edu/~kruschke/BEST/
This gives you the posterior distribution of the sample means for comparison.
x<-c(rep(1,200),rep(2,200))
y<-c(c.dots,w.dots)
require(R2jags) #open jags console.
dataList<-list(x=x,y... | Comparing two vectors from negative binomial distribution in R
You can use a Bayesian technique. http://www.indiana.edu/~kruschke/BEST/
This gives you the posterior distribution of the sample means for comparison.
x<-c(rep(1,200),rep(2,200))
y<-c(c.dots,w.dots)
|
38,549 | Temporal trend visualizations for regions | You can make each of the plots easily enough. Sticking with your example, I'll use unemployment data from the European countries between 1999 and 2011 (from Eurostat), called unempd (sorry it's long!):
> dput(unempd)
structure(list(Year = c(1999L, 2000L, 2001L, 2002L, 2003L, 2004L,
2005L, 2006L, 2007L, 2008L, 2009L, 2... | Temporal trend visualizations for regions | You can make each of the plots easily enough. Sticking with your example, I'll use unemployment data from the European countries between 1999 and 2011 (from Eurostat), called unempd (sorry it's long!) | Temporal trend visualizations for regions
You can make each of the plots easily enough. Sticking with your example, I'll use unemployment data from the European countries between 1999 and 2011 (from Eurostat), called unempd (sorry it's long!):
> dput(unempd)
structure(list(Year = c(1999L, 2000L, 2001L, 2002L, 2003L, 20... | Temporal trend visualizations for regions
You can make each of the plots easily enough. Sticking with your example, I'll use unemployment data from the European countries between 1999 and 2011 (from Eurostat), called unempd (sorry it's long!) |
38,550 | Temporal trend visualizations for regions | I know your answer was marked for R, but if you're open to an Excel solution, its relatively easy to work up the same sort of graphic:
From my perspective, Excel has a couple of advantages over R. First more people have access to it then can use R (I think I'm a prime example of that), so you have more audience reac... | Temporal trend visualizations for regions | I know your answer was marked for R, but if you're open to an Excel solution, its relatively easy to work up the same sort of graphic:
From my perspective, Excel has a couple of advantages over R. | Temporal trend visualizations for regions
I know your answer was marked for R, but if you're open to an Excel solution, its relatively easy to work up the same sort of graphic:
From my perspective, Excel has a couple of advantages over R. First more people have access to it then can use R (I think I'm a prime exampl... | Temporal trend visualizations for regions
I know your answer was marked for R, but if you're open to an Excel solution, its relatively easy to work up the same sort of graphic:
From my perspective, Excel has a couple of advantages over R. |
38,551 | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$ | Define $Y_n = \sum_{i=1} X_n^2$.
As you mentioned, $Y_n$ is distributed according to chi-squared with density:
$$p(y) = C(n)x^{n/2-1}e^{-x/2}$$
where $C(n)$ is some normalization constant (defined only for $y \ge 0$).
The probability of $Y_n$ being larger than $a$ is (as a function of $n$):
$$\int_0^a C(n) x^{n/2-1} e^... | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$ | Define $Y_n = \sum_{i=1} X_n^2$.
As you mentioned, $Y_n$ is distributed according to chi-squared with density:
$$p(y) = C(n)x^{n/2-1}e^{-x/2}$$
where $C(n)$ is some normalization constant (defined onl | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
Define $Y_n = \sum_{i=1} X_n^2$.
As you mentioned, $Y_n$ is distributed according to chi-squared with density:
$$p(y) = C(n)x^{n/2-1}e^{-x/2}$$
where $C(n)$ is some normalization constant (defined only for $y \ge 0$).
The... | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
Define $Y_n = \sum_{i=1} X_n^2$.
As you mentioned, $Y_n$ is distributed according to chi-squared with density:
$$p(y) = C(n)x^{n/2-1}e^{-x/2}$$
where $C(n)$ is some normalization constant (defined onl |
38,552 | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$ | The stated result has nothing to do with the normal distribution and is fully general. It can also be proven using only the most basic properties of cumulative distribution functions. In particular, it is unnecessary to appeal to (relatively) "high-powered" theorems like the Law of Large Numbers.
Proposition: Let $X_i ... | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$ | The stated result has nothing to do with the normal distribution and is fully general. It can also be proven using only the most basic properties of cumulative distribution functions. In particular, i | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
The stated result has nothing to do with the normal distribution and is fully general. It can also be proven using only the most basic properties of cumulative distribution functions. In particular, it is unnecessary to a... | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
The stated result has nothing to do with the normal distribution and is fully general. It can also be proven using only the most basic properties of cumulative distribution functions. In particular, i |
38,553 | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$ | We note that since each $X_i$ has mean 0 and variance 1, $(\sum_i X_i^2)/n$ converges to 1 a.s.
But if
$$
\lim_{n\to\infty} \mathbb P\Big( \sum_i X_i^2 < a \Big) > 0 \,,
$$ then with positive probability
$$
\frac{1}{n}\sum_i X_i^2
$$ goes to 0, which is a contradiction because if the sum have a positive probability o... | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$ | We note that since each $X_i$ has mean 0 and variance 1, $(\sum_i X_i^2)/n$ converges to 1 a.s.
But if
$$
\lim_{n\to\infty} \mathbb P\Big( \sum_i X_i^2 < a \Big) > 0 \,,
$$ then with positive probabi | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
We note that since each $X_i$ has mean 0 and variance 1, $(\sum_i X_i^2)/n$ converges to 1 a.s.
But if
$$
\lim_{n\to\infty} \mathbb P\Big( \sum_i X_i^2 < a \Big) > 0 \,,
$$ then with positive probability
$$
\frac{1}{n}\... | How can I show that for any $a > 0$, $\lim_{n\to \infty}P \left(\sum_{i=1}^n X_i^2\leq a\right)=0$
We note that since each $X_i$ has mean 0 and variance 1, $(\sum_i X_i^2)/n$ converges to 1 a.s.
But if
$$
\lim_{n\to\infty} \mathbb P\Big( \sum_i X_i^2 < a \Big) > 0 \,,
$$ then with positive probabi |
38,554 | How to conduct a meta-analysis using raw data? | As @Alexander already mentioned, you are looking for an approach that is called "individual participant/person/patient data meta-analysis" (IPD meta-analysis). He also refered to an article by Richard Riley, who has published a lot in this field. Please find below a collection of articles that I used for our advanced m... | How to conduct a meta-analysis using raw data? | As @Alexander already mentioned, you are looking for an approach that is called "individual participant/person/patient data meta-analysis" (IPD meta-analysis). He also refered to an article by Richard | How to conduct a meta-analysis using raw data?
As @Alexander already mentioned, you are looking for an approach that is called "individual participant/person/patient data meta-analysis" (IPD meta-analysis). He also refered to an article by Richard Riley, who has published a lot in this field. Please find below a collec... | How to conduct a meta-analysis using raw data?
As @Alexander already mentioned, you are looking for an approach that is called "individual participant/person/patient data meta-analysis" (IPD meta-analysis). He also refered to an article by Richard |
38,555 | How to conduct a meta-analysis using raw data? | Yes. It can be a problem, especially in scenarios where pharmaceutical clinical trials are involved and due to competition companies may not want to share their data. Nevertheless, such studies have been carried out in recent years in such settings. Combining raw data when the studies involve the same endpoints and ... | How to conduct a meta-analysis using raw data? | Yes. It can be a problem, especially in scenarios where pharmaceutical clinical trials are involved and due to competition companies may not want to share their data. Nevertheless, such studies have | How to conduct a meta-analysis using raw data?
Yes. It can be a problem, especially in scenarios where pharmaceutical clinical trials are involved and due to competition companies may not want to share their data. Nevertheless, such studies have been carried out in recent years in such settings. Combining raw data w... | How to conduct a meta-analysis using raw data?
Yes. It can be a problem, especially in scenarios where pharmaceutical clinical trials are involved and due to competition companies may not want to share their data. Nevertheless, such studies have |
38,556 | How to display multiple density or distribution functions on a single plot? | The question asks for "easiest." Interpreting that in terms of either (i) lines of code, (ii) naturality of expression, or (iii) raw capabilities, I find the Mathematica solutions to be well worth considering.
For example,
Plot[Evaluate[
PDF[WeibullDistribution[#, 20]][x] & /@ {1/2, 1/3, 1/4, 1/5}], {x, 0, 1},
... | How to display multiple density or distribution functions on a single plot? | The question asks for "easiest." Interpreting that in terms of either (i) lines of code, (ii) naturality of expression, or (iii) raw capabilities, I find the Mathematica solutions to be well worth co | How to display multiple density or distribution functions on a single plot?
The question asks for "easiest." Interpreting that in terms of either (i) lines of code, (ii) naturality of expression, or (iii) raw capabilities, I find the Mathematica solutions to be well worth considering.
For example,
Plot[Evaluate[
PDF... | How to display multiple density or distribution functions on a single plot?
The question asks for "easiest." Interpreting that in terms of either (i) lines of code, (ii) naturality of expression, or (iii) raw capabilities, I find the Mathematica solutions to be well worth co |
38,557 | How to display multiple density or distribution functions on a single plot? | I love R, easy and free. Here's an example:
# The par removes the "padding" from the axis
par(xaxs="i", yaxs="i")
# Initiate the x, a small "by" is neat for a smooth curve
# Can't use 0 since it gives produces an integrate() error
x <- seq(0.0001, 3, by=.01)
# Just some vanity - adding a little color :-), heat.color... | How to display multiple density or distribution functions on a single plot? | I love R, easy and free. Here's an example:
# The par removes the "padding" from the axis
par(xaxs="i", yaxs="i")
# Initiate the x, a small "by" is neat for a smooth curve
# Can't use 0 since it give | How to display multiple density or distribution functions on a single plot?
I love R, easy and free. Here's an example:
# The par removes the "padding" from the axis
par(xaxs="i", yaxs="i")
# Initiate the x, a small "by" is neat for a smooth curve
# Can't use 0 since it gives produces an integrate() error
x <- seq(0.0... | How to display multiple density or distribution functions on a single plot?
I love R, easy and free. Here's an example:
# The par removes the "padding" from the axis
par(xaxs="i", yaxs="i")
# Initiate the x, a small "by" is neat for a smooth curve
# Can't use 0 since it give |
38,558 | How to display multiple density or distribution functions on a single plot? | I like R too. Here is a more or less generic function to plot any probability distribution from the base R functions. It should not be difficult to extend the code with functions available in other packages, e.g. SuppDists.
plot.func <- function(distr=c("beta", "binom", "cauchy", "chisq",
... | How to display multiple density or distribution functions on a single plot? | I like R too. Here is a more or less generic function to plot any probability distribution from the base R functions. It should not be difficult to extend the code with functions available in other pa | How to display multiple density or distribution functions on a single plot?
I like R too. Here is a more or less generic function to plot any probability distribution from the base R functions. It should not be difficult to extend the code with functions available in other packages, e.g. SuppDists.
plot.func <- functio... | How to display multiple density or distribution functions on a single plot?
I like R too. Here is a more or less generic function to plot any probability distribution from the base R functions. It should not be difficult to extend the code with functions available in other pa |
38,559 | When should dimensional-reduction be used? | Rather than asking "when use" let's look at "why use" - I believe this nicely leads us to the "when" answer.
My understanding is that dimensionality reduction is mainly done to
speed up learning (many features lead to longer computations) and compress data (many features take a lot of disk/memory space). In this view,... | When should dimensional-reduction be used? | Rather than asking "when use" let's look at "why use" - I believe this nicely leads us to the "when" answer.
My understanding is that dimensionality reduction is mainly done to
speed up learning (man | When should dimensional-reduction be used?
Rather than asking "when use" let's look at "why use" - I believe this nicely leads us to the "when" answer.
My understanding is that dimensionality reduction is mainly done to
speed up learning (many features lead to longer computations) and compress data (many features take... | When should dimensional-reduction be used?
Rather than asking "when use" let's look at "why use" - I believe this nicely leads us to the "when" answer.
My understanding is that dimensionality reduction is mainly done to
speed up learning (man |
38,560 | When should dimensional-reduction be used? | As far as I know, we don't have a rule of thumb regarding when to use dimensional reduction. I'm also thinking that, is depends upon the ratio between the number of subjects and features. Also other factors such as processing power of the system you are going to deploy your learning algorithm, might have to consider.
F... | When should dimensional-reduction be used? | As far as I know, we don't have a rule of thumb regarding when to use dimensional reduction. I'm also thinking that, is depends upon the ratio between the number of subjects and features. Also other f | When should dimensional-reduction be used?
As far as I know, we don't have a rule of thumb regarding when to use dimensional reduction. I'm also thinking that, is depends upon the ratio between the number of subjects and features. Also other factors such as processing power of the system you are going to deploy your le... | When should dimensional-reduction be used?
As far as I know, we don't have a rule of thumb regarding when to use dimensional reduction. I'm also thinking that, is depends upon the ratio between the number of subjects and features. Also other f |
38,561 | When should dimensional-reduction be used? | The number of features is not the only reason for reduction. It is also important to check what are these features.
Although this is a computer science oriented site, the issues of memory and run time are relevant but they shouldn't be the only focus of many of the learning tasks.
When you are selecting your features,... | When should dimensional-reduction be used? | The number of features is not the only reason for reduction. It is also important to check what are these features.
Although this is a computer science oriented site, the issues of memory and run tim | When should dimensional-reduction be used?
The number of features is not the only reason for reduction. It is also important to check what are these features.
Although this is a computer science oriented site, the issues of memory and run time are relevant but they shouldn't be the only focus of many of the learning t... | When should dimensional-reduction be used?
The number of features is not the only reason for reduction. It is also important to check what are these features.
Although this is a computer science oriented site, the issues of memory and run tim |
38,562 | When should dimensional-reduction be used? | If the complexity of your model or classifier trained on those n features scales badly (e.g. the number of parameters grows as O(n^3)), then even 500 features can be a problem. Not only because the optimization takes longer, but also because you might not have enough data to constrain your parameters, which would lead ... | When should dimensional-reduction be used? | If the complexity of your model or classifier trained on those n features scales badly (e.g. the number of parameters grows as O(n^3)), then even 500 features can be a problem. Not only because the op | When should dimensional-reduction be used?
If the complexity of your model or classifier trained on those n features scales badly (e.g. the number of parameters grows as O(n^3)), then even 500 features can be a problem. Not only because the optimization takes longer, but also because you might not have enough data to c... | When should dimensional-reduction be used?
If the complexity of your model or classifier trained on those n features scales badly (e.g. the number of parameters grows as O(n^3)), then even 500 features can be a problem. Not only because the op |
38,563 | When should dimensional-reduction be used? | I saw another very interesting usage case for dimensionality reduction in a video from stanford a while ago. They scanned a bunch of people with a body scanner, and used that to generate 3d models. After they had a bunch of data they applied dimensionality reduction to reduce the amount of variables they had to work wi... | When should dimensional-reduction be used? | I saw another very interesting usage case for dimensionality reduction in a video from stanford a while ago. They scanned a bunch of people with a body scanner, and used that to generate 3d models. Af | When should dimensional-reduction be used?
I saw another very interesting usage case for dimensionality reduction in a video from stanford a while ago. They scanned a bunch of people with a body scanner, and used that to generate 3d models. After they had a bunch of data they applied dimensionality reduction to reduce ... | When should dimensional-reduction be used?
I saw another very interesting usage case for dimensionality reduction in a video from stanford a while ago. They scanned a bunch of people with a body scanner, and used that to generate 3d models. Af |
38,564 | How to test a logistic regression model developed on a training sample on the data left out using R? | You can use predict() for that. You need the model fitted to the training data, and the data from your test group. With type="response", you'll get the predicted probabilities, the default is the predicted logits.
# generate some data for a logistic regression, all observations
x <- rnorm(100, 175, 7) ... | How to test a logistic regression model developed on a training sample on the data left out using R | You can use predict() for that. You need the model fitted to the training data, and the data from your test group. With type="response", you'll get the predicted probabilities, the default is the pred | How to test a logistic regression model developed on a training sample on the data left out using R?
You can use predict() for that. You need the model fitted to the training data, and the data from your test group. With type="response", you'll get the predicted probabilities, the default is the predicted logits.
# ge... | How to test a logistic regression model developed on a training sample on the data left out using R
You can use predict() for that. You need the model fitted to the training data, and the data from your test group. With type="response", you'll get the predicted probabilities, the default is the pred |
38,565 | How to test a logistic regression model developed on a training sample on the data left out using R? | You may want to take a close look at the caret package which has a lot of support for this type of analysis. Its four vignettes give a good overview of how it can help you with this. | How to test a logistic regression model developed on a training sample on the data left out using R | You may want to take a close look at the caret package which has a lot of support for this type of analysis. Its four vignettes give a good overview of how it can help you with this. | How to test a logistic regression model developed on a training sample on the data left out using R?
You may want to take a close look at the caret package which has a lot of support for this type of analysis. Its four vignettes give a good overview of how it can help you with this. | How to test a logistic regression model developed on a training sample on the data left out using R
You may want to take a close look at the caret package which has a lot of support for this type of analysis. Its four vignettes give a good overview of how it can help you with this. |
38,566 | Understanding statistical control charts | The purpose of a control chart is to identify, as quickly as possible, when something fixable is going wrong. For it to work well, it must not identify random or uncontrollable changes as being "out of control."
The problems with the procedure described are manifold. They include
The "stable" section of the graph is... | Understanding statistical control charts | The purpose of a control chart is to identify, as quickly as possible, when something fixable is going wrong. For it to work well, it must not identify random or uncontrollable changes as being "out | Understanding statistical control charts
The purpose of a control chart is to identify, as quickly as possible, when something fixable is going wrong. For it to work well, it must not identify random or uncontrollable changes as being "out of control."
The problems with the procedure described are manifold. They incl... | Understanding statistical control charts
The purpose of a control chart is to identify, as quickly as possible, when something fixable is going wrong. For it to work well, it must not identify random or uncontrollable changes as being "out |
38,567 | Understanding statistical control charts | The general idea of control charts is to distinguish between common cause variation and special cause variation. The idea is that the process is fairly stable and generates data from a given distribution (though the Poisson makes more sense for number of calls than the normal). One big advantage of control charts is ... | Understanding statistical control charts | The general idea of control charts is to distinguish between common cause variation and special cause variation. The idea is that the process is fairly stable and generates data from a given distribu | Understanding statistical control charts
The general idea of control charts is to distinguish between common cause variation and special cause variation. The idea is that the process is fairly stable and generates data from a given distribution (though the Poisson makes more sense for number of calls than the normal).... | Understanding statistical control charts
The general idea of control charts is to distinguish between common cause variation and special cause variation. The idea is that the process is fairly stable and generates data from a given distribu |
38,568 | When does a logistic regression model have a unique solution? | The solution of logistic regression is a solution of maximization of certain function, namely log-likelihood:
$$\sum_{i=1}^ny_i\log p_i+(1-y_i)\log(1-p_i),$$
where
$$p_i=\frac{\exp(\beta_0+\beta_1x_{1i}+...+\beta_kx_{ik})}{1+\exp(\beta_0+\beta_1x_{1i}+...+\beta_kx_{ik})},$$
and $(y_i,x_{1i},...,x_{ki})$, $i=1,...,n$ i... | When does a logistic regression model have a unique solution? | The solution of logistic regression is a solution of maximization of certain function, namely log-likelihood:
$$\sum_{i=1}^ny_i\log p_i+(1-y_i)\log(1-p_i),$$
where
$$p_i=\frac{\exp(\beta_0+\beta_1x_{ | When does a logistic regression model have a unique solution?
The solution of logistic regression is a solution of maximization of certain function, namely log-likelihood:
$$\sum_{i=1}^ny_i\log p_i+(1-y_i)\log(1-p_i),$$
where
$$p_i=\frac{\exp(\beta_0+\beta_1x_{1i}+...+\beta_kx_{ik})}{1+\exp(\beta_0+\beta_1x_{1i}+...+\... | When does a logistic regression model have a unique solution?
The solution of logistic regression is a solution of maximization of certain function, namely log-likelihood:
$$\sum_{i=1}^ny_i\log p_i+(1-y_i)\log(1-p_i),$$
where
$$p_i=\frac{\exp(\beta_0+\beta_1x_{ |
38,569 | When does a logistic regression model have a unique solution? | I believe you are looking for the concept of orthogonality of the covariates. As soon as one of the covariates can be written as a linear combination of one of the others, you will not have a unique solution.
As an extreme case: say you have 2 covariates, and one is (in your dataset) always the double of the other, the... | When does a logistic regression model have a unique solution? | I believe you are looking for the concept of orthogonality of the covariates. As soon as one of the covariates can be written as a linear combination of one of the others, you will not have a unique s | When does a logistic regression model have a unique solution?
I believe you are looking for the concept of orthogonality of the covariates. As soon as one of the covariates can be written as a linear combination of one of the others, you will not have a unique solution.
As an extreme case: say you have 2 covariates, an... | When does a logistic regression model have a unique solution?
I believe you are looking for the concept of orthogonality of the covariates. As soon as one of the covariates can be written as a linear combination of one of the others, you will not have a unique s |
38,570 | When does a logistic regression model have a unique solution? | I think an interesting point is, that when the data is separable there should be infinite solutions. But if u use GD you converge to the max-margin solution (intuition I have is that GD for linear regression when its overparametrized converges to pseudo-inverse which is min-norm which is max margin since margin is some... | When does a logistic regression model have a unique solution? | I think an interesting point is, that when the data is separable there should be infinite solutions. But if u use GD you converge to the max-margin solution (intuition I have is that GD for linear reg | When does a logistic regression model have a unique solution?
I think an interesting point is, that when the data is separable there should be infinite solutions. But if u use GD you converge to the max-margin solution (intuition I have is that GD for linear regression when its overparametrized converges to pseudo-inve... | When does a logistic regression model have a unique solution?
I think an interesting point is, that when the data is separable there should be infinite solutions. But if u use GD you converge to the max-margin solution (intuition I have is that GD for linear reg |
38,571 | How to calculate confidence interval for count data in R? | You are looking for a confidence interval around the count from a Poisson process. If you put for example 42 into your linked example you get
You observed 42 objects in a certain
volume or 42 events in a certain time
period.
Exact Poisson confidence interval:
The 90% confidence interval extends from 31.94 to 5... | How to calculate confidence interval for count data in R? | You are looking for a confidence interval around the count from a Poisson process. If you put for example 42 into your linked example you get
You observed 42 objects in a certain
volume or 42 eve | How to calculate confidence interval for count data in R?
You are looking for a confidence interval around the count from a Poisson process. If you put for example 42 into your linked example you get
You observed 42 objects in a certain
volume or 42 events in a certain time
period.
Exact Poisson confidence inter... | How to calculate confidence interval for count data in R?
You are looking for a confidence interval around the count from a Poisson process. If you put for example 42 into your linked example you get
You observed 42 objects in a certain
volume or 42 eve |
38,572 | How to calculate confidence interval for count data in R? | If the number of event is too small, it would be better to use the exact method.
exactPoiCI <- function (X, conf.level=0.95) {
alpha = 1 - conf.level
upper <- 0.5 * qchisq((1-(alpha/2)), (2*X))
lower <- 0.5 * qchisq(alpha/2, (2*X +2))
return(c(lower, upper))
}
exactPoiCI(42, 0.9)
exactPoiCI(42)
exactPoiCI(42, 0... | How to calculate confidence interval for count data in R? | If the number of event is too small, it would be better to use the exact method.
exactPoiCI <- function (X, conf.level=0.95) {
alpha = 1 - conf.level
upper <- 0.5 * qchisq((1-(alpha/2)), (2*X))
| How to calculate confidence interval for count data in R?
If the number of event is too small, it would be better to use the exact method.
exactPoiCI <- function (X, conf.level=0.95) {
alpha = 1 - conf.level
upper <- 0.5 * qchisq((1-(alpha/2)), (2*X))
lower <- 0.5 * qchisq(alpha/2, (2*X +2))
return(c(lower, upp... | How to calculate confidence interval for count data in R?
If the number of event is too small, it would be better to use the exact method.
exactPoiCI <- function (X, conf.level=0.95) {
alpha = 1 - conf.level
upper <- 0.5 * qchisq((1-(alpha/2)), (2*X))
|
38,573 | How to calculate confidence interval for count data in R? | The first answer using poisson.test does give the exact confidence interval. However, this calculation is so simple that I prefer to calculate it directly instead of using a library function. In the second answer, there is a minor error. The +2 should be in the degree of freedom for the upper CI calculation, not for th... | How to calculate confidence interval for count data in R? | The first answer using poisson.test does give the exact confidence interval. However, this calculation is so simple that I prefer to calculate it directly instead of using a library function. In the s | How to calculate confidence interval for count data in R?
The first answer using poisson.test does give the exact confidence interval. However, this calculation is so simple that I prefer to calculate it directly instead of using a library function. In the second answer, there is a minor error. The +2 should be in the ... | How to calculate confidence interval for count data in R?
The first answer using poisson.test does give the exact confidence interval. However, this calculation is so simple that I prefer to calculate it directly instead of using a library function. In the s |
38,574 | Visualizing two scalar variables over time | The other idea is to plot one series as x and the second as y -- the time dependency will be hidden, but this plots shows correlations pretty well. (Yet time can be shown to some extent by connecting points chronologically; if the series are quite short and continuous it should be readable.) | Visualizing two scalar variables over time | The other idea is to plot one series as x and the second as y -- the time dependency will be hidden, but this plots shows correlations pretty well. (Yet time can be shown to some extent by connecting | Visualizing two scalar variables over time
The other idea is to plot one series as x and the second as y -- the time dependency will be hidden, but this plots shows correlations pretty well. (Yet time can be shown to some extent by connecting points chronologically; if the series are quite short and continuous it shou... | Visualizing two scalar variables over time
The other idea is to plot one series as x and the second as y -- the time dependency will be hidden, but this plots shows correlations pretty well. (Yet time can be shown to some extent by connecting |
38,575 | Visualizing two scalar variables over time | I sometimes make the x-axis time and plot both scalar variables on the y-axis.
When the two scalar variables are on a different metric, I rescale one or both of the scalar variables so they can be displayed on the same plot.
I use things like colour and shape to discriminate the two scalar variables.
I've often used xy... | Visualizing two scalar variables over time | I sometimes make the x-axis time and plot both scalar variables on the y-axis.
When the two scalar variables are on a different metric, I rescale one or both of the scalar variables so they can be dis | Visualizing two scalar variables over time
I sometimes make the x-axis time and plot both scalar variables on the y-axis.
When the two scalar variables are on a different metric, I rescale one or both of the scalar variables so they can be displayed on the same plot.
I use things like colour and shape to discriminate t... | Visualizing two scalar variables over time
I sometimes make the x-axis time and plot both scalar variables on the y-axis.
When the two scalar variables are on a different metric, I rescale one or both of the scalar variables so they can be dis |
38,576 | Visualizing two scalar variables over time | A method that can be very effective--one I have found extremely useful--is to sort the data by time and draw a connected X,Y scatterplot. (That is, successive points are connected by line segments or a spline.) This much is straightforward in almost any statistical plotting package. If the result is too confusing, a... | Visualizing two scalar variables over time | A method that can be very effective--one I have found extremely useful--is to sort the data by time and draw a connected X,Y scatterplot. (That is, successive points are connected by line segments or | Visualizing two scalar variables over time
A method that can be very effective--one I have found extremely useful--is to sort the data by time and draw a connected X,Y scatterplot. (That is, successive points are connected by line segments or a spline.) This much is straightforward in almost any statistical plotting ... | Visualizing two scalar variables over time
A method that can be very effective--one I have found extremely useful--is to sort the data by time and draw a connected X,Y scatterplot. (That is, successive points are connected by line segments or |
38,577 | Why is the Central Limit applicable in A/B testing? | Suppose you have two populations: A and B.
You draw samples from A: $a_1,a_2,...,a_n$
You draw samples from B: $b_1,b_2,...,b_n$
The actual values of $a$'s and $b$'s are just the numbers $0$'s and $1$'s, which represent success/failures.
Now let $\alpha$ and $\beta$ denote the averages of these samples, i.e.
$$ \alpha ... | Why is the Central Limit applicable in A/B testing? | Suppose you have two populations: A and B.
You draw samples from A: $a_1,a_2,...,a_n$
You draw samples from B: $b_1,b_2,...,b_n$
The actual values of $a$'s and $b$'s are just the numbers $0$'s and $1$ | Why is the Central Limit applicable in A/B testing?
Suppose you have two populations: A and B.
You draw samples from A: $a_1,a_2,...,a_n$
You draw samples from B: $b_1,b_2,...,b_n$
The actual values of $a$'s and $b$'s are just the numbers $0$'s and $1$'s, which represent success/failures.
Now let $\alpha$ and $\beta$ d... | Why is the Central Limit applicable in A/B testing?
Suppose you have two populations: A and B.
You draw samples from A: $a_1,a_2,...,a_n$
You draw samples from B: $b_1,b_2,...,b_n$
The actual values of $a$'s and $b$'s are just the numbers $0$'s and $1$ |
38,578 | Why is the Central Limit applicable in A/B testing? | we only draw two samples
You can consider a sample of size $n$ as $n$ samples of size $1$.
The outcome can be seen as a sum of $n$ independent Bernoulli distributed variables (if the people in the sample are independent), also know as a binomial distribution.
the distribution of their means tends towards a normal dis... | Why is the Central Limit applicable in A/B testing? | we only draw two samples
You can consider a sample of size $n$ as $n$ samples of size $1$.
The outcome can be seen as a sum of $n$ independent Bernoulli distributed variables (if the people in the sa | Why is the Central Limit applicable in A/B testing?
we only draw two samples
You can consider a sample of size $n$ as $n$ samples of size $1$.
The outcome can be seen as a sum of $n$ independent Bernoulli distributed variables (if the people in the sample are independent), also know as a binomial distribution.
the di... | Why is the Central Limit applicable in A/B testing?
we only draw two samples
You can consider a sample of size $n$ as $n$ samples of size $1$.
The outcome can be seen as a sum of $n$ independent Bernoulli distributed variables (if the people in the sa |
38,579 | Why is the Central Limit applicable in A/B testing? | The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
Not quite, though maybe you have a book that says something vague and not particularly accurate like this. Such vagueness of language has misled you about what it is even referring to.
... | Why is the Central Limit applicable in A/B testing? | The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
Not quite, though maybe you have a book that says something vague | Why is the Central Limit applicable in A/B testing?
The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
Not quite, though maybe you have a book that says something vague and not particularly accurate like this. Such vagueness of language... | Why is the Central Limit applicable in A/B testing?
The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
Not quite, though maybe you have a book that says something vague |
38,580 | Why is the Central Limit applicable in A/B testing? | Your question is full of incoherent statements.
The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
In math, "tends to" is used to refer to a limit, and a limit always has some independent variable, and we take the limit as that variabl... | Why is the Central Limit applicable in A/B testing? | Your question is full of incoherent statements.
The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
In math, "tends | Why is the Central Limit applicable in A/B testing?
Your question is full of incoherent statements.
The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
In math, "tends to" is used to refer to a limit, and a limit always has some indepen... | Why is the Central Limit applicable in A/B testing?
Your question is full of incoherent statements.
The CLT states that as we draw random samples from a population, the distribution of their means tends towards a normal distribution.
In math, "tends |
38,581 | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule? | Starting with a $\operatorname{Beta}(1,1)$ prior, your posterior would be $\operatorname{Beta}(k+1,n-k+1)$.
The mode of a $\operatorname{Beta}(k+1,n-k+1)$ distribution is $\frac{k}{n}$, which is the result you seem to want for an MAP (or MLE) estimator.
But Laplace's rule of succession instead takes the mean of the $\... | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule? | Starting with a $\operatorname{Beta}(1,1)$ prior, your posterior would be $\operatorname{Beta}(k+1,n-k+1)$.
The mode of a $\operatorname{Beta}(k+1,n-k+1)$ distribution is $\frac{k}{n}$, which is the r | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule?
Starting with a $\operatorname{Beta}(1,1)$ prior, your posterior would be $\operatorname{Beta}(k+1,n-k+1)$.
The mode of a $\operatorname{Beta}(k+1,n-k+1)$ distribution is $\frac{k}{n}$, which is the result you seem to want for an MAP (or MLE)... | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule?
Starting with a $\operatorname{Beta}(1,1)$ prior, your posterior would be $\operatorname{Beta}(k+1,n-k+1)$.
The mode of a $\operatorname{Beta}(k+1,n-k+1)$ distribution is $\frac{k}{n}$, which is the r |
38,582 | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule? | There is no such thing as an "uninformative" prior, that brings no information to a model.
For beta-binomial model, with uniform prior $\mathcal{B}(1, 1)$ the mode of the posterior (MAP) is $\frac{x+1-1}{x+1+x-n+1-2} = \frac{x}{x+n-x} = \frac{x}{n}$, so it's the same as MLE.
If you want the mean of the posterior to be ... | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule? | There is no such thing as an "uninformative" prior, that brings no information to a model.
For beta-binomial model, with uniform prior $\mathcal{B}(1, 1)$ the mode of the posterior (MAP) is $\frac{x+1 | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule?
There is no such thing as an "uninformative" prior, that brings no information to a model.
For beta-binomial model, with uniform prior $\mathcal{B}(1, 1)$ the mode of the posterior (MAP) is $\frac{x+1-1}{x+1+x-n+1-2} = \frac{x}{x+n-x} = \frac... | Why does the MAP differ from the MLE for the uniform prior in Laplace's Rule?
There is no such thing as an "uninformative" prior, that brings no information to a model.
For beta-binomial model, with uniform prior $\mathcal{B}(1, 1)$ the mode of the posterior (MAP) is $\frac{x+1 |
38,583 | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell | In statistics, a spurious relationship or spurious correlation is a
mathematical relationship in which two or more events or variables are
associated but not causally related, due to either coincidence or the
presence of a certain third, unseen factor (referred to as a "common
response variable", "confounding factor", ... | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell | In statistics, a spurious relationship or spurious correlation is a
mathematical relationship in which two or more events or variables are
associated but not causally related, due to either coincidenc | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell
In statistics, a spurious relationship or spurious correlation is a
mathematical relationship in which two or more events or variables are
associated but not causally related, due to either coincidence or the
presence of a cert... | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell
In statistics, a spurious relationship or spurious correlation is a
mathematical relationship in which two or more events or variables are
associated but not causally related, due to either coincidenc |
38,584 | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell | I'd say your understanding is correct. Philosophically, it's not truly possible to "prove" causation with 100% certainty, but we can convince ourselves that the alternative is arbitrarily unlikely. Most methods of determining causation rely on manipulating pertinent factors and randomizing all other possibly contributi... | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell | I'd say your understanding is correct. Philosophically, it's not truly possible to "prove" causation with 100% certainty, but we can convince ourselves that the alternative is arbitrarily unlikely. Mo | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell
I'd say your understanding is correct. Philosophically, it's not truly possible to "prove" causation with 100% certainty, but we can convince ourselves that the alternative is arbitrarily unlikely. Most methods of determining c... | "Are All Correlations Spurious But Some Correlations Are More Spurious?" - Not George Orwell
I'd say your understanding is correct. Philosophically, it's not truly possible to "prove" causation with 100% certainty, but we can convince ourselves that the alternative is arbitrarily unlikely. Mo |
38,585 | Statistically compare two large continuous datasets | You could try some sampling techniques. In more detail, you could select smaller random samples from the blue, red and green populations and compare those samples using the traditional statistical tests you mentioned. Run that multiple times and count how many times the null hypothesis (that the means are equal) got re... | Statistically compare two large continuous datasets | You could try some sampling techniques. In more detail, you could select smaller random samples from the blue, red and green populations and compare those samples using the traditional statistical tes | Statistically compare two large continuous datasets
You could try some sampling techniques. In more detail, you could select smaller random samples from the blue, red and green populations and compare those samples using the traditional statistical tests you mentioned. Run that multiple times and count how many times t... | Statistically compare two large continuous datasets
You could try some sampling techniques. In more detail, you could select smaller random samples from the blue, red and green populations and compare those samples using the traditional statistical tes |
38,586 | Statistically compare two large continuous datasets | One feature (not a bug) of hypothesis testing is that it gets more sensitive to small differences as the sample size increases. Consequently, hypothesis testing considers more than just effect size, and you’re really only interested in the effect size (perhaps in addition to some quantification of the uncertainty).
How... | Statistically compare two large continuous datasets | One feature (not a bug) of hypothesis testing is that it gets more sensitive to small differences as the sample size increases. Consequently, hypothesis testing considers more than just effect size, a | Statistically compare two large continuous datasets
One feature (not a bug) of hypothesis testing is that it gets more sensitive to small differences as the sample size increases. Consequently, hypothesis testing considers more than just effect size, and you’re really only interested in the effect size (perhaps in addi... | Statistically compare two large continuous datasets
One feature (not a bug) of hypothesis testing is that it gets more sensitive to small differences as the sample size increases. Consequently, hypothesis testing considers more than just effect size, a |
38,587 | Statistically compare two large continuous datasets | With such large sample sizes, you may get a clearer view of the relatively small (but obvious) differences between red and blue by looking at your histograms than from formal tests.
Consider the (roughly similar) fictitious data below:
set.seed(2022)
r = rbeta(50000,7,3)
summary(r)
Min. 1st Qu. Median Mean 3rd Q... | Statistically compare two large continuous datasets | With such large sample sizes, you may get a clearer view of the relatively small (but obvious) differences between red and blue by looking at your histograms than from formal tests.
Consider the (roug | Statistically compare two large continuous datasets
With such large sample sizes, you may get a clearer view of the relatively small (but obvious) differences between red and blue by looking at your histograms than from formal tests.
Consider the (roughly similar) fictitious data below:
set.seed(2022)
r = rbeta(50000,7... | Statistically compare two large continuous datasets
With such large sample sizes, you may get a clearer view of the relatively small (but obvious) differences between red and blue by looking at your histograms than from formal tests.
Consider the (roug |
38,588 | Statistically compare two large continuous datasets | The t-test and z-test do not work here because the degree of freedom is huge hence the p-value is 0
Yes. If you're testing the null hypothesis that the two datasets are unrelated, the p-value will be tiny. Even for the red versus green datasets, you should reject the null hypothesis.
If you're not testing the null hyp... | Statistically compare two large continuous datasets | The t-test and z-test do not work here because the degree of freedom is huge hence the p-value is 0
Yes. If you're testing the null hypothesis that the two datasets are unrelated, the p-value will be | Statistically compare two large continuous datasets
The t-test and z-test do not work here because the degree of freedom is huge hence the p-value is 0
Yes. If you're testing the null hypothesis that the two datasets are unrelated, the p-value will be tiny. Even for the red versus green datasets, you should reject the... | Statistically compare two large continuous datasets
The t-test and z-test do not work here because the degree of freedom is huge hence the p-value is 0
Yes. If you're testing the null hypothesis that the two datasets are unrelated, the p-value will be |
38,589 | Statistically compare two large continuous datasets | I'm not sure what your data represents, but in landscape/spatial ecology, it's common to have multiple raster datasets representing different variables for a given spatial area. One of the first issues that comes up is Spatial Autocorrelation.
Put simply, spatial autocorrelation occurs when you have measured variables ... | Statistically compare two large continuous datasets | I'm not sure what your data represents, but in landscape/spatial ecology, it's common to have multiple raster datasets representing different variables for a given spatial area. One of the first issue | Statistically compare two large continuous datasets
I'm not sure what your data represents, but in landscape/spatial ecology, it's common to have multiple raster datasets representing different variables for a given spatial area. One of the first issues that comes up is Spatial Autocorrelation.
Put simply, spatial auto... | Statistically compare two large continuous datasets
I'm not sure what your data represents, but in landscape/spatial ecology, it's common to have multiple raster datasets representing different variables for a given spatial area. One of the first issue |
38,590 | Statistically compare two large continuous datasets | In machine learning for generative adversarial networks (GANs), it is common to use Wasserstein metric / Earthmover's distance to compare output images from the well-known paper 2017 on Wasserstein GAN. Traditional measures like K-L divergence may be too stringent: see What is the advantages of Wasserstein metric compa... | Statistically compare two large continuous datasets | In machine learning for generative adversarial networks (GANs), it is common to use Wasserstein metric / Earthmover's distance to compare output images from the well-known paper 2017 on Wasserstein GA | Statistically compare two large continuous datasets
In machine learning for generative adversarial networks (GANs), it is common to use Wasserstein metric / Earthmover's distance to compare output images from the well-known paper 2017 on Wasserstein GAN. Traditional measures like K-L divergence may be too stringent: se... | Statistically compare two large continuous datasets
In machine learning for generative adversarial networks (GANs), it is common to use Wasserstein metric / Earthmover's distance to compare output images from the well-known paper 2017 on Wasserstein GA |
38,591 | Statistically compare two large continuous datasets | I would like to perform a statistical test that will quantify this difference and then I can choose a threshold and decide accordingly if these are similar enough for my application or not.
A statistical test will be based on statistical variations and will rank samples based on probability.
For instance the chi-squar... | Statistically compare two large continuous datasets | I would like to perform a statistical test that will quantify this difference and then I can choose a threshold and decide accordingly if these are similar enough for my application or not.
A statist | Statistically compare two large continuous datasets
I would like to perform a statistical test that will quantify this difference and then I can choose a threshold and decide accordingly if these are similar enough for my application or not.
A statistical test will be based on statistical variations and will rank samp... | Statistically compare two large continuous datasets
I would like to perform a statistical test that will quantify this difference and then I can choose a threshold and decide accordingly if these are similar enough for my application or not.
A statist |
38,592 | Statistically compare two large continuous datasets | Since you are dealing with histograms of the channels of an image, you could consider using OpenCV to compare the histograms via a distance metric to express how well they match.
In OpenCV, this task is somewhat trivial: you could use the function cv.compareHist to compare histograms using a given metric; you can selec... | Statistically compare two large continuous datasets | Since you are dealing with histograms of the channels of an image, you could consider using OpenCV to compare the histograms via a distance metric to express how well they match.
In OpenCV, this task | Statistically compare two large continuous datasets
Since you are dealing with histograms of the channels of an image, you could consider using OpenCV to compare the histograms via a distance metric to express how well they match.
In OpenCV, this task is somewhat trivial: you could use the function cv.compareHist to co... | Statistically compare two large continuous datasets
Since you are dealing with histograms of the channels of an image, you could consider using OpenCV to compare the histograms via a distance metric to express how well they match.
In OpenCV, this task |
38,593 | Why are confidence intervals of hazard ratios not symmetric? | The log (partial) likelihood maximization methods used to fit survival models work in the log-hazard scale. The regression coefficient estimates are in that scale, and in that scale the covariance of the estimates is assumed to be multivariate normal. In the log-hazard scale, confidence intervals (CI) are thus symmetri... | Why are confidence intervals of hazard ratios not symmetric? | The log (partial) likelihood maximization methods used to fit survival models work in the log-hazard scale. The regression coefficient estimates are in that scale, and in that scale the covariance of | Why are confidence intervals of hazard ratios not symmetric?
The log (partial) likelihood maximization methods used to fit survival models work in the log-hazard scale. The regression coefficient estimates are in that scale, and in that scale the covariance of the estimates is assumed to be multivariate normal. In the ... | Why are confidence intervals of hazard ratios not symmetric?
The log (partial) likelihood maximization methods used to fit survival models work in the log-hazard scale. The regression coefficient estimates are in that scale, and in that scale the covariance of |
38,594 | Why are confidence intervals of hazard ratios not symmetric? | My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean and the upper limit).
This is not correct. Hazard ratios have no reason to be symmetric. (They could in principle be s... | Why are confidence intervals of hazard ratios not symmetric? | My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean | Why are confidence intervals of hazard ratios not symmetric?
My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean and the upper limit).
This is not correct. Hazard ratios ... | Why are confidence intervals of hazard ratios not symmetric?
My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean |
38,595 | Why are confidence intervals of hazard ratios not symmetric? | It is just that we are used to symmetric confidence intervals, because this is the most typical/common situation: the case of some sort of linear regression with Gaussian distributed errors.
But... there is not a single unique confidence interval. Any region with 95% confidence will do.
Often one chooses the region tha... | Why are confidence intervals of hazard ratios not symmetric? | It is just that we are used to symmetric confidence intervals, because this is the most typical/common situation: the case of some sort of linear regression with Gaussian distributed errors.
But... th | Why are confidence intervals of hazard ratios not symmetric?
It is just that we are used to symmetric confidence intervals, because this is the most typical/common situation: the case of some sort of linear regression with Gaussian distributed errors.
But... there is not a single unique confidence interval. Any region ... | Why are confidence intervals of hazard ratios not symmetric?
It is just that we are used to symmetric confidence intervals, because this is the most typical/common situation: the case of some sort of linear regression with Gaussian distributed errors.
But... th |
38,596 | Plotting binary vs. binary to identify relationship | Really, for only two variables with only two possible values, you just make a contingency table. If you want, you can compute the rowwise / columnwise / tablewise proportions. If you really need a plot, a mosaic plot would be fine, or a four fold plot, but it doesn't seem very necessary to me. Here is an example in ... | Plotting binary vs. binary to identify relationship | Really, for only two variables with only two possible values, you just make a contingency table. If you want, you can compute the rowwise / columnwise / tablewise proportions. If you really need a p | Plotting binary vs. binary to identify relationship
Really, for only two variables with only two possible values, you just make a contingency table. If you want, you can compute the rowwise / columnwise / tablewise proportions. If you really need a plot, a mosaic plot would be fine, or a four fold plot, but it doesn'... | Plotting binary vs. binary to identify relationship
Really, for only two variables with only two possible values, you just make a contingency table. If you want, you can compute the rowwise / columnwise / tablewise proportions. If you really need a p |
38,597 | Plotting binary vs. binary to identify relationship | Such relationships are conventionally summarized with contingency tables, as in this (random) example:
Col 1 Col 2 Col 3 Col 4
Row 1 3 6 40 34
Row 2 18 6 9 1
Typically we are interested in comparing these data to values suggested by some default model, such as a null model of indepen... | Plotting binary vs. binary to identify relationship | Such relationships are conventionally summarized with contingency tables, as in this (random) example:
Col 1 Col 2 Col 3 Col 4
Row 1 3 6 40 34
Row 2 18 6 9 1
Typica | Plotting binary vs. binary to identify relationship
Such relationships are conventionally summarized with contingency tables, as in this (random) example:
Col 1 Col 2 Col 3 Col 4
Row 1 3 6 40 34
Row 2 18 6 9 1
Typically we are interested in comparing these data to values suggested by... | Plotting binary vs. binary to identify relationship
Such relationships are conventionally summarized with contingency tables, as in this (random) example:
Col 1 Col 2 Col 3 Col 4
Row 1 3 6 40 34
Row 2 18 6 9 1
Typica |
38,598 | Plotting binary vs. binary to identify relationship | For your data, as @gung has pointed out, you can make a confusion matrix, so something like below:
df.columns=['a','b']
sns.heatmap(pd.crosstab(df['a'],df['b']), annot=True)
Or you can call a mosaic plot from statsmodels that shows the deviation from expected:
import matplotlib.pyplot as plt
from statsmodels.graphics... | Plotting binary vs. binary to identify relationship | For your data, as @gung has pointed out, you can make a confusion matrix, so something like below:
df.columns=['a','b']
sns.heatmap(pd.crosstab(df['a'],df['b']), annot=True)
Or you can call a mosaic | Plotting binary vs. binary to identify relationship
For your data, as @gung has pointed out, you can make a confusion matrix, so something like below:
df.columns=['a','b']
sns.heatmap(pd.crosstab(df['a'],df['b']), annot=True)
Or you can call a mosaic plot from statsmodels that shows the deviation from expected:
impor... | Plotting binary vs. binary to identify relationship
For your data, as @gung has pointed out, you can make a confusion matrix, so something like below:
df.columns=['a','b']
sns.heatmap(pd.crosstab(df['a'],df['b']), annot=True)
Or you can call a mosaic |
38,599 | Inference in Time Series: Prophet vs. ARIMA | ARIMA and similar models assume some sort of causal relationship between past values and past errors and future values of the time series: $$Y_{t+h}=f(Y_{t},Y_{t-1},Y_{t-2},....,\epsilon_{t},\epsilon_{t-1},\epsilon_{t-2},...)$$ e.g. the volatility of a stock today is causally driven by the volatility of that stock yest... | Inference in Time Series: Prophet vs. ARIMA | ARIMA and similar models assume some sort of causal relationship between past values and past errors and future values of the time series: $$Y_{t+h}=f(Y_{t},Y_{t-1},Y_{t-2},....,\epsilon_{t},\epsilon_ | Inference in Time Series: Prophet vs. ARIMA
ARIMA and similar models assume some sort of causal relationship between past values and past errors and future values of the time series: $$Y_{t+h}=f(Y_{t},Y_{t-1},Y_{t-2},....,\epsilon_{t},\epsilon_{t-1},\epsilon_{t-2},...)$$ e.g. the volatility of a stock today is causally... | Inference in Time Series: Prophet vs. ARIMA
ARIMA and similar models assume some sort of causal relationship between past values and past errors and future values of the time series: $$Y_{t+h}=f(Y_{t},Y_{t-1},Y_{t-2},....,\epsilon_{t},\epsilon_ |
38,600 | Inference in Time Series: Prophet vs. ARIMA | I played with Prophet a bit. They promise big. As I understood their claim was for the framework for massive forecasting. If you have 10,000 series to forecast, there's no way to do it manually. So, let's just run the thing on all of them automatically, and maybe we'll get a decent set of forecast on average.
In financ... | Inference in Time Series: Prophet vs. ARIMA | I played with Prophet a bit. They promise big. As I understood their claim was for the framework for massive forecasting. If you have 10,000 series to forecast, there's no way to do it manually. So, l | Inference in Time Series: Prophet vs. ARIMA
I played with Prophet a bit. They promise big. As I understood their claim was for the framework for massive forecasting. If you have 10,000 series to forecast, there's no way to do it manually. So, let's just run the thing on all of them automatically, and maybe we'll get a ... | Inference in Time Series: Prophet vs. ARIMA
I played with Prophet a bit. They promise big. As I understood their claim was for the framework for massive forecasting. If you have 10,000 series to forecast, there's no way to do it manually. So, l |
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