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 |
|---|---|---|---|---|---|---|
37,901 | Can PC1 explain more than 90% of variance? | Let $S \in \mathbb{R}^{p \times p}$ be the sample covariance matrix (which equals to $X'X$ for centered and intercept-free design matrix $X$), and $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_p \geq 0$ be all the non-negative eigenvalues of $S$, then the total variation percentage explained by the first $k$ PCs i... | Can PC1 explain more than 90% of variance? | Let $S \in \mathbb{R}^{p \times p}$ be the sample covariance matrix (which equals to $X'X$ for centered and intercept-free design matrix $X$), and $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_p | Can PC1 explain more than 90% of variance?
Let $S \in \mathbb{R}^{p \times p}$ be the sample covariance matrix (which equals to $X'X$ for centered and intercept-free design matrix $X$), and $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_p \geq 0$ be all the non-negative eigenvalues of $S$, then the total variation ... | Can PC1 explain more than 90% of variance?
Let $S \in \mathbb{R}^{p \times p}$ be the sample covariance matrix (which equals to $X'X$ for centered and intercept-free design matrix $X$), and $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_p |
37,902 | Best Practices with Data Wrangling before running Random Forest Predictions | When doing predictions with Random Forests, we very often (or always)
need to perform some pre-processing.
This is not true. Random Forest is really "off-the-shelf".
Outliers. Should we remove them all? If so, we consider an outlier
based on the 3/2 rule? Should we keep them? Why?
The base model used in RF is a ... | Best Practices with Data Wrangling before running Random Forest Predictions | When doing predictions with Random Forests, we very often (or always)
need to perform some pre-processing.
This is not true. Random Forest is really "off-the-shelf".
Outliers. Should we remove the | Best Practices with Data Wrangling before running Random Forest Predictions
When doing predictions with Random Forests, we very often (or always)
need to perform some pre-processing.
This is not true. Random Forest is really "off-the-shelf".
Outliers. Should we remove them all? If so, we consider an outlier
based... | Best Practices with Data Wrangling before running Random Forest Predictions
When doing predictions with Random Forests, we very often (or always)
need to perform some pre-processing.
This is not true. Random Forest is really "off-the-shelf".
Outliers. Should we remove the |
37,903 | Best Practices with Data Wrangling before running Random Forest Predictions | Theoretically, Random Forest is ideal as it is commonly assumed and described by Breiman and Cuttler. In practice, it is very good but far from ideal. Therefore, these questions are very valid.
RF are not handling outliers as ideally as it is widely assumed. They are susceptible to even a single outlier with extreme v... | Best Practices with Data Wrangling before running Random Forest Predictions | Theoretically, Random Forest is ideal as it is commonly assumed and described by Breiman and Cuttler. In practice, it is very good but far from ideal. Therefore, these questions are very valid.
RF ar | Best Practices with Data Wrangling before running Random Forest Predictions
Theoretically, Random Forest is ideal as it is commonly assumed and described by Breiman and Cuttler. In practice, it is very good but far from ideal. Therefore, these questions are very valid.
RF are not handling outliers as ideally as it is ... | Best Practices with Data Wrangling before running Random Forest Predictions
Theoretically, Random Forest is ideal as it is commonly assumed and described by Breiman and Cuttler. In practice, it is very good but far from ideal. Therefore, these questions are very valid.
RF ar |
37,904 | Best Practices with Data Wrangling before running Random Forest Predictions | When pre-processing data, you are generally trying to achieve the following:
A. Removal of errors from your data. If your outliers are due to data
recording errors, for example, you would want to fix this in the
pre-processing stage. The various rules for identifying outliers
should be treated as providing ... | Best Practices with Data Wrangling before running Random Forest Predictions | When pre-processing data, you are generally trying to achieve the following:
A. Removal of errors from your data. If your outliers are due to data
recording errors, for example, you would want to | Best Practices with Data Wrangling before running Random Forest Predictions
When pre-processing data, you are generally trying to achieve the following:
A. Removal of errors from your data. If your outliers are due to data
recording errors, for example, you would want to fix this in the
pre-processing stage. Th... | Best Practices with Data Wrangling before running Random Forest Predictions
When pre-processing data, you are generally trying to achieve the following:
A. Removal of errors from your data. If your outliers are due to data
recording errors, for example, you would want to |
37,905 | Getting P value with mixed effect with lme4 package [duplicate] | I'm pasting the information from help("pvalues",package="lme4") here.
Users who need p-values have a variety of options. In the list below, the methods marked MC provide explicit model comparisons; CI denotes confidence intervals; and P denotes parameter-level or sequential tests of all effects in a model. The starred ... | Getting P value with mixed effect with lme4 package [duplicate] | I'm pasting the information from help("pvalues",package="lme4") here.
Users who need p-values have a variety of options. In the list below, the methods marked MC provide explicit model comparisons; CI | Getting P value with mixed effect with lme4 package [duplicate]
I'm pasting the information from help("pvalues",package="lme4") here.
Users who need p-values have a variety of options. In the list below, the methods marked MC provide explicit model comparisons; CI denotes confidence intervals; and P denotes parameter-l... | Getting P value with mixed effect with lme4 package [duplicate]
I'm pasting the information from help("pvalues",package="lme4") here.
Users who need p-values have a variety of options. In the list below, the methods marked MC provide explicit model comparisons; CI |
37,906 | Getting P value with mixed effect with lme4 package [duplicate] | p-values in lme4 are deliberately not listed by default, see:
Bates (author of lme4) on p-values in linear mixed models
or here
see also:
How to get an "overall" p-value and effect size for a categorical factor in a mixed model (lme4)?
There are some "approximations" but better just forget about p-values in lmm (or g... | Getting P value with mixed effect with lme4 package [duplicate] | p-values in lme4 are deliberately not listed by default, see:
Bates (author of lme4) on p-values in linear mixed models
or here
see also:
How to get an "overall" p-value and effect size for a categor | Getting P value with mixed effect with lme4 package [duplicate]
p-values in lme4 are deliberately not listed by default, see:
Bates (author of lme4) on p-values in linear mixed models
or here
see also:
How to get an "overall" p-value and effect size for a categorical factor in a mixed model (lme4)?
There are some "ap... | Getting P value with mixed effect with lme4 package [duplicate]
p-values in lme4 are deliberately not listed by default, see:
Bates (author of lme4) on p-values in linear mixed models
or here
see also:
How to get an "overall" p-value and effect size for a categor |
37,907 | Can a mathematically sound prediction interval have a negative lower bound? | Mathematics are reality-agnostic. So your negative lower prediction band can certainly be mathematically sound.
I would argue, however, that this is a good indication that you are using the wrong mathematics, e.g., Ordinary Least Squares (which assumes a normal distribution of errors) with count data (where a normal di... | Can a mathematically sound prediction interval have a negative lower bound? | Mathematics are reality-agnostic. So your negative lower prediction band can certainly be mathematically sound.
I would argue, however, that this is a good indication that you are using the wrong math | Can a mathematically sound prediction interval have a negative lower bound?
Mathematics are reality-agnostic. So your negative lower prediction band can certainly be mathematically sound.
I would argue, however, that this is a good indication that you are using the wrong mathematics, e.g., Ordinary Least Squares (which... | Can a mathematically sound prediction interval have a negative lower bound?
Mathematics are reality-agnostic. So your negative lower prediction band can certainly be mathematically sound.
I would argue, however, that this is a good indication that you are using the wrong math |
37,908 | Can a mathematically sound prediction interval have a negative lower bound? | It suggests to me that you haven't used any analytic approach with an appropriate transformation of the outcome. With count data, for instance, popular linear models (Poisson Regression or Negative Binomial Regression in particular) model the log of the process as a linear function of predictors. Then, any predicted va... | Can a mathematically sound prediction interval have a negative lower bound? | It suggests to me that you haven't used any analytic approach with an appropriate transformation of the outcome. With count data, for instance, popular linear models (Poisson Regression or Negative Bi | Can a mathematically sound prediction interval have a negative lower bound?
It suggests to me that you haven't used any analytic approach with an appropriate transformation of the outcome. With count data, for instance, popular linear models (Poisson Regression or Negative Binomial Regression in particular) model the l... | Can a mathematically sound prediction interval have a negative lower bound?
It suggests to me that you haven't used any analytic approach with an appropriate transformation of the outcome. With count data, for instance, popular linear models (Poisson Regression or Negative Bi |
37,909 | Why is the arithmetic mean > median on a histogram skewed to the right? | A histogram represents probability by area:
In this figure, the white region (to the left of $x=1$) comprises half the area. The blue region comprises the other half. The boundary between them at $x=1$ is, by definition, the median: it splits the total probability exactly in half.
The areas in the next figure are sh... | Why is the arithmetic mean > median on a histogram skewed to the right? | A histogram represents probability by area:
In this figure, the white region (to the left of $x=1$) comprises half the area. The blue region comprises the other half. The boundary between them at $ | Why is the arithmetic mean > median on a histogram skewed to the right?
A histogram represents probability by area:
In this figure, the white region (to the left of $x=1$) comprises half the area. The blue region comprises the other half. The boundary between them at $x=1$ is, by definition, the median: it splits th... | Why is the arithmetic mean > median on a histogram skewed to the right?
A histogram represents probability by area:
In this figure, the white region (to the left of $x=1$) comprises half the area. The blue region comprises the other half. The boundary between them at $ |
37,910 | Why is the arithmetic mean > median on a histogram skewed to the right? | Here is a simple answer:
Skew to the right means that the largest values are farther from the mean than the smallest values are (I know that isn't technically right, and not specific, but it gets the idea). If the largest values are farther from the mean they will influence the mean more than the smallest values will... | Why is the arithmetic mean > median on a histogram skewed to the right? | Here is a simple answer:
Skew to the right means that the largest values are farther from the mean than the smallest values are (I know that isn't technically right, and not specific, but it gets the | Why is the arithmetic mean > median on a histogram skewed to the right?
Here is a simple answer:
Skew to the right means that the largest values are farther from the mean than the smallest values are (I know that isn't technically right, and not specific, but it gets the idea). If the largest values are farther from ... | Why is the arithmetic mean > median on a histogram skewed to the right?
Here is a simple answer:
Skew to the right means that the largest values are farther from the mean than the smallest values are (I know that isn't technically right, and not specific, but it gets the |
37,911 | Why is the arithmetic mean > median on a histogram skewed to the right? | "Always" is wrong: take for example the data $\{1,1,2,2,3\}$ which has a mean of $1.8$, a median of $2$ and a positive skewness.
But more typically, positive skewness is associated with some extreme values above the median and fewer or less extreme values below the median. These will typically push up both the skewnes... | Why is the arithmetic mean > median on a histogram skewed to the right? | "Always" is wrong: take for example the data $\{1,1,2,2,3\}$ which has a mean of $1.8$, a median of $2$ and a positive skewness.
But more typically, positive skewness is associated with some extreme v | Why is the arithmetic mean > median on a histogram skewed to the right?
"Always" is wrong: take for example the data $\{1,1,2,2,3\}$ which has a mean of $1.8$, a median of $2$ and a positive skewness.
But more typically, positive skewness is associated with some extreme values above the median and fewer or less extreme... | Why is the arithmetic mean > median on a histogram skewed to the right?
"Always" is wrong: take for example the data $\{1,1,2,2,3\}$ which has a mean of $1.8$, a median of $2$ and a positive skewness.
But more typically, positive skewness is associated with some extreme v |
37,912 | How to learn statistics for medical research? | What would you think about that?
This is a good question. I've spent a good amount of time during my Ph.D in Biostatistics consulting for academic physicians and their research. If you (and moderators) will allow for an opinion based answer then I'm happy to give it.
Medicine for some reason has created a culture in... | How to learn statistics for medical research? | What would you think about that?
This is a good question. I've spent a good amount of time during my Ph.D in Biostatistics consulting for academic physicians and their research. If you (and moderat | How to learn statistics for medical research?
What would you think about that?
This is a good question. I've spent a good amount of time during my Ph.D in Biostatistics consulting for academic physicians and their research. If you (and moderators) will allow for an opinion based answer then I'm happy to give it.
Med... | How to learn statistics for medical research?
What would you think about that?
This is a good question. I've spent a good amount of time during my Ph.D in Biostatistics consulting for academic physicians and their research. If you (and moderat |
37,913 | How to learn statistics for medical research? | I spent the last 14 years trying to get better at statistics including earning an applied master's in it (which in honesty was disappointing). I think the answer is that there is no simple way to do this. This is made worse by the fact that much of the academic literature that uses statistics is not done by true statis... | How to learn statistics for medical research? | I spent the last 14 years trying to get better at statistics including earning an applied master's in it (which in honesty was disappointing). I think the answer is that there is no simple way to do t | How to learn statistics for medical research?
I spent the last 14 years trying to get better at statistics including earning an applied master's in it (which in honesty was disappointing). I think the answer is that there is no simple way to do this. This is made worse by the fact that much of the academic literature t... | How to learn statistics for medical research?
I spent the last 14 years trying to get better at statistics including earning an applied master's in it (which in honesty was disappointing). I think the answer is that there is no simple way to do t |
37,914 | How to learn statistics for medical research? | The discussions above make fantastic points. I recommend a parallel approach of finding a biostatistician collaborator and learning about biostatistics. On the latter, concentrate on learning things that the biostatistician is unlikely to already know, to spur them on to a better understanding. I've tried to cover l... | How to learn statistics for medical research? | The discussions above make fantastic points. I recommend a parallel approach of finding a biostatistician collaborator and learning about biostatistics. On the latter, concentrate on learning things | How to learn statistics for medical research?
The discussions above make fantastic points. I recommend a parallel approach of finding a biostatistician collaborator and learning about biostatistics. On the latter, concentrate on learning things that the biostatistician is unlikely to already know, to spur them on to ... | How to learn statistics for medical research?
The discussions above make fantastic points. I recommend a parallel approach of finding a biostatistician collaborator and learning about biostatistics. On the latter, concentrate on learning things |
37,915 | How to learn statistics for medical research? | You're Getting The Order Wrong.
It's as though you've said "I want to learn medicine, therefor I bought a scalpel." R is a very useful tool. But it will be much harder to learn statistics from using R than it would to learn to use R after already knowing statistics.
If I were learning statistics from scratch, I would n... | How to learn statistics for medical research? | You're Getting The Order Wrong.
It's as though you've said "I want to learn medicine, therefor I bought a scalpel." R is a very useful tool. But it will be much harder to learn statistics from using R | How to learn statistics for medical research?
You're Getting The Order Wrong.
It's as though you've said "I want to learn medicine, therefor I bought a scalpel." R is a very useful tool. But it will be much harder to learn statistics from using R than it would to learn to use R after already knowing statistics.
If I we... | How to learn statistics for medical research?
You're Getting The Order Wrong.
It's as though you've said "I want to learn medicine, therefor I bought a scalpel." R is a very useful tool. But it will be much harder to learn statistics from using R |
37,916 | How to learn statistics for medical research? | It sounds like that you just have started with statistics and you do not have experience with it. That is totally OK.
But your goal is the other extrem that you want to be a statistic pro. That is impossible. Relax your self and do not push you to much here.
Keep one very important thing in mind. A professional (or how... | How to learn statistics for medical research? | It sounds like that you just have started with statistics and you do not have experience with it. That is totally OK.
But your goal is the other extrem that you want to be a statistic pro. That is imp | How to learn statistics for medical research?
It sounds like that you just have started with statistics and you do not have experience with it. That is totally OK.
But your goal is the other extrem that you want to be a statistic pro. That is impossible. Relax your self and do not push you to much here.
Keep one very i... | How to learn statistics for medical research?
It sounds like that you just have started with statistics and you do not have experience with it. That is totally OK.
But your goal is the other extrem that you want to be a statistic pro. That is imp |
37,917 | How do we know if the correlation is significant? | For what range of values of rx,y, can we [...] proceed to predict Y by using a linear regression?
If the relationship is indeed linear, any value of correlation can work; linear regression behaves as it should across the entire range of correlations, including 0. You don't even need to examine the correlation beforeha... | How do we know if the correlation is significant? | For what range of values of rx,y, can we [...] proceed to predict Y by using a linear regression?
If the relationship is indeed linear, any value of correlation can work; linear regression behaves as | How do we know if the correlation is significant?
For what range of values of rx,y, can we [...] proceed to predict Y by using a linear regression?
If the relationship is indeed linear, any value of correlation can work; linear regression behaves as it should across the entire range of correlations, including 0. You d... | How do we know if the correlation is significant?
For what range of values of rx,y, can we [...] proceed to predict Y by using a linear regression?
If the relationship is indeed linear, any value of correlation can work; linear regression behaves as |
37,918 | How do we know if the correlation is significant? | There is a difference between a well-evidenced effect and a strong effect. For example, there is good evidence that eating bacon causes cancer, but the risk is low; and there is weak evidence that smoking marijuana leaf causes cancer, but the risk is probably high. (The reason for the gap is that the bacon eaters are s... | How do we know if the correlation is significant? | There is a difference between a well-evidenced effect and a strong effect. For example, there is good evidence that eating bacon causes cancer, but the risk is low; and there is weak evidence that smo | How do we know if the correlation is significant?
There is a difference between a well-evidenced effect and a strong effect. For example, there is good evidence that eating bacon causes cancer, but the risk is low; and there is weak evidence that smoking marijuana leaf causes cancer, but the risk is probably high. (The... | How do we know if the correlation is significant?
There is a difference between a well-evidenced effect and a strong effect. For example, there is good evidence that eating bacon causes cancer, but the risk is low; and there is weak evidence that smo |
37,919 | How do we know if the correlation is significant? | Often the term "significance" is used in the meaning "$\rho$ is statistically significantly different from zero". This is, however, not what most users of $\rho$ are interested in, because the null hypothesis that $\rho$ is exactly zero is almost certainly false. Hence even the tiniest deviation from zero becomes "sign... | How do we know if the correlation is significant? | Often the term "significance" is used in the meaning "$\rho$ is statistically significantly different from zero". This is, however, not what most users of $\rho$ are interested in, because the null hy | How do we know if the correlation is significant?
Often the term "significance" is used in the meaning "$\rho$ is statistically significantly different from zero". This is, however, not what most users of $\rho$ are interested in, because the null hypothesis that $\rho$ is exactly zero is almost certainly false. Hence ... | How do we know if the correlation is significant?
Often the term "significance" is used in the meaning "$\rho$ is statistically significantly different from zero". This is, however, not what most users of $\rho$ are interested in, because the null hy |
37,920 | How do we know if the correlation is significant? | You could use the following test to check whether there is significant correlation between $X$ and $Y$. Assume that you have the observations $(x_i,y_i), i =1,\dots,n$.
The null and alternative hypothesis are given by:
$$
H_0: \, \rho = 0 \quad vs. \quad H_1: \rho \neq 0
$$
The test statistic is given by:
$$
T = \sqrt{... | How do we know if the correlation is significant? | You could use the following test to check whether there is significant correlation between $X$ and $Y$. Assume that you have the observations $(x_i,y_i), i =1,\dots,n$.
The null and alternative hypoth | How do we know if the correlation is significant?
You could use the following test to check whether there is significant correlation between $X$ and $Y$. Assume that you have the observations $(x_i,y_i), i =1,\dots,n$.
The null and alternative hypothesis are given by:
$$
H_0: \, \rho = 0 \quad vs. \quad H_1: \rho \neq ... | How do we know if the correlation is significant?
You could use the following test to check whether there is significant correlation between $X$ and $Y$. Assume that you have the observations $(x_i,y_i), i =1,\dots,n$.
The null and alternative hypoth |
37,921 | How do we know if the correlation is significant? | All you need is to compute the degree of freedom of the system, which is the number of participants minus $2$, and then refer to the table of critical values for $r$, which can be found here.
However, this gives you nothing but the mathematical significance, you still need to have a look at the scatterplot to see if a ... | How do we know if the correlation is significant? | All you need is to compute the degree of freedom of the system, which is the number of participants minus $2$, and then refer to the table of critical values for $r$, which can be found here.
However, | How do we know if the correlation is significant?
All you need is to compute the degree of freedom of the system, which is the number of participants minus $2$, and then refer to the table of critical values for $r$, which can be found here.
However, this gives you nothing but the mathematical significance, you still n... | How do we know if the correlation is significant?
All you need is to compute the degree of freedom of the system, which is the number of participants minus $2$, and then refer to the table of critical values for $r$, which can be found here.
However, |
37,922 | How do we know if the correlation is significant? | Like hypothesis testing in general, all you can do is propose a null hypothesis and calculate the probability of seeing the data given that null hypothesis. There is no point at which the data "definitely" comes from correlated sources, only some line in the sand where you decide that the data is "unlikely enough" to r... | How do we know if the correlation is significant? | Like hypothesis testing in general, all you can do is propose a null hypothesis and calculate the probability of seeing the data given that null hypothesis. There is no point at which the data "defini | How do we know if the correlation is significant?
Like hypothesis testing in general, all you can do is propose a null hypothesis and calculate the probability of seeing the data given that null hypothesis. There is no point at which the data "definitely" comes from correlated sources, only some line in the sand where ... | How do we know if the correlation is significant?
Like hypothesis testing in general, all you can do is propose a null hypothesis and calculate the probability of seeing the data given that null hypothesis. There is no point at which the data "defini |
37,923 | Usefulness of the confidence interval | A confidence interval is typically more useful than a hypothesis test. A hypothesis test tells you if you can rule out a specific null hypothesis (typically, $0$). On the other hand a confidence interval demarcates an infinite set of values that, if they had been your null, would have been rejected similarly. (Likew... | Usefulness of the confidence interval | A confidence interval is typically more useful than a hypothesis test. A hypothesis test tells you if you can rule out a specific null hypothesis (typically, $0$). On the other hand a confidence int | Usefulness of the confidence interval
A confidence interval is typically more useful than a hypothesis test. A hypothesis test tells you if you can rule out a specific null hypothesis (typically, $0$). On the other hand a confidence interval demarcates an infinite set of values that, if they had been your null, would... | Usefulness of the confidence interval
A confidence interval is typically more useful than a hypothesis test. A hypothesis test tells you if you can rule out a specific null hypothesis (typically, $0$). On the other hand a confidence int |
37,924 | Usefulness of the confidence interval | I think it's best understood with a simple example.
Imagine you are on a farm that raises sheep. The farm has a lot of sheep but you only observe 5. Out of those 5 sheep, 1 sheep was black and 4 sheep were white. And you are interested in the real proportion of black/white sheep within the farm. What can you tell about... | Usefulness of the confidence interval | I think it's best understood with a simple example.
Imagine you are on a farm that raises sheep. The farm has a lot of sheep but you only observe 5. Out of those 5 sheep, 1 sheep was black and 4 sheep | Usefulness of the confidence interval
I think it's best understood with a simple example.
Imagine you are on a farm that raises sheep. The farm has a lot of sheep but you only observe 5. Out of those 5 sheep, 1 sheep was black and 4 sheep were white. And you are interested in the real proportion of black/white sheep wi... | Usefulness of the confidence interval
I think it's best understood with a simple example.
Imagine you are on a farm that raises sheep. The farm has a lot of sheep but you only observe 5. Out of those 5 sheep, 1 sheep was black and 4 sheep |
37,925 | Usefulness of the confidence interval | The answer by gung-Reinstate Monica is fine.
I add the following. In reality there is no such thing as a true model. There is no true parameter either (as such a parameter is only defined within a model). What we do is we use models to think about a reality that is different, however we don't have better tools than art... | Usefulness of the confidence interval | The answer by gung-Reinstate Monica is fine.
I add the following. In reality there is no such thing as a true model. There is no true parameter either (as such a parameter is only defined within a mod | Usefulness of the confidence interval
The answer by gung-Reinstate Monica is fine.
I add the following. In reality there is no such thing as a true model. There is no true parameter either (as such a parameter is only defined within a model). What we do is we use models to think about a reality that is different, howev... | Usefulness of the confidence interval
The answer by gung-Reinstate Monica is fine.
I add the following. In reality there is no such thing as a true model. There is no true parameter either (as such a parameter is only defined within a mod |
37,926 | When two events $A$ and $B$ have no result in common | No, events with no result in common are not independent if the events come from the same sample space.
An example: Throw a single fair die. Let event A be 'throw is a 1', and event B be 'throw is a 2'. Then $P(A) = P(B) = 1/6$, but $P(A|B) = P(B|A) = 0$, as the die throw can't be both 1 and 2. | When two events $A$ and $B$ have no result in common | No, events with no result in common are not independent if the events come from the same sample space.
An example: Throw a single fair die. Let event A be 'throw is a 1', and event B be 'throw is a 2 | When two events $A$ and $B$ have no result in common
No, events with no result in common are not independent if the events come from the same sample space.
An example: Throw a single fair die. Let event A be 'throw is a 1', and event B be 'throw is a 2'. Then $P(A) = P(B) = 1/6$, but $P(A|B) = P(B|A) = 0$, as the die ... | When two events $A$ and $B$ have no result in common
No, events with no result in common are not independent if the events come from the same sample space.
An example: Throw a single fair die. Let event A be 'throw is a 1', and event B be 'throw is a 2 |
37,927 | When two events $A$ and $B$ have no result in common | Independence can be thought of as "If event A occurs it tells you nothing about the probability of event B occurring".
However, if two events share nothing in common then clearly if I know that one event occurred then I know that the other event COULDN'T have occurred. So I am getting information about the other event... | When two events $A$ and $B$ have no result in common | Independence can be thought of as "If event A occurs it tells you nothing about the probability of event B occurring".
However, if two events share nothing in common then clearly if I know that one ev | When two events $A$ and $B$ have no result in common
Independence can be thought of as "If event A occurs it tells you nothing about the probability of event B occurring".
However, if two events share nothing in common then clearly if I know that one event occurred then I know that the other event COULDN'T have occurre... | When two events $A$ and $B$ have no result in common
Independence can be thought of as "If event A occurs it tells you nothing about the probability of event B occurring".
However, if two events share nothing in common then clearly if I know that one ev |
37,928 | When two events $A$ and $B$ have no result in common | It is true that if $P(A)=P(A\mid B)$ then the two events are intependent.
Now we know that: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. Note the intersection in the numerator. If the two events didn't have "anything in common" then we would have $P(A\cap B)=0$ since the set $A\cap B$ would be empty. However independence work... | When two events $A$ and $B$ have no result in common | It is true that if $P(A)=P(A\mid B)$ then the two events are intependent.
Now we know that: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. Note the intersection in the numerator. If the two events didn't have | When two events $A$ and $B$ have no result in common
It is true that if $P(A)=P(A\mid B)$ then the two events are intependent.
Now we know that: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. Note the intersection in the numerator. If the two events didn't have "anything in common" then we would have $P(A\cap B)=0$ since the se... | When two events $A$ and $B$ have no result in common
It is true that if $P(A)=P(A\mid B)$ then the two events are intependent.
Now we know that: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. Note the intersection in the numerator. If the two events didn't have |
37,929 | When two events $A$ and $B$ have no result in common | You are confusing dependence with mutual-exclusivity. Two events $A$ and $B$ are independent if and only if $P(A \cap B) = P(A)P(B)$. They are disjoint if and only if $A \cap B = \emptyset$.
Consider a normally-distributed random variable $X$ with mean 0 and variance 1.
Here is a pair of events for each of the four c... | When two events $A$ and $B$ have no result in common | You are confusing dependence with mutual-exclusivity. Two events $A$ and $B$ are independent if and only if $P(A \cap B) = P(A)P(B)$. They are disjoint if and only if $A \cap B = \emptyset$.
Conside | When two events $A$ and $B$ have no result in common
You are confusing dependence with mutual-exclusivity. Two events $A$ and $B$ are independent if and only if $P(A \cap B) = P(A)P(B)$. They are disjoint if and only if $A \cap B = \emptyset$.
Consider a normally-distributed random variable $X$ with mean 0 and varian... | When two events $A$ and $B$ have no result in common
You are confusing dependence with mutual-exclusivity. Two events $A$ and $B$ are independent if and only if $P(A \cap B) = P(A)P(B)$. They are disjoint if and only if $A \cap B = \emptyset$.
Conside |
37,930 | When two events $A$ and $B$ have no result in common | Let $A$ and $B$ denote two events defined on a sample space $\Omega$.
The formal definition of independent events is as follows.
Definition: $A$ and $B$ are said to be (stochastically)
mutually independent events if
$$P(A\cap B) = P(A)P(B).$$
It is easily shown that any one of the four relations
shown below implies th... | When two events $A$ and $B$ have no result in common | Let $A$ and $B$ denote two events defined on a sample space $\Omega$.
The formal definition of independent events is as follows.
Definition: $A$ and $B$ are said to be (stochastically)
mutually indepe | When two events $A$ and $B$ have no result in common
Let $A$ and $B$ denote two events defined on a sample space $\Omega$.
The formal definition of independent events is as follows.
Definition: $A$ and $B$ are said to be (stochastically)
mutually independent events if
$$P(A\cap B) = P(A)P(B).$$
It is easily shown that ... | When two events $A$ and $B$ have no result in common
Let $A$ and $B$ denote two events defined on a sample space $\Omega$.
The formal definition of independent events is as follows.
Definition: $A$ and $B$ are said to be (stochastically)
mutually indepe |
37,931 | When two events $A$ and $B$ have no result in common | mutually exclusive events.. natural blonde hair, and black skin. If I know someone has black skin, I know they will not have naturally blonde hair. Therefore, the characteristic of hair color and skin color are dependent.. Knowing that someone has black skin tells me information about what their hair will be like.... | When two events $A$ and $B$ have no result in common | mutually exclusive events.. natural blonde hair, and black skin. If I know someone has black skin, I know they will not have naturally blonde hair. Therefore, the characteristic of hair color and | When two events $A$ and $B$ have no result in common
mutually exclusive events.. natural blonde hair, and black skin. If I know someone has black skin, I know they will not have naturally blonde hair. Therefore, the characteristic of hair color and skin color are dependent.. Knowing that someone has black skin tel... | When two events $A$ and $B$ have no result in common
mutually exclusive events.. natural blonde hair, and black skin. If I know someone has black skin, I know they will not have naturally blonde hair. Therefore, the characteristic of hair color and |
37,932 | If X=Y+Z, Is it ever useful to regress X on Y? | If you know $X = Y + Z$ and you have $Y$ and $Z$ measured, why would you need to run a regression of $X$ on $Y$ and $Z$? It provides no additional information and does not allow you to make "better" predictions about $X$ (since you know $X$ exactly from $Y$ and $Z$). But if you don't have $Z$, don't know the exact rela... | If X=Y+Z, Is it ever useful to regress X on Y? | If you know $X = Y + Z$ and you have $Y$ and $Z$ measured, why would you need to run a regression of $X$ on $Y$ and $Z$? It provides no additional information and does not allow you to make "better" p | If X=Y+Z, Is it ever useful to regress X on Y?
If you know $X = Y + Z$ and you have $Y$ and $Z$ measured, why would you need to run a regression of $X$ on $Y$ and $Z$? It provides no additional information and does not allow you to make "better" predictions about $X$ (since you know $X$ exactly from $Y$ and $Z$). But i... | If X=Y+Z, Is it ever useful to regress X on Y?
If you know $X = Y + Z$ and you have $Y$ and $Z$ measured, why would you need to run a regression of $X$ on $Y$ and $Z$? It provides no additional information and does not allow you to make "better" p |
37,933 | If X=Y+Z, Is it ever useful to regress X on Y? | Linear regression is a tool that is used to achieve a goal. So any answer will depend on the goal to be achieved. As said already in the answer of @Noah, if you already know $X$, $Y$, and $Z$, I can't see any goal worth achieving that is achieved by this regression. Why would you want imprecise predictions of $X$ if yo... | If X=Y+Z, Is it ever useful to regress X on Y? | Linear regression is a tool that is used to achieve a goal. So any answer will depend on the goal to be achieved. As said already in the answer of @Noah, if you already know $X$, $Y$, and $Z$, I can't | If X=Y+Z, Is it ever useful to regress X on Y?
Linear regression is a tool that is used to achieve a goal. So any answer will depend on the goal to be achieved. As said already in the answer of @Noah, if you already know $X$, $Y$, and $Z$, I can't see any goal worth achieving that is achieved by this regression. Why wo... | If X=Y+Z, Is it ever useful to regress X on Y?
Linear regression is a tool that is used to achieve a goal. So any answer will depend on the goal to be achieved. As said already in the answer of @Noah, if you already know $X$, $Y$, and $Z$, I can't |
37,934 | If X=Y+Z, Is it ever useful to regress X on Y? | Two people step on a scale. The scale outputs only the total weight of the couple.
If you know the weight of the first person ($Y$) can you guess what the scale will output ($X$) without knowing anything about the weight of the second person ($Z$)?
Intuitively, there has to be some connection. If $Y$ is very heavy, it ... | If X=Y+Z, Is it ever useful to regress X on Y? | Two people step on a scale. The scale outputs only the total weight of the couple.
If you know the weight of the first person ($Y$) can you guess what the scale will output ($X$) without knowing anyth | If X=Y+Z, Is it ever useful to regress X on Y?
Two people step on a scale. The scale outputs only the total weight of the couple.
If you know the weight of the first person ($Y$) can you guess what the scale will output ($X$) without knowing anything about the weight of the second person ($Z$)?
Intuitively, there has t... | If X=Y+Z, Is it ever useful to regress X on Y?
Two people step on a scale. The scale outputs only the total weight of the couple.
If you know the weight of the first person ($Y$) can you guess what the scale will output ($X$) without knowing anyth |
37,935 | Lasso centering and standarization with R | If you use glmnet, the scaling is performed by the package. You don't need to worry about scaling the test set because the "coefficients are always returned on the original scale".
By default:
glmnet(x, y, [...]
standardize = TRUE,
intercept = TRUE,
standardize.response = FALSE [...])
As for the standardization of the... | Lasso centering and standarization with R | If you use glmnet, the scaling is performed by the package. You don't need to worry about scaling the test set because the "coefficients are always returned on the original scale".
By default:
glmnet( | Lasso centering and standarization with R
If you use glmnet, the scaling is performed by the package. You don't need to worry about scaling the test set because the "coefficients are always returned on the original scale".
By default:
glmnet(x, y, [...]
standardize = TRUE,
intercept = TRUE,
standardize.response = FALSE... | Lasso centering and standarization with R
If you use glmnet, the scaling is performed by the package. You don't need to worry about scaling the test set because the "coefficients are always returned on the original scale".
By default:
glmnet( |
37,936 | Lasso centering and standarization with R | In general, you are right to worry about scaling the responses. If you optimize a function of the kind that LASSO is based on,
$$
\min_{\beta} || Y - X\beta ||_{2}^{2} + \lambda || \beta ||_1,
$$
then scaling the response $Y$ with some constant $\alpha$,
$$
\min_{\beta} || \alpha Y - X\beta ||_{2}^{2} + \lambda || \bet... | Lasso centering and standarization with R | In general, you are right to worry about scaling the responses. If you optimize a function of the kind that LASSO is based on,
$$
\min_{\beta} || Y - X\beta ||_{2}^{2} + \lambda || \beta ||_1,
$$
then | Lasso centering and standarization with R
In general, you are right to worry about scaling the responses. If you optimize a function of the kind that LASSO is based on,
$$
\min_{\beta} || Y - X\beta ||_{2}^{2} + \lambda || \beta ||_1,
$$
then scaling the response $Y$ with some constant $\alpha$,
$$
\min_{\beta} || \alp... | Lasso centering and standarization with R
In general, you are right to worry about scaling the responses. If you optimize a function of the kind that LASSO is based on,
$$
\min_{\beta} || Y - X\beta ||_{2}^{2} + \lambda || \beta ||_1,
$$
then |
37,937 | Lasso centering and standarization with R | With a lasso regression, standardization is essential. That's because lasso finds the best solution subject to a constraint on the absolute value of the sum of the coefficients. If one didn't scale the coefficients the answer would totally depend on the scaling of the coefficient. For example using lasso on $x_1, x_... | Lasso centering and standarization with R | With a lasso regression, standardization is essential. That's because lasso finds the best solution subject to a constraint on the absolute value of the sum of the coefficients. If one didn't scale | Lasso centering and standarization with R
With a lasso regression, standardization is essential. That's because lasso finds the best solution subject to a constraint on the absolute value of the sum of the coefficients. If one didn't scale the coefficients the answer would totally depend on the scaling of the coeffic... | Lasso centering and standarization with R
With a lasso regression, standardization is essential. That's because lasso finds the best solution subject to a constraint on the absolute value of the sum of the coefficients. If one didn't scale |
37,938 | Probability density function between -1 and 1? | A beta distribution seems to suit your needs, but you'll have to perform a transformation in order to change its $(0,1)$ (finite) support to $(-1,1)$ support.
Let $X$ be distributed with a beta distribution, then the random variable $Y$ given by the transformation
$$Y=(b-a)X+a$$
is beta distributed and the PDF has fini... | Probability density function between -1 and 1? | A beta distribution seems to suit your needs, but you'll have to perform a transformation in order to change its $(0,1)$ (finite) support to $(-1,1)$ support.
Let $X$ be distributed with a beta distri | Probability density function between -1 and 1?
A beta distribution seems to suit your needs, but you'll have to perform a transformation in order to change its $(0,1)$ (finite) support to $(-1,1)$ support.
Let $X$ be distributed with a beta distribution, then the random variable $Y$ given by the transformation
$$Y=(b-a... | Probability density function between -1 and 1?
A beta distribution seems to suit your needs, but you'll have to perform a transformation in order to change its $(0,1)$ (finite) support to $(-1,1)$ support.
Let $X$ be distributed with a beta distri |
37,939 | Probability density function between -1 and 1? | Here is an attempt to further illustrate how to apply Néstor's suggestion (+1, btw) of using the beta distribution.
The beta distribution has two parameters $\alpha$ and $\beta$. These determine the shape of the distribution - it can look like the distributions in your figure, like a box, like a straight line, and so ... | Probability density function between -1 and 1? | Here is an attempt to further illustrate how to apply Néstor's suggestion (+1, btw) of using the beta distribution.
The beta distribution has two parameters $\alpha$ and $\beta$. These determine the | Probability density function between -1 and 1?
Here is an attempt to further illustrate how to apply Néstor's suggestion (+1, btw) of using the beta distribution.
The beta distribution has two parameters $\alpha$ and $\beta$. These determine the shape of the distribution - it can look like the distributions in your fi... | Probability density function between -1 and 1?
Here is an attempt to further illustrate how to apply Néstor's suggestion (+1, btw) of using the beta distribution.
The beta distribution has two parameters $\alpha$ and $\beta$. These determine the |
37,940 | What are the primary differences between z-scores and t-scores, and are they both considered standard scores? | What you are reporting is a standardized score. It just isn't the standardized score most statisticians are familiar with. Likewise, the t-score you are talking about, isn't what most of the people answering the question think it is.
I only ran into these issues before because I volunteered in a psychometric testing la... | What are the primary differences between z-scores and t-scores, and are they both considered standar | What you are reporting is a standardized score. It just isn't the standardized score most statisticians are familiar with. Likewise, the t-score you are talking about, isn't what most of the people an | What are the primary differences between z-scores and t-scores, and are they both considered standard scores?
What you are reporting is a standardized score. It just isn't the standardized score most statisticians are familiar with. Likewise, the t-score you are talking about, isn't what most of the people answering th... | What are the primary differences between z-scores and t-scores, and are they both considered standar
What you are reporting is a standardized score. It just isn't the standardized score most statisticians are familiar with. Likewise, the t-score you are talking about, isn't what most of the people an |
37,941 | What are the primary differences between z-scores and t-scores, and are they both considered standard scores? | Your question pertains to terminology used in the reporting of standardised psychometric tests.
Charles Hale has notes on terminology in standardised testing.
My understanding:
z-score: mean = 0; sd = 1
t-score: mean = 50; sd = 10 (example test using t-scores) (interestingly, t-score means something different in the... | What are the primary differences between z-scores and t-scores, and are they both considered standar | Your question pertains to terminology used in the reporting of standardised psychometric tests.
Charles Hale has notes on terminology in standardised testing.
My understanding:
z-score: mean = 0; s | What are the primary differences between z-scores and t-scores, and are they both considered standard scores?
Your question pertains to terminology used in the reporting of standardised psychometric tests.
Charles Hale has notes on terminology in standardised testing.
My understanding:
z-score: mean = 0; sd = 1
t-sc... | What are the primary differences between z-scores and t-scores, and are they both considered standar
Your question pertains to terminology used in the reporting of standardised psychometric tests.
Charles Hale has notes on terminology in standardised testing.
My understanding:
z-score: mean = 0; s |
37,942 | What are the primary differences between z-scores and t-scores, and are they both considered standard scores? | Most basic texts on statistics will define these as $z= \frac{\bar{x}-\mu}{ \sigma/\sqrt{n} }$ and $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$. The difference is that $z$ uses $\sigma$ which is the known population standard deviation and $t$ uses $s$ which is the sample standard devition used as an estimate of the population $... | What are the primary differences between z-scores and t-scores, and are they both considered standar | Most basic texts on statistics will define these as $z= \frac{\bar{x}-\mu}{ \sigma/\sqrt{n} }$ and $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$. The difference is that $z$ uses $\sigma$ which is the known popu | What are the primary differences between z-scores and t-scores, and are they both considered standard scores?
Most basic texts on statistics will define these as $z= \frac{\bar{x}-\mu}{ \sigma/\sqrt{n} }$ and $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$. The difference is that $z$ uses $\sigma$ which is the known population sta... | What are the primary differences between z-scores and t-scores, and are they both considered standar
Most basic texts on statistics will define these as $z= \frac{\bar{x}-\mu}{ \sigma/\sqrt{n} }$ and $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$. The difference is that $z$ uses $\sigma$ which is the known popu |
37,943 | What are the primary differences between z-scores and t-scores, and are they both considered standard scores? | The Student's t test is used when you have a small sample and have to approximate the standard deviation (SD, $\sigma$). If you look at the distribution tables for the z-score and t-score you can see that they quickly approach similar values and that with more than 50 observations the difference is so small that it rea... | What are the primary differences between z-scores and t-scores, and are they both considered standar | The Student's t test is used when you have a small sample and have to approximate the standard deviation (SD, $\sigma$). If you look at the distribution tables for the z-score and t-score you can see | What are the primary differences between z-scores and t-scores, and are they both considered standard scores?
The Student's t test is used when you have a small sample and have to approximate the standard deviation (SD, $\sigma$). If you look at the distribution tables for the z-score and t-score you can see that they ... | What are the primary differences between z-scores and t-scores, and are they both considered standar
The Student's t test is used when you have a small sample and have to approximate the standard deviation (SD, $\sigma$). If you look at the distribution tables for the z-score and t-score you can see |
37,944 | What is likelihood actually? | The likelihood function parametrized by a parameter $\theta$ in statistics is defined as
$$
\mathcal{L}(\theta \mid x) = f_{\theta}(x)
$$
where $f_{\theta}$ is the probability density or mass function with parameter $\theta$ and $x$ is the data.
If for some data $x$ you evaluate the function for the parameter $\theta$ ... | What is likelihood actually? | The likelihood function parametrized by a parameter $\theta$ in statistics is defined as
$$
\mathcal{L}(\theta \mid x) = f_{\theta}(x)
$$
where $f_{\theta}$ is the probability density or mass function | What is likelihood actually?
The likelihood function parametrized by a parameter $\theta$ in statistics is defined as
$$
\mathcal{L}(\theta \mid x) = f_{\theta}(x)
$$
where $f_{\theta}$ is the probability density or mass function with parameter $\theta$ and $x$ is the data.
If for some data $x$ you evaluate the functio... | What is likelihood actually?
The likelihood function parametrized by a parameter $\theta$ in statistics is defined as
$$
\mathcal{L}(\theta \mid x) = f_{\theta}(x)
$$
where $f_{\theta}$ is the probability density or mass function |
37,945 | What is likelihood actually? | There have been numerous responses including some to your very posts earlier and the present one too.
It should be reiterated that $\mathcal L(\theta\mid \mathbf x) $ or $\ell_\mathbf x(\theta)$ (to emphasize what the argument here is) even though has the same functional form as the corresponding density function of th... | What is likelihood actually? | There have been numerous responses including some to your very posts earlier and the present one too.
It should be reiterated that $\mathcal L(\theta\mid \mathbf x) $ or $\ell_\mathbf x(\theta)$ (to e | What is likelihood actually?
There have been numerous responses including some to your very posts earlier and the present one too.
It should be reiterated that $\mathcal L(\theta\mid \mathbf x) $ or $\ell_\mathbf x(\theta)$ (to emphasize what the argument here is) even though has the same functional form as the corresp... | What is likelihood actually?
There have been numerous responses including some to your very posts earlier and the present one too.
It should be reiterated that $\mathcal L(\theta\mid \mathbf x) $ or $\ell_\mathbf x(\theta)$ (to e |
37,946 | What is likelihood actually? | As stated by many others: the likelihood function $\mathcal L_y$ is the probability density function $f_\theta$ of the observed data $y$, but viewed as a function of the (unknown) parameter $\theta$, i.e., $\mathcal L_y(\theta) = f_\theta(y)$.
To provide some intuition, let's consider discrete data1 and continuous data... | What is likelihood actually? | As stated by many others: the likelihood function $\mathcal L_y$ is the probability density function $f_\theta$ of the observed data $y$, but viewed as a function of the (unknown) parameter $\theta$, | What is likelihood actually?
As stated by many others: the likelihood function $\mathcal L_y$ is the probability density function $f_\theta$ of the observed data $y$, but viewed as a function of the (unknown) parameter $\theta$, i.e., $\mathcal L_y(\theta) = f_\theta(y)$.
To provide some intuition, let's consider discr... | What is likelihood actually?
As stated by many others: the likelihood function $\mathcal L_y$ is the probability density function $f_\theta$ of the observed data $y$, but viewed as a function of the (unknown) parameter $\theta$, |
37,947 | What is likelihood actually? | Likelihood is a slippery concept. The likelihood function, $L(t | w)$, expresses how probable the data $t_n$ are in relation to the model function $y(x,w)$.
The uncertainty in the empirical measurements enters the modeling through the misfits $ε_n$; one misfit for each data point. We introduce a misfit probability dist... | What is likelihood actually? | Likelihood is a slippery concept. The likelihood function, $L(t | w)$, expresses how probable the data $t_n$ are in relation to the model function $y(x,w)$.
The uncertainty in the empirical measuremen | What is likelihood actually?
Likelihood is a slippery concept. The likelihood function, $L(t | w)$, expresses how probable the data $t_n$ are in relation to the model function $y(x,w)$.
The uncertainty in the empirical measurements enters the modeling through the misfits $ε_n$; one misfit for each data point. We introd... | What is likelihood actually?
Likelihood is a slippery concept. The likelihood function, $L(t | w)$, expresses how probable the data $t_n$ are in relation to the model function $y(x,w)$.
The uncertainty in the empirical measuremen |
37,948 | What is likelihood actually? | I am not exactly sure I fully understand the question but I suspect it might come down to understanding what the likelihood function is measuring exactly.
Let $X$ be a (absolutely) continuous random variable and let $f_X(\cdot)$ denote its PDF, also known as the likelihood function. The value of $f_X(a)$ is not equal t... | What is likelihood actually? | I am not exactly sure I fully understand the question but I suspect it might come down to understanding what the likelihood function is measuring exactly.
Let $X$ be a (absolutely) continuous random v | What is likelihood actually?
I am not exactly sure I fully understand the question but I suspect it might come down to understanding what the likelihood function is measuring exactly.
Let $X$ be a (absolutely) continuous random variable and let $f_X(\cdot)$ denote its PDF, also known as the likelihood function. The val... | What is likelihood actually?
I am not exactly sure I fully understand the question but I suspect it might come down to understanding what the likelihood function is measuring exactly.
Let $X$ be a (absolutely) continuous random v |
37,949 | What is likelihood actually? | After studying Tim's answer and realising that code can give me the best short sentences. I realised that I could understand best via code.
The following code outputs the likelihood of a particular mean and variance combination, for a normal distribution and some generated data.
import numpy as np
from scipy.stats impo... | What is likelihood actually? | After studying Tim's answer and realising that code can give me the best short sentences. I realised that I could understand best via code.
The following code outputs the likelihood of a particular me | What is likelihood actually?
After studying Tim's answer and realising that code can give me the best short sentences. I realised that I could understand best via code.
The following code outputs the likelihood of a particular mean and variance combination, for a normal distribution and some generated data.
import nump... | What is likelihood actually?
After studying Tim's answer and realising that code can give me the best short sentences. I realised that I could understand best via code.
The following code outputs the likelihood of a particular me |
37,950 | Is there a GLM bible? | Is there consensus in the field of statistics that one book is the
absolute best source and completely covering every aspect of GLM -
detailing everything from estimation to inference?
No, there is not. However the classic reference about GLM's would be:
McCullagh, P., & Nelder, J.A. (1989). Generalized linear mod... | Is there a GLM bible? | Is there consensus in the field of statistics that one book is the
absolute best source and completely covering every aspect of GLM -
detailing everything from estimation to inference?
No, there | Is there a GLM bible?
Is there consensus in the field of statistics that one book is the
absolute best source and completely covering every aspect of GLM -
detailing everything from estimation to inference?
No, there is not. However the classic reference about GLM's would be:
McCullagh, P., & Nelder, J.A. (1989). ... | Is there a GLM bible?
Is there consensus in the field of statistics that one book is the
absolute best source and completely covering every aspect of GLM -
detailing everything from estimation to inference?
No, there |
37,951 | Is there a GLM bible? | It's hard to beat
Generalized Linear Models.
P. McCullagh, J. Nelder.
CRC Press.
2nd edition, 1989
It is comprehensive. | Is there a GLM bible? | It's hard to beat
Generalized Linear Models.
P. McCullagh, J. Nelder.
CRC Press.
2nd edition, 1989
It is comprehensive. | Is there a GLM bible?
It's hard to beat
Generalized Linear Models.
P. McCullagh, J. Nelder.
CRC Press.
2nd edition, 1989
It is comprehensive. | Is there a GLM bible?
It's hard to beat
Generalized Linear Models.
P. McCullagh, J. Nelder.
CRC Press.
2nd edition, 1989
It is comprehensive. |
37,952 | Is there a GLM bible? | I don't think there is a single book that will be exactly what you want. From your description, I think the best fit would be:
Dobson, AJ & Barnett, A. (2008). An Introduction to Generalized Linear Models. Chapman and Hall.
It is a classic. It does cover the math, but is also more introductory than other books... | Is there a GLM bible? | I don't think there is a single book that will be exactly what you want. From your description, I think the best fit would be:
Dobson, AJ & Barnett, A. (2008). An Introduction to Generalized Linea | Is there a GLM bible?
I don't think there is a single book that will be exactly what you want. From your description, I think the best fit would be:
Dobson, AJ & Barnett, A. (2008). An Introduction to Generalized Linear Models. Chapman and Hall.
It is a classic. It does cover the math, but is also more introdu... | Is there a GLM bible?
I don't think there is a single book that will be exactly what you want. From your description, I think the best fit would be:
Dobson, AJ & Barnett, A. (2008). An Introduction to Generalized Linea |
37,953 | Is there a GLM bible? | The closest thing I've found to a GLM Bible is Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li. It's over 1400 pages and covers linear regression and GLMs. Virtually anything involving GLMs can be found in that book. | Is there a GLM bible? | The closest thing I've found to a GLM Bible is Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li. It's over 1400 pages and covers linear regression and GLMs. Virtually anything | Is there a GLM bible?
The closest thing I've found to a GLM Bible is Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li. It's over 1400 pages and covers linear regression and GLMs. Virtually anything involving GLMs can be found in that book. | Is there a GLM bible?
The closest thing I've found to a GLM Bible is Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li. It's over 1400 pages and covers linear regression and GLMs. Virtually anything |
37,954 | Is there a GLM bible? | A good book is the one by Fahrmeir et al https://www.amazon.com/Multivariate-Statistical-Modelling-Generalized-Statistics/dp/0387951873/ref=sr_1_1?s=books&ie=UTF8&qid=1506715879&sr=1-1 "Multivariate Statistical Modelling Based on Generalized Linear Models (second edition)", maybe not for a first treatment, but for var... | Is there a GLM bible? | A good book is the one by Fahrmeir et al https://www.amazon.com/Multivariate-Statistical-Modelling-Generalized-Statistics/dp/0387951873/ref=sr_1_1?s=books&ie=UTF8&qid=1506715879&sr=1-1 "Multivariate | Is there a GLM bible?
A good book is the one by Fahrmeir et al https://www.amazon.com/Multivariate-Statistical-Modelling-Generalized-Statistics/dp/0387951873/ref=sr_1_1?s=books&ie=UTF8&qid=1506715879&sr=1-1 "Multivariate Statistical Modelling Based on Generalized Linear Models (second edition)", maybe not for a first ... | Is there a GLM bible?
A good book is the one by Fahrmeir et al https://www.amazon.com/Multivariate-Statistical-Modelling-Generalized-Statistics/dp/0387951873/ref=sr_1_1?s=books&ie=UTF8&qid=1506715879&sr=1-1 "Multivariate |
37,955 | Is there a GLM bible? | Introductory books:
An introduction to generalized linear models, by George Dunteman and Moon-Ho Ho (2006). Only 72 pages.
Generalized linear models : a unified approach, by Jeff Gill (2001) This is also short (101 pages).
Then you have more textbook-like, longer books like the one you mention (444 pages), or the one... | Is there a GLM bible? | Introductory books:
An introduction to generalized linear models, by George Dunteman and Moon-Ho Ho (2006). Only 72 pages.
Generalized linear models : a unified approach, by Jeff Gill (2001) This is | Is there a GLM bible?
Introductory books:
An introduction to generalized linear models, by George Dunteman and Moon-Ho Ho (2006). Only 72 pages.
Generalized linear models : a unified approach, by Jeff Gill (2001) This is also short (101 pages).
Then you have more textbook-like, longer books like the one you mention (... | Is there a GLM bible?
Introductory books:
An introduction to generalized linear models, by George Dunteman and Moon-Ho Ho (2006). Only 72 pages.
Generalized linear models : a unified approach, by Jeff Gill (2001) This is |
37,956 | Is there a GLM bible? | The Nelder book already mentioned is a good one.
Just for more consideration I would recommend Elements of Statistical Learning Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman. I Like ESL because it covers such a breadth of statistical and machine learning topics. It shows how GLMs fit in with o... | Is there a GLM bible? | The Nelder book already mentioned is a good one.
Just for more consideration I would recommend Elements of Statistical Learning Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman. | Is there a GLM bible?
The Nelder book already mentioned is a good one.
Just for more consideration I would recommend Elements of Statistical Learning Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman. I Like ESL because it covers such a breadth of statistical and machine learning topics. It shows ... | Is there a GLM bible?
The Nelder book already mentioned is a good one.
Just for more consideration I would recommend Elements of Statistical Learning Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman. |
37,957 | Is the likelihood a true function? | Many books and many posts on this site define the likelihood as a function of model parameters.
If you specify a value for each of the parameters*, you will have at most one value for the likelihood.
(along with everything else you need to have specified, of course)
However, does the output associated with every p... | Is the likelihood a true function? | Many books and many posts on this site define the likelihood as a function of model parameters.
If you specify a value for each of the parameters*, you will have at most one value for the likelihood | Is the likelihood a true function?
Many books and many posts on this site define the likelihood as a function of model parameters.
If you specify a value for each of the parameters*, you will have at most one value for the likelihood.
(along with everything else you need to have specified, of course)
However, does... | Is the likelihood a true function?
Many books and many posts on this site define the likelihood as a function of model parameters.
If you specify a value for each of the parameters*, you will have at most one value for the likelihood |
37,958 | Is the likelihood a true function? | A real-valued function $f$ associates to a vector or real entry $θ\in\Theta$ a real number $f(θ)$, that is,
\begin{align*}f:\ \Theta &\longrightarrow \mathbb{R}\\ \theta &\longrightarrow f(\theta)\end{align*}Once the data $(x_1,\ldots,x_n)$ is observed and thus fixed, the likelihood associates with a given value of the... | Is the likelihood a true function? | A real-valued function $f$ associates to a vector or real entry $θ\in\Theta$ a real number $f(θ)$, that is,
\begin{align*}f:\ \Theta &\longrightarrow \mathbb{R}\\ \theta &\longrightarrow f(\theta)\end | Is the likelihood a true function?
A real-valued function $f$ associates to a vector or real entry $θ\in\Theta$ a real number $f(θ)$, that is,
\begin{align*}f:\ \Theta &\longrightarrow \mathbb{R}\\ \theta &\longrightarrow f(\theta)\end{align*}Once the data $(x_1,\ldots,x_n)$ is observed and thus fixed, the likelihood a... | Is the likelihood a true function?
A real-valued function $f$ associates to a vector or real entry $θ\in\Theta$ a real number $f(θ)$, that is,
\begin{align*}f:\ \Theta &\longrightarrow \mathbb{R}\\ \theta &\longrightarrow f(\theta)\end |
37,959 | Is the likelihood a true function? | This is closely related to the concept of identifiability in mathematical statistics, which I think relates to your question. Identifiability deals with the possibility that a poorly-specified model may lack a one-to-one relationship between parameter sets and probability distributions over the data, and this causes p... | Is the likelihood a true function? | This is closely related to the concept of identifiability in mathematical statistics, which I think relates to your question. Identifiability deals with the possibility that a poorly-specified model | Is the likelihood a true function?
This is closely related to the concept of identifiability in mathematical statistics, which I think relates to your question. Identifiability deals with the possibility that a poorly-specified model may lack a one-to-one relationship between parameter sets and probability distributio... | Is the likelihood a true function?
This is closely related to the concept of identifiability in mathematical statistics, which I think relates to your question. Identifiability deals with the possibility that a poorly-specified model |
37,960 | What is it called to use random error as evidence? | $p$-value hacking
I’ve learned that the headline-grabbing cases of misconduct and fraud are mere distractions. The state of our science is strong, but it’s plagued by a universal problem: Science is hard — really f**ing hard. If we’re going to rely on science as a means for reaching the truth — and it’s still the best... | What is it called to use random error as evidence? | $p$-value hacking
I’ve learned that the headline-grabbing cases of misconduct and fraud are mere distractions. The state of our science is strong, but it’s plagued by a universal problem: Science is | What is it called to use random error as evidence?
$p$-value hacking
I’ve learned that the headline-grabbing cases of misconduct and fraud are mere distractions. The state of our science is strong, but it’s plagued by a universal problem: Science is hard — really f**ing hard. If we’re going to rely on science as a mea... | What is it called to use random error as evidence?
$p$-value hacking
I’ve learned that the headline-grabbing cases of misconduct and fraud are mere distractions. The state of our science is strong, but it’s plagued by a universal problem: Science is |
37,961 | What is it called to use random error as evidence? | Cherry picking, suppressing evidence, or the fallacy of incomplete evidence ... you can check Wikipedia:
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular position while ignoring a significant portion of rela... | What is it called to use random error as evidence? | Cherry picking, suppressing evidence, or the fallacy of incomplete evidence ... you can check Wikipedia:
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of poin | What is it called to use random error as evidence?
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence ... you can check Wikipedia:
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of pointing to individual cases or data that seem to confirm a particular po... | What is it called to use random error as evidence?
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence ... you can check Wikipedia:
Cherry picking, suppressing evidence, or the fallacy of incomplete evidence is the act of poin |
37,962 | What is it called to use random error as evidence? | Although the technical details may deter folk from answering, they are secondary to your main question about English terminology.
Nevertheless, let's get them out of the way. You have 95% confidence in the results; I take this to mean you knew that 5 in a hundred fail. The chance of randomly picking 1 success from a ba... | What is it called to use random error as evidence? | Although the technical details may deter folk from answering, they are secondary to your main question about English terminology.
Nevertheless, let's get them out of the way. You have 95% confidence i | What is it called to use random error as evidence?
Although the technical details may deter folk from answering, they are secondary to your main question about English terminology.
Nevertheless, let's get them out of the way. You have 95% confidence in the results; I take this to mean you knew that 5 in a hundred fail.... | What is it called to use random error as evidence?
Although the technical details may deter folk from answering, they are secondary to your main question about English terminology.
Nevertheless, let's get them out of the way. You have 95% confidence i |
37,963 | What is it called to use random error as evidence? | If the trials are being tested with a variety of statistical methods, and only the "successful" ones publicized, then the primary term for this would be data dredging. From Wikipedia:
Data dredging (also data fishing, data snooping, data butchery, and p-hacking) is the misuse of data analysis to find
patterns in data ... | What is it called to use random error as evidence? | If the trials are being tested with a variety of statistical methods, and only the "successful" ones publicized, then the primary term for this would be data dredging. From Wikipedia:
Data dredging ( | What is it called to use random error as evidence?
If the trials are being tested with a variety of statistical methods, and only the "successful" ones publicized, then the primary term for this would be data dredging. From Wikipedia:
Data dredging (also data fishing, data snooping, data butchery, and p-hacking) is th... | What is it called to use random error as evidence?
If the trials are being tested with a variety of statistical methods, and only the "successful" ones publicized, then the primary term for this would be data dredging. From Wikipedia:
Data dredging ( |
37,964 | What is it called to use random error as evidence? | There's the term publication bias, but that's more about studies done by different researchers where only the researchers who get "good" results publish them. A similar term is "file drawer effect".
The term p-hacking doesn't quite apply, as p-hacking refers to cherry-picking a metric for a particular data set, not che... | What is it called to use random error as evidence? | There's the term publication bias, but that's more about studies done by different researchers where only the researchers who get "good" results publish them. A similar term is "file drawer effect".
T | What is it called to use random error as evidence?
There's the term publication bias, but that's more about studies done by different researchers where only the researchers who get "good" results publish them. A similar term is "file drawer effect".
The term p-hacking doesn't quite apply, as p-hacking refers to cherry-... | What is it called to use random error as evidence?
There's the term publication bias, but that's more about studies done by different researchers where only the researchers who get "good" results publish them. A similar term is "file drawer effect".
T |
37,965 | In training a triplet network, I first have a solid drop in loss, but eventually the loss slowly but consistently increases. What could cause this? | Triplet models are notoriously tricky to train. Before starting a triplet loss project, I strongly recommend reading "FaceNet: A Unified Embedding for Face Recognition and Clustering" by Florian Schroff, Dmitry Kalenichenko, James Philbin because it outlines some of the key problems that arise when using triplet losses... | In training a triplet network, I first have a solid drop in loss, but eventually the loss slowly but | Triplet models are notoriously tricky to train. Before starting a triplet loss project, I strongly recommend reading "FaceNet: A Unified Embedding for Face Recognition and Clustering" by Florian Schro | In training a triplet network, I first have a solid drop in loss, but eventually the loss slowly but consistently increases. What could cause this?
Triplet models are notoriously tricky to train. Before starting a triplet loss project, I strongly recommend reading "FaceNet: A Unified Embedding for Face Recognition and ... | In training a triplet network, I first have a solid drop in loss, but eventually the loss slowly but
Triplet models are notoriously tricky to train. Before starting a triplet loss project, I strongly recommend reading "FaceNet: A Unified Embedding for Face Recognition and Clustering" by Florian Schro |
37,966 | Jaccard similarity in R | Looking at the Wikipedia page's edit history, it seems the problem was due to a confusion about the two types of mathematical notation that are used to represent the index. Using notation from set theory, we have:
$$
J(A,B) = \frac{|A\cap B|}{|A\cup B|} = \frac{|A\cap B|}{|A| + |B| - |A\cap B|}
$$
where $\cap$ denotes... | Jaccard similarity in R | Looking at the Wikipedia page's edit history, it seems the problem was due to a confusion about the two types of mathematical notation that are used to represent the index. Using notation from set th | Jaccard similarity in R
Looking at the Wikipedia page's edit history, it seems the problem was due to a confusion about the two types of mathematical notation that are used to represent the index. Using notation from set theory, we have:
$$
J(A,B) = \frac{|A\cap B|}{|A\cup B|} = \frac{|A\cap B|}{|A| + |B| - |A\cap B|}... | Jaccard similarity in R
Looking at the Wikipedia page's edit history, it seems the problem was due to a confusion about the two types of mathematical notation that are used to represent the index. Using notation from set th |
37,967 | Jaccard similarity in R | That formula is wrong indeed.
It should be m11 / (m01 + m10 + m11), since the Jaccard index is the size of the intersection between two sets, divided by the size of the union between those sets.
The correct value is 8 / (12 + 23 + 8) = 0.186. I find it weird though, that this is not the same value you get from the R p... | Jaccard similarity in R | That formula is wrong indeed.
It should be m11 / (m01 + m10 + m11), since the Jaccard index is the size of the intersection between two sets, divided by the size of the union between those sets.
The | Jaccard similarity in R
That formula is wrong indeed.
It should be m11 / (m01 + m10 + m11), since the Jaccard index is the size of the intersection between two sets, divided by the size of the union between those sets.
The correct value is 8 / (12 + 23 + 8) = 0.186. I find it weird though, that this is not the same va... | Jaccard similarity in R
That formula is wrong indeed.
It should be m11 / (m01 + m10 + m11), since the Jaccard index is the size of the intersection between two sets, divided by the size of the union between those sets.
The |
37,968 | Jaccard similarity in R | I wrote a simple function for calculating the Jaccard index (similarity coefficient) and the complementary Jaccard distance for binary attributes:
# Your dataset
df2 <- data.frame(
IDS = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),... | Jaccard similarity in R | I wrote a simple function for calculating the Jaccard index (similarity coefficient) and the complementary Jaccard distance for binary attributes:
# Your dataset
df2 <- data.frame(
IDS = c(1, 1, 1, | Jaccard similarity in R
I wrote a simple function for calculating the Jaccard index (similarity coefficient) and the complementary Jaccard distance for binary attributes:
# Your dataset
df2 <- data.frame(
IDS = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, ... | Jaccard similarity in R
I wrote a simple function for calculating the Jaccard index (similarity coefficient) and the complementary Jaccard distance for binary attributes:
# Your dataset
df2 <- data.frame(
IDS = c(1, 1, 1, |
37,969 | Jaccard similarity in R | Solved. The problem was that Wikipedia actually is wrong, specifically the formula:
m11/(m10+m01-m11) | Jaccard similarity in R | Solved. The problem was that Wikipedia actually is wrong, specifically the formula:
m11/(m10+m01-m11) | Jaccard similarity in R
Solved. The problem was that Wikipedia actually is wrong, specifically the formula:
m11/(m10+m01-m11) | Jaccard similarity in R
Solved. The problem was that Wikipedia actually is wrong, specifically the formula:
m11/(m10+m01-m11) |
37,970 | Jaccard similarity in R | Augmentation of @jsb's code to enable a similarity measure across all observations.
# Jaccar Index
library(dplyr)
# Your dataset
df <- data.frame(t(data.frame(c1=rnorm(100),
c2=rnorm(100),
c3=rnorm(100),
c4=rnorm(100),
... | Jaccard similarity in R | Augmentation of @jsb's code to enable a similarity measure across all observations.
# Jaccar Index
library(dplyr)
# Your dataset
df <- data.frame(t(data.frame(c1=rnorm(100),
| Jaccard similarity in R
Augmentation of @jsb's code to enable a similarity measure across all observations.
# Jaccar Index
library(dplyr)
# Your dataset
df <- data.frame(t(data.frame(c1=rnorm(100),
c2=rnorm(100),
c3=rnorm(100),
c... | Jaccard similarity in R
Augmentation of @jsb's code to enable a similarity measure across all observations.
# Jaccar Index
library(dplyr)
# Your dataset
df <- data.frame(t(data.frame(c1=rnorm(100),
|
37,971 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | Short answer in words: they're both equal to the probability of (A and B) occurring.
(Probability of A) times (Probability of B, given that A has happened) equals (Probability that both A and B happen).
Similarly, (Probability of B) times (Probability of A, given that B has happened) equals (Probability that both A an... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | Short answer in words: they're both equal to the probability of (A and B) occurring.
(Probability of A) times (Probability of B, given that A has happened) equals (Probability that both A and B happe | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
Short answer in words: they're both equal to the probability of (A and B) occurring.
(Probability of A) times (Probability of B, given that A has happened) equals (Probability that both A and B happen).
Similarly, (Probability of B) times (Probability of A, given that ... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
Short answer in words: they're both equal to the probability of (A and B) occurring.
(Probability of A) times (Probability of B, given that A has happened) equals (Probability that both A and B happe |
37,972 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | First, recall
$$P(A|B)=\frac{P(A∩B)}{P(B)}$$
and consequently
$$P(A∩B)=P(A|B)P(B)$$
The trick here is to realize the very simple fact that $P(A∩B)= P(B∩A)$. This fact is quite intuitive; the probability that UNC wins and Duke loses is the same as the probability that Duke loses and UNC wins. So, in reality, we have tw... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | First, recall
$$P(A|B)=\frac{P(A∩B)}{P(B)}$$
and consequently
$$P(A∩B)=P(A|B)P(B)$$
The trick here is to realize the very simple fact that $P(A∩B)= P(B∩A)$. This fact is quite intuitive; the probabil | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
First, recall
$$P(A|B)=\frac{P(A∩B)}{P(B)}$$
and consequently
$$P(A∩B)=P(A|B)P(B)$$
The trick here is to realize the very simple fact that $P(A∩B)= P(B∩A)$. This fact is quite intuitive; the probability that UNC wins and Duke loses is the same as the probability that D... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
First, recall
$$P(A|B)=\frac{P(A∩B)}{P(B)}$$
and consequently
$$P(A∩B)=P(A|B)P(B)$$
The trick here is to realize the very simple fact that $P(A∩B)= P(B∩A)$. This fact is quite intuitive; the probabil |
37,973 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | If $A$ and $B$ are events such that $P(A), P(B) > 0$, how can I compute the probability that both events occurred? That is, how can I determine $P(A\cap B)$?
Well, if $A$ and $B$ are independent events, then I know that
$$P(A\cap B) = P(A)P(B)\tag{1}$$
(that is just the definition of independence) and so $P(A\cap B)$ i... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | If $A$ and $B$ are events such that $P(A), P(B) > 0$, how can I compute the probability that both events occurred? That is, how can I determine $P(A\cap B)$?
Well, if $A$ and $B$ are independent event | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
If $A$ and $B$ are events such that $P(A), P(B) > 0$, how can I compute the probability that both events occurred? That is, how can I determine $P(A\cap B)$?
Well, if $A$ and $B$ are independent events, then I know that
$$P(A\cap B) = P(A)P(B)\tag{1}$$
(that is just the... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
If $A$ and $B$ are events such that $P(A), P(B) > 0$, how can I compute the probability that both events occurred? That is, how can I determine $P(A\cap B)$?
Well, if $A$ and $B$ are independent event |
37,974 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | Just trying a graphical intuition... Hope it flies... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | Just trying a graphical intuition... Hope it flies... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
Just trying a graphical intuition... Hope it flies... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
Just trying a graphical intuition... Hope it flies... |
37,975 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | $p(B\mid A)p(A) = p(B\cap A)=p(A\mid B)p(B)$ | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | $p(B\mid A)p(A) = p(B\cap A)=p(A\mid B)p(B)$ | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
$p(B\mid A)p(A) = p(B\cap A)=p(A\mid B)p(B)$ | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
$p(B\mid A)p(A) = p(B\cap A)=p(A\mid B)p(B)$ |
37,976 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | A simple example is like this. Suppose we have A containing two events, "A = 1" or "A = 2", and B containing three events, "B = 1", "B = 2", or "B = 3". The (arbitrary) cell counts for the occurrence of the events are listed in the following table.
Now we can do a simple example:
\begin{align*}
P(A=1) & = \frac{6}{21}... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | A simple example is like this. Suppose we have A containing two events, "A = 1" or "A = 2", and B containing three events, "B = 1", "B = 2", or "B = 3". The (arbitrary) cell counts for the occurrence | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
A simple example is like this. Suppose we have A containing two events, "A = 1" or "A = 2", and B containing three events, "B = 1", "B = 2", or "B = 3". The (arbitrary) cell counts for the occurrence of the events are listed in the following table.
Now we can do a simp... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
A simple example is like this. Suppose we have A containing two events, "A = 1" or "A = 2", and B containing three events, "B = 1", "B = 2", or "B = 3". The (arbitrary) cell counts for the occurrence |
37,977 | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | Let us motivate the formula for conditional probability. We keep things are simple as possible. $S$, our sample space, will be finite. Let $E$ and $F$ be subsets of it (events).
When we write, $P(E|F)$ we are saying, "probability of $E$ given $F$". Thus, instead of the possibilities being in $S$, they are now all in $F... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$? | Let us motivate the formula for conditional probability. We keep things are simple as possible. $S$, our sample space, will be finite. Let $E$ and $F$ be subsets of it (events).
When we write, $P(E|F) | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
Let us motivate the formula for conditional probability. We keep things are simple as possible. $S$, our sample space, will be finite. Let $E$ and $F$ be subsets of it (events).
When we write, $P(E|F)$ we are saying, "probability of $E$ given $F$". Thus, instead of the ... | Why is $p(A) \times p(B|A) = p(B) \times p(A|B)$?
Let us motivate the formula for conditional probability. We keep things are simple as possible. $S$, our sample space, will be finite. Let $E$ and $F$ be subsets of it (events).
When we write, $P(E|F) |
37,978 | Model evaluation and comparison for selecting the best model | You are using a wide range of different types of models, and that makes this an interesting situation. Usually, when people say they are engaged in model selection, they mean that they have one type of model, with differing sets of predictors (for example, a multiple regression model with variables A, B, C & D, versus... | Model evaluation and comparison for selecting the best model | You are using a wide range of different types of models, and that makes this an interesting situation. Usually, when people say they are engaged in model selection, they mean that they have one type | Model evaluation and comparison for selecting the best model
You are using a wide range of different types of models, and that makes this an interesting situation. Usually, when people say they are engaged in model selection, they mean that they have one type of model, with differing sets of predictors (for example,... | Model evaluation and comparison for selecting the best model
You are using a wide range of different types of models, and that makes this an interesting situation. Usually, when people say they are engaged in model selection, they mean that they have one type |
37,979 | Model evaluation and comparison for selecting the best model | In my mind, cross-validation is a pretty solid gold standard for making comparisons that focus on models' abilities to predict new data. That said, for the GLM case at least, AIC has been demonstrated (Stone, 1977) to be asymptotically equivalent to cross-validation, so if you're ok with asymptotic assumption, you can ... | Model evaluation and comparison for selecting the best model | In my mind, cross-validation is a pretty solid gold standard for making comparisons that focus on models' abilities to predict new data. That said, for the GLM case at least, AIC has been demonstrated | Model evaluation and comparison for selecting the best model
In my mind, cross-validation is a pretty solid gold standard for making comparisons that focus on models' abilities to predict new data. That said, for the GLM case at least, AIC has been demonstrated (Stone, 1977) to be asymptotically equivalent to cross-v... | Model evaluation and comparison for selecting the best model
In my mind, cross-validation is a pretty solid gold standard for making comparisons that focus on models' abilities to predict new data. That said, for the GLM case at least, AIC has been demonstrated |
37,980 | Model evaluation and comparison for selecting the best model | Assuming yo are using classification error or something similar as your performance measure, then why don't you try cross validation of all models?
Split your data into, say, 10 chunks, and then do 10 rounds of build and test using one of those chunks as the test set and the other nine as the training (ie. round1: trai... | Model evaluation and comparison for selecting the best model | Assuming yo are using classification error or something similar as your performance measure, then why don't you try cross validation of all models?
Split your data into, say, 10 chunks, and then do 10 | Model evaluation and comparison for selecting the best model
Assuming yo are using classification error or something similar as your performance measure, then why don't you try cross validation of all models?
Split your data into, say, 10 chunks, and then do 10 rounds of build and test using one of those chunks as th... | Model evaluation and comparison for selecting the best model
Assuming yo are using classification error or something similar as your performance measure, then why don't you try cross validation of all models?
Split your data into, say, 10 chunks, and then do 10 |
37,981 | Transforming the dummy values to be able to take logs | Just because you're taking logs of some of the variables in your model, there's no reason you have to take logs of all of them. Leave a 0/1 coded dummy variable as it is. | Transforming the dummy values to be able to take logs | Just because you're taking logs of some of the variables in your model, there's no reason you have to take logs of all of them. Leave a 0/1 coded dummy variable as it is. | Transforming the dummy values to be able to take logs
Just because you're taking logs of some of the variables in your model, there's no reason you have to take logs of all of them. Leave a 0/1 coded dummy variable as it is. | Transforming the dummy values to be able to take logs
Just because you're taking logs of some of the variables in your model, there's no reason you have to take logs of all of them. Leave a 0/1 coded dummy variable as it is. |
37,982 | Transforming the dummy values to be able to take logs | I agree with onestop. You may also find this blog post from Econometrics Beat useful in learning how to interpret the coefficients on dummy variables when the dependent variable is logged:
http://davegiles.blogspot.com/2011/03/dummies-for-dummies.html
The Cliffs Notes version is that for a model like
\begin{equation}... | Transforming the dummy values to be able to take logs | I agree with onestop. You may also find this blog post from Econometrics Beat useful in learning how to interpret the coefficients on dummy variables when the dependent variable is logged:
http://dave | Transforming the dummy values to be able to take logs
I agree with onestop. You may also find this blog post from Econometrics Beat useful in learning how to interpret the coefficients on dummy variables when the dependent variable is logged:
http://davegiles.blogspot.com/2011/03/dummies-for-dummies.html
The Cliffs No... | Transforming the dummy values to be able to take logs
I agree with onestop. You may also find this blog post from Econometrics Beat useful in learning how to interpret the coefficients on dummy variables when the dependent variable is logged:
http://dave |
37,983 | Efficient way to merge multiple dataframes in R [closed] | You could cat them within R as follows:
read.table(pipe("cat bigfile1.txt bigfile2.txt bigfile3.txt")) | Efficient way to merge multiple dataframes in R [closed] | You could cat them within R as follows:
read.table(pipe("cat bigfile1.txt bigfile2.txt bigfile3.txt")) | Efficient way to merge multiple dataframes in R [closed]
You could cat them within R as follows:
read.table(pipe("cat bigfile1.txt bigfile2.txt bigfile3.txt")) | Efficient way to merge multiple dataframes in R [closed]
You could cat them within R as follows:
read.table(pipe("cat bigfile1.txt bigfile2.txt bigfile3.txt")) |
37,984 | Efficient way to merge multiple dataframes in R [closed] | Since you mention that they have the same column layout, you probably want the three (or more) data.frames to be appended below eachother, right?
In that case, you can look at rbind:
cres = rbind(c, c1, c2)
Beware, though: with a lot of data.frames, I've noticed the performance to be subpar (this has to do with the wa... | Efficient way to merge multiple dataframes in R [closed] | Since you mention that they have the same column layout, you probably want the three (or more) data.frames to be appended below eachother, right?
In that case, you can look at rbind:
cres = rbind(c, c | Efficient way to merge multiple dataframes in R [closed]
Since you mention that they have the same column layout, you probably want the three (or more) data.frames to be appended below eachother, right?
In that case, you can look at rbind:
cres = rbind(c, c1, c2)
Beware, though: with a lot of data.frames, I've noticed... | Efficient way to merge multiple dataframes in R [closed]
Since you mention that they have the same column layout, you probably want the three (or more) data.frames to be appended below eachother, right?
In that case, you can look at rbind:
cres = rbind(c, c |
37,985 | Efficient way to merge multiple dataframes in R [closed] | Check out rbind.fill from plyr package. I've recently seen Hadley's comment that it is efficient but unable to find it. | Efficient way to merge multiple dataframes in R [closed] | Check out rbind.fill from plyr package. I've recently seen Hadley's comment that it is efficient but unable to find it. | Efficient way to merge multiple dataframes in R [closed]
Check out rbind.fill from plyr package. I've recently seen Hadley's comment that it is efficient but unable to find it. | Efficient way to merge multiple dataframes in R [closed]
Check out rbind.fill from plyr package. I've recently seen Hadley's comment that it is efficient but unable to find it. |
37,986 | Efficient way to merge multiple dataframes in R [closed] | If by efficient you mean "fast," check out the data.table package. It has very fast mergers. | Efficient way to merge multiple dataframes in R [closed] | If by efficient you mean "fast," check out the data.table package. It has very fast mergers. | Efficient way to merge multiple dataframes in R [closed]
If by efficient you mean "fast," check out the data.table package. It has very fast mergers. | Efficient way to merge multiple dataframes in R [closed]
If by efficient you mean "fast," check out the data.table package. It has very fast mergers. |
37,987 | Efficient way to merge multiple dataframes in R [closed] | You can try join statement in sqldf package. I find working with SQL in case large dataset much easier. Please find the link here for reference | Efficient way to merge multiple dataframes in R [closed] | You can try join statement in sqldf package. I find working with SQL in case large dataset much easier. Please find the link here for reference | Efficient way to merge multiple dataframes in R [closed]
You can try join statement in sqldf package. I find working with SQL in case large dataset much easier. Please find the link here for reference | Efficient way to merge multiple dataframes in R [closed]
You can try join statement in sqldf package. I find working with SQL in case large dataset much easier. Please find the link here for reference |
37,988 | Can arbitrary precision calculations be useful for machine learning? | No, it is almost never a problem. First of all, there's a measurement error—even physicists account for it, while the rest of us rarely can be lucky enough for as precise measurements as theirs. Second, you are dealing with sampled data, so there is error due to sampling. Finally, we have all kinds of biases and noise ... | Can arbitrary precision calculations be useful for machine learning? | No, it is almost never a problem. First of all, there's a measurement error—even physicists account for it, while the rest of us rarely can be lucky enough for as precise measurements as theirs. Secon | Can arbitrary precision calculations be useful for machine learning?
No, it is almost never a problem. First of all, there's a measurement error—even physicists account for it, while the rest of us rarely can be lucky enough for as precise measurements as theirs. Second, you are dealing with sampled data, so there is e... | Can arbitrary precision calculations be useful for machine learning?
No, it is almost never a problem. First of all, there's a measurement error—even physicists account for it, while the rest of us rarely can be lucky enough for as precise measurements as theirs. Secon |
37,989 | Can arbitrary precision calculations be useful for machine learning? | Yes, precision can be problematic on multiple fronts. First, regression itself generally approaches a flat region, like the bottom of a parabola, where the minimum loss function of the regression is located. This typically halves the number of significant figures in the loss function and may reduce the precision of any... | Can arbitrary precision calculations be useful for machine learning? | Yes, precision can be problematic on multiple fronts. First, regression itself generally approaches a flat region, like the bottom of a parabola, where the minimum loss function of the regression is l | Can arbitrary precision calculations be useful for machine learning?
Yes, precision can be problematic on multiple fronts. First, regression itself generally approaches a flat region, like the bottom of a parabola, where the minimum loss function of the regression is located. This typically halves the number of signifi... | Can arbitrary precision calculations be useful for machine learning?
Yes, precision can be problematic on multiple fronts. First, regression itself generally approaches a flat region, like the bottom of a parabola, where the minimum loss function of the regression is l |
37,990 | Are discrete random variables, with same domain and uniform probability, always independent? | It is simple to construct an example where both variables are marginally uniformly distributed, but they are not independent. The simplest example is to take $X \sim \text{U} \{ -1,0,1 \}$ and let $Y=X$. In this case both of the variables have a uniform distribution, but they are perfectly correlated. | Are discrete random variables, with same domain and uniform probability, always independent? | It is simple to construct an example where both variables are marginally uniformly distributed, but they are not independent. The simplest example is to take $X \sim \text{U} \{ -1,0,1 \}$ and let $Y | Are discrete random variables, with same domain and uniform probability, always independent?
It is simple to construct an example where both variables are marginally uniformly distributed, but they are not independent. The simplest example is to take $X \sim \text{U} \{ -1,0,1 \}$ and let $Y=X$. In this case both of ... | Are discrete random variables, with same domain and uniform probability, always independent?
It is simple to construct an example where both variables are marginally uniformly distributed, but they are not independent. The simplest example is to take $X \sim \text{U} \{ -1,0,1 \}$ and let $Y |
37,991 | Are discrete random variables, with same domain and uniform probability, always independent? | You can say $X$ and $Y$ each have mean $0$ and variance $\frac23$ and in general
Their covariance is equal to $\mathbb E[XY]$ here and can be any value between $-\frac23$ and $+\frac23$ so their correlation can be any value between $-1$ and $+1$
$\mathbb P[XY=+1]$ and $\mathbb P[XY=-1]$ can each be between $0$ and $\f... | Are discrete random variables, with same domain and uniform probability, always independent? | You can say $X$ and $Y$ each have mean $0$ and variance $\frac23$ and in general
Their covariance is equal to $\mathbb E[XY]$ here and can be any value between $-\frac23$ and $+\frac23$ so their corr | Are discrete random variables, with same domain and uniform probability, always independent?
You can say $X$ and $Y$ each have mean $0$ and variance $\frac23$ and in general
Their covariance is equal to $\mathbb E[XY]$ here and can be any value between $-\frac23$ and $+\frac23$ so their correlation can be any value be... | Are discrete random variables, with same domain and uniform probability, always independent?
You can say $X$ and $Y$ each have mean $0$ and variance $\frac23$ and in general
Their covariance is equal to $\mathbb E[XY]$ here and can be any value between $-\frac23$ and $+\frac23$ so their corr |
37,992 | Are discrete random variables, with same domain and uniform probability, always independent? | No, suppose you have $X$ as you described and for $Y$ you flip a coin and in 0.5 probability it takes the value of $X$ otherwise you uniformly sample from $\{-1,0,1\}$.
The marginal probabilities will be uniform yet they are obviously dependent. Short simulation below.
x <- sample(c(-1, 0, 1), 100000, TRUE)
coin <- ... | Are discrete random variables, with same domain and uniform probability, always independent? | No, suppose you have $X$ as you described and for $Y$ you flip a coin and in 0.5 probability it takes the value of $X$ otherwise you uniformly sample from $\{-1,0,1\}$.
The marginal probabilities will | Are discrete random variables, with same domain and uniform probability, always independent?
No, suppose you have $X$ as you described and for $Y$ you flip a coin and in 0.5 probability it takes the value of $X$ otherwise you uniformly sample from $\{-1,0,1\}$.
The marginal probabilities will be uniform yet they are ob... | Are discrete random variables, with same domain and uniform probability, always independent?
No, suppose you have $X$ as you described and for $Y$ you flip a coin and in 0.5 probability it takes the value of $X$ otherwise you uniformly sample from $\{-1,0,1\}$.
The marginal probabilities will |
37,993 | Why do I see a pattern in the residuals in this well specified model? | How close the residuals at specific $x$ values are to zero depends on the sample size. Now, the sample size in real examples will be whatever it is, so there's not much use saying it should be bigger, but you do need to calibrate your expectations of what sort of departures from zero mean are detectable with small samp... | Why do I see a pattern in the residuals in this well specified model? | How close the residuals at specific $x$ values are to zero depends on the sample size. Now, the sample size in real examples will be whatever it is, so there's not much use saying it should be bigger, | Why do I see a pattern in the residuals in this well specified model?
How close the residuals at specific $x$ values are to zero depends on the sample size. Now, the sample size in real examples will be whatever it is, so there's not much use saying it should be bigger, but you do need to calibrate your expectations of... | Why do I see a pattern in the residuals in this well specified model?
How close the residuals at specific $x$ values are to zero depends on the sample size. Now, the sample size in real examples will be whatever it is, so there's not much use saying it should be bigger, |
37,994 | Why do I see a pattern in the residuals in this well specified model? | Thomas answer is great (+1), I just wanted to clear up a particular confusion in the wording of your question:
there is a pattern in the residuals, they don't seem to be zero-mean.
The mean is zero. You can easily check this:
set.seed(1)
df <- data.frame(id=seq(1, 12, 1))
df$age <- c(18, 19, 20, 40, 41, 42,
... | Why do I see a pattern in the residuals in this well specified model? | Thomas answer is great (+1), I just wanted to clear up a particular confusion in the wording of your question:
there is a pattern in the residuals, they don't seem to be zero-mean.
The mean is zero. | Why do I see a pattern in the residuals in this well specified model?
Thomas answer is great (+1), I just wanted to clear up a particular confusion in the wording of your question:
there is a pattern in the residuals, they don't seem to be zero-mean.
The mean is zero. You can easily check this:
set.seed(1)
df <- data... | Why do I see a pattern in the residuals in this well specified model?
Thomas answer is great (+1), I just wanted to clear up a particular confusion in the wording of your question:
there is a pattern in the residuals, they don't seem to be zero-mean.
The mean is zero. |
37,995 | Understanding standard errors on a regression table | The standard error determines how much variability "surrounds" a coefficient estimate. A coefficient is significant if it is non-zero. The typical rule of thumb, is that you go about two standard deviations above and below the estimate to get a 95% confidence interval for a coefficient estimate.
So most likely what... | Understanding standard errors on a regression table | The standard error determines how much variability "surrounds" a coefficient estimate. A coefficient is significant if it is non-zero. The typical rule of thumb, is that you go about two standard de | Understanding standard errors on a regression table
The standard error determines how much variability "surrounds" a coefficient estimate. A coefficient is significant if it is non-zero. The typical rule of thumb, is that you go about two standard deviations above and below the estimate to get a 95% confidence interv... | Understanding standard errors on a regression table
The standard error determines how much variability "surrounds" a coefficient estimate. A coefficient is significant if it is non-zero. The typical rule of thumb, is that you go about two standard de |
37,996 | Understanding standard errors on a regression table | I will stick to the case of a simple linear regression. Generalisation to multiple regression is straightforward in the principles albeit ugly in the algebra. Imagine we have some values of a predictor or explanatory variable, $x_i$, and we observe the values of the response variable at those points, $y_i$. If the true... | Understanding standard errors on a regression table | I will stick to the case of a simple linear regression. Generalisation to multiple regression is straightforward in the principles albeit ugly in the algebra. Imagine we have some values of a predicto | Understanding standard errors on a regression table
I will stick to the case of a simple linear regression. Generalisation to multiple regression is straightforward in the principles albeit ugly in the algebra. Imagine we have some values of a predictor or explanatory variable, $x_i$, and we observe the values of the r... | Understanding standard errors on a regression table
I will stick to the case of a simple linear regression. Generalisation to multiple regression is straightforward in the principles albeit ugly in the algebra. Imagine we have some values of a predicto |
37,997 | Understanding standard errors on a regression table | The SE is a measure of precision of the estimate. It also can indicate model fit problems. For example, if it is abnormally large relative to the coefficient then that is a red flag for (multi)collinearity. The model is essentially unable to precisely estimate the parameter because of collinearity with one or more o... | Understanding standard errors on a regression table | The SE is a measure of precision of the estimate. It also can indicate model fit problems. For example, if it is abnormally large relative to the coefficient then that is a red flag for (multi)colli | Understanding standard errors on a regression table
The SE is a measure of precision of the estimate. It also can indicate model fit problems. For example, if it is abnormally large relative to the coefficient then that is a red flag for (multi)collinearity. The model is essentially unable to precisely estimate the ... | Understanding standard errors on a regression table
The SE is a measure of precision of the estimate. It also can indicate model fit problems. For example, if it is abnormally large relative to the coefficient then that is a red flag for (multi)colli |
37,998 | Understanding standard errors on a regression table | If you can divide the coefficient by its standard error in your head, you can use these rough rules of thumb assuming the sample size is "large" and you don't have "too many" regressors. When this is not the case, you should really be using the $t$ distribution, but most people don't have it readily available in their ... | Understanding standard errors on a regression table | If you can divide the coefficient by its standard error in your head, you can use these rough rules of thumb assuming the sample size is "large" and you don't have "too many" regressors. When this is | Understanding standard errors on a regression table
If you can divide the coefficient by its standard error in your head, you can use these rough rules of thumb assuming the sample size is "large" and you don't have "too many" regressors. When this is not the case, you should really be using the $t$ distribution, but m... | Understanding standard errors on a regression table
If you can divide the coefficient by its standard error in your head, you can use these rough rules of thumb assuming the sample size is "large" and you don't have "too many" regressors. When this is |
37,999 | Understanding standard errors on a regression table | Picking up on Underminer, regression coefficients are estimates of a population parameter. Due to sampling error (and other things if you have accounted for them), the SE shows you how much uncertainty there is around your estimate. If you calculate a 95% confidence interval using the standard error, that will give you... | Understanding standard errors on a regression table | Picking up on Underminer, regression coefficients are estimates of a population parameter. Due to sampling error (and other things if you have accounted for them), the SE shows you how much uncertaint | Understanding standard errors on a regression table
Picking up on Underminer, regression coefficients are estimates of a population parameter. Due to sampling error (and other things if you have accounted for them), the SE shows you how much uncertainty there is around your estimate. If you calculate a 95% confidence i... | Understanding standard errors on a regression table
Picking up on Underminer, regression coefficients are estimates of a population parameter. Due to sampling error (and other things if you have accounted for them), the SE shows you how much uncertaint |
38,000 | Are there useful applications of SVD that use only the smallest singular values? | It acts like a highpass filter in a slightly different space.
There is lots of linear data, and in many cases you are looking for that linear relationship, so a low-pass (high-blocking) filter lets you retain the important part.
For non-linear data, usually stuff that you have applied the simple methods without suc... | Are there useful applications of SVD that use only the smallest singular values? | It acts like a highpass filter in a slightly different space.
There is lots of linear data, and in many cases you are looking for that linear relationship, so a low-pass (high-blocking) filter lets | Are there useful applications of SVD that use only the smallest singular values?
It acts like a highpass filter in a slightly different space.
There is lots of linear data, and in many cases you are looking for that linear relationship, so a low-pass (high-blocking) filter lets you retain the important part.
For no... | Are there useful applications of SVD that use only the smallest singular values?
It acts like a highpass filter in a slightly different space.
There is lots of linear data, and in many cases you are looking for that linear relationship, so a low-pass (high-blocking) filter lets |
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