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 |
|---|---|---|---|---|---|---|
6,201 | Logistic Regression: Bernoulli vs. Binomial Response Variables | 1) Yes. You can aggregate/de-aggregate (?) binomial data from individuals with the same covariates. This comes from the fact that the sufficient statistic for a binomial model is the total number of events for each covariate vector; and the Bernoulli is just a special case of the binomial. Intuitively, each Bernoulli t... | Logistic Regression: Bernoulli vs. Binomial Response Variables | 1) Yes. You can aggregate/de-aggregate (?) binomial data from individuals with the same covariates. This comes from the fact that the sufficient statistic for a binomial model is the total number of e | Logistic Regression: Bernoulli vs. Binomial Response Variables
1) Yes. You can aggregate/de-aggregate (?) binomial data from individuals with the same covariates. This comes from the fact that the sufficient statistic for a binomial model is the total number of events for each covariate vector; and the Bernoulli is jus... | Logistic Regression: Bernoulli vs. Binomial Response Variables
1) Yes. You can aggregate/de-aggregate (?) binomial data from individuals with the same covariates. This comes from the fact that the sufficient statistic for a binomial model is the total number of e |
6,202 | Logistic Regression: Bernoulli vs. Binomial Response Variables | I just want make comments on the last paragraph, “The fact that the AIC is different (but the change in deviance is not) comes back to the constant term that was the difference between the log-likelihoods of the two models. When calculating the change in deviance, this is cancelled out because it is the same in all mod... | Logistic Regression: Bernoulli vs. Binomial Response Variables | I just want make comments on the last paragraph, “The fact that the AIC is different (but the change in deviance is not) comes back to the constant term that was the difference between the log-likelih | Logistic Regression: Bernoulli vs. Binomial Response Variables
I just want make comments on the last paragraph, “The fact that the AIC is different (but the change in deviance is not) comes back to the constant term that was the difference between the log-likelihoods of the two models. When calculating the change in de... | Logistic Regression: Bernoulli vs. Binomial Response Variables
I just want make comments on the last paragraph, “The fact that the AIC is different (but the change in deviance is not) comes back to the constant term that was the difference between the log-likelih |
6,203 | Logistic Regression: Bernoulli vs. Binomial Response Variables | The AIC are different since the response data changes. The important thing is that differences (i.e. delta) in the AIC, within models with the same response, are the same for the binomial versus Bernoulli:
binom.data <- data.frame(Successes = c(2, 3, 3), Trials = c(3, 4,
5), X1 = c("Yes", "No", ... | Logistic Regression: Bernoulli vs. Binomial Response Variables | The AIC are different since the response data changes. The important thing is that differences (i.e. delta) in the AIC, within models with the same response, are the same for the binomial versus Berno | Logistic Regression: Bernoulli vs. Binomial Response Variables
The AIC are different since the response data changes. The important thing is that differences (i.e. delta) in the AIC, within models with the same response, are the same for the binomial versus Bernoulli:
binom.data <- data.frame(Successes = c(2, 3, 3)... | Logistic Regression: Bernoulli vs. Binomial Response Variables
The AIC are different since the response data changes. The important thing is that differences (i.e. delta) in the AIC, within models with the same response, are the same for the binomial versus Berno |
6,204 | Are your chances of dying in a plane crash reduced if you fly direct? | Actual odds of planes crashing aside, you're falling into a logical trap here:
...each time one flies on an airplane, it does not increase the likelihood that he will die in a future airplane crash.
This is completely correct: whether you've never flown before or you've flown thousands of times, the chance of dying i... | Are your chances of dying in a plane crash reduced if you fly direct? | Actual odds of planes crashing aside, you're falling into a logical trap here:
...each time one flies on an airplane, it does not increase the likelihood that he will die in a future airplane crash.
| Are your chances of dying in a plane crash reduced if you fly direct?
Actual odds of planes crashing aside, you're falling into a logical trap here:
...each time one flies on an airplane, it does not increase the likelihood that he will die in a future airplane crash.
This is completely correct: whether you've never ... | Are your chances of dying in a plane crash reduced if you fly direct?
Actual odds of planes crashing aside, you're falling into a logical trap here:
...each time one flies on an airplane, it does not increase the likelihood that he will die in a future airplane crash.
|
6,205 | Are your chances of dying in a plane crash reduced if you fly direct? | Not only do you spend more time in-flight when you have two flights to your destination, even if the layover is collinear as the crow flies (since you will interrupt cruising speed), the greatest likelihood of accidents is in take-off and landing. | Are your chances of dying in a plane crash reduced if you fly direct? | Not only do you spend more time in-flight when you have two flights to your destination, even if the layover is collinear as the crow flies (since you will interrupt cruising speed), the greatest like | Are your chances of dying in a plane crash reduced if you fly direct?
Not only do you spend more time in-flight when you have two flights to your destination, even if the layover is collinear as the crow flies (since you will interrupt cruising speed), the greatest likelihood of accidents is in take-off and landing. | Are your chances of dying in a plane crash reduced if you fly direct?
Not only do you spend more time in-flight when you have two flights to your destination, even if the layover is collinear as the crow flies (since you will interrupt cruising speed), the greatest like |
6,206 | Are your chances of dying in a plane crash reduced if you fly direct? | I'm going to answer all your questions. No, theory, all numbers.
My point was that each time one flies on an airplane, it does not
increase the likelihood that he will die in a future airplane crash.
That is, each airplane flight is independent. Whether someone has
flown on 100 planes that year or just 1, both f... | Are your chances of dying in a plane crash reduced if you fly direct? | I'm going to answer all your questions. No, theory, all numbers.
My point was that each time one flies on an airplane, it does not
increase the likelihood that he will die in a future airplane cras | Are your chances of dying in a plane crash reduced if you fly direct?
I'm going to answer all your questions. No, theory, all numbers.
My point was that each time one flies on an airplane, it does not
increase the likelihood that he will die in a future airplane crash.
That is, each airplane flight is independent.... | Are your chances of dying in a plane crash reduced if you fly direct?
I'm going to answer all your questions. No, theory, all numbers.
My point was that each time one flies on an airplane, it does not
increase the likelihood that he will die in a future airplane cras |
6,207 | Are your chances of dying in a plane crash reduced if you fly direct? | He stated that he prefers to fly direct to a destination, as it decreases the probability that he will die in an airplane crash.
If your friend is genuinely concerned about this incredibly low probability then they should not be flying at all, or, for that matter, driving to the airport.
His logic was that if the pr... | Are your chances of dying in a plane crash reduced if you fly direct? | He stated that he prefers to fly direct to a destination, as it decreases the probability that he will die in an airplane crash.
If your friend is genuinely concerned about this incredibly low proba | Are your chances of dying in a plane crash reduced if you fly direct?
He stated that he prefers to fly direct to a destination, as it decreases the probability that he will die in an airplane crash.
If your friend is genuinely concerned about this incredibly low probability then they should not be flying at all, or, ... | Are your chances of dying in a plane crash reduced if you fly direct?
He stated that he prefers to fly direct to a destination, as it decreases the probability that he will die in an airplane crash.
If your friend is genuinely concerned about this incredibly low proba |
6,208 | Are your chances of dying in a plane crash reduced if you fly direct? | Simple answer. You are correct in assuming the probability is the same for each flight, but when you make a connection you're effectively "rolling the dice" again.
Furthermore, it's commonly known that the most dangerous points of any flight are take off and landing—thus taking a connection exposes yourself to these r... | Are your chances of dying in a plane crash reduced if you fly direct? | Simple answer. You are correct in assuming the probability is the same for each flight, but when you make a connection you're effectively "rolling the dice" again.
Furthermore, it's commonly known th | Are your chances of dying in a plane crash reduced if you fly direct?
Simple answer. You are correct in assuming the probability is the same for each flight, but when you make a connection you're effectively "rolling the dice" again.
Furthermore, it's commonly known that the most dangerous points of any flight are tak... | Are your chances of dying in a plane crash reduced if you fly direct?
Simple answer. You are correct in assuming the probability is the same for each flight, but when you make a connection you're effectively "rolling the dice" again.
Furthermore, it's commonly known th |
6,209 | Are your chances of dying in a plane crash reduced if you fly direct? | Your friend is right (on the probability theoretical side, not in in practice).
Apply your logic to throwing dice: you are saying that the chances of not throwing snake eyes once in 100 throws (i.e. surviving 100 flights) are the same as those of not throwing snake eyes in one throw (i.e. surviving one flight). If yo... | Are your chances of dying in a plane crash reduced if you fly direct? | Your friend is right (on the probability theoretical side, not in in practice).
Apply your logic to throwing dice: you are saying that the chances of not throwing snake eyes once in 100 throws (i.e. | Are your chances of dying in a plane crash reduced if you fly direct?
Your friend is right (on the probability theoretical side, not in in practice).
Apply your logic to throwing dice: you are saying that the chances of not throwing snake eyes once in 100 throws (i.e. surviving 100 flights) are the same as those of n... | Are your chances of dying in a plane crash reduced if you fly direct?
Your friend is right (on the probability theoretical side, not in in practice).
Apply your logic to throwing dice: you are saying that the chances of not throwing snake eyes once in 100 throws (i.e. |
6,210 | Are your chances of dying in a plane crash reduced if you fly direct? | Your chances of a coin flip coming up heads or tails are 50/50, on EVERY flip.
However, it is highly unlikely you would ever get a run of 10 heads in a row.
A little mathematics can be a dangerous thing :-) | Are your chances of dying in a plane crash reduced if you fly direct? | Your chances of a coin flip coming up heads or tails are 50/50, on EVERY flip.
However, it is highly unlikely you would ever get a run of 10 heads in a row.
A little mathematics can be a dangerous thi | Are your chances of dying in a plane crash reduced if you fly direct?
Your chances of a coin flip coming up heads or tails are 50/50, on EVERY flip.
However, it is highly unlikely you would ever get a run of 10 heads in a row.
A little mathematics can be a dangerous thing :-) | Are your chances of dying in a plane crash reduced if you fly direct?
Your chances of a coin flip coming up heads or tails are 50/50, on EVERY flip.
However, it is highly unlikely you would ever get a run of 10 heads in a row.
A little mathematics can be a dangerous thi |
6,211 | Are your chances of dying in a plane crash reduced if you fly direct? | An intuitive way of looking at this, in my opinion, is the concept of micromort (one-in-a-million probability of death).
According to Wikipedia, you'll 'accumulate' roughly one micromort due to accidents for each 1000 miles traveled and roughly one micromort due to terrorism for every 12'000 miles (in the U.S.).
This ... | Are your chances of dying in a plane crash reduced if you fly direct? | An intuitive way of looking at this, in my opinion, is the concept of micromort (one-in-a-million probability of death).
According to Wikipedia, you'll 'accumulate' roughly one micromort due to accide | Are your chances of dying in a plane crash reduced if you fly direct?
An intuitive way of looking at this, in my opinion, is the concept of micromort (one-in-a-million probability of death).
According to Wikipedia, you'll 'accumulate' roughly one micromort due to accidents for each 1000 miles traveled and roughly one m... | Are your chances of dying in a plane crash reduced if you fly direct?
An intuitive way of looking at this, in my opinion, is the concept of micromort (one-in-a-million probability of death).
According to Wikipedia, you'll 'accumulate' roughly one micromort due to accide |
6,212 | Are your chances of dying in a plane crash reduced if you fly direct? | I believe that you and your friend have missed one important variable. That is are the chances of dying in a plane crash disproportionately concentrated in the takeoff and landing. Off the top of my head, I believe the answer is yes.
Your friend's argument is, if you fly direct for 1000 miles, versus flying two flights... | Are your chances of dying in a plane crash reduced if you fly direct? | I believe that you and your friend have missed one important variable. That is are the chances of dying in a plane crash disproportionately concentrated in the takeoff and landing. Off the top of my h | Are your chances of dying in a plane crash reduced if you fly direct?
I believe that you and your friend have missed one important variable. That is are the chances of dying in a plane crash disproportionately concentrated in the takeoff and landing. Off the top of my head, I believe the answer is yes.
Your friend's ar... | Are your chances of dying in a plane crash reduced if you fly direct?
I believe that you and your friend have missed one important variable. That is are the chances of dying in a plane crash disproportionately concentrated in the takeoff and landing. Off the top of my h |
6,213 | Are your chances of dying in a plane crash reduced if you fly direct? | You have to ask yourself what this “probability of dying in plane crash” represents and how it applies to your problem (or not).
Look at it this way:
If you never fly at all, your chances to die in a plane crash are going to be much lower (but not nil, cf. El Al Flight 1862 or Air France Flight 4590).
If you fly every... | Are your chances of dying in a plane crash reduced if you fly direct? | You have to ask yourself what this “probability of dying in plane crash” represents and how it applies to your problem (or not).
Look at it this way:
If you never fly at all, your chances to die in a | Are your chances of dying in a plane crash reduced if you fly direct?
You have to ask yourself what this “probability of dying in plane crash” represents and how it applies to your problem (or not).
Look at it this way:
If you never fly at all, your chances to die in a plane crash are going to be much lower (but not n... | Are your chances of dying in a plane crash reduced if you fly direct?
You have to ask yourself what this “probability of dying in plane crash” represents and how it applies to your problem (or not).
Look at it this way:
If you never fly at all, your chances to die in a |
6,214 | Computing p-value using bootstrap with R | You are using bootstrap to generate data under the empirical distribution of the observed data. This can be useful to give a confidence interval on the difference between the two means:
> quantile(b3$t,c(0.025,0.975))
2.5% 97.5%
0.4166667 5.5833333
To get a $p$-value, you need to generate permutations under... | Computing p-value using bootstrap with R | You are using bootstrap to generate data under the empirical distribution of the observed data. This can be useful to give a confidence interval on the difference between the two means:
> quantile(b3$ | Computing p-value using bootstrap with R
You are using bootstrap to generate data under the empirical distribution of the observed data. This can be useful to give a confidence interval on the difference between the two means:
> quantile(b3$t,c(0.025,0.975))
2.5% 97.5%
0.4166667 5.5833333
To get a $p$-value... | Computing p-value using bootstrap with R
You are using bootstrap to generate data under the empirical distribution of the observed data. This can be useful to give a confidence interval on the difference between the two means:
> quantile(b3$ |
6,215 | Computing p-value using bootstrap with R | There are numerous ways of calculating bootstrap CIs and p-values. The main issue is that it is impossible for the bootstrap to generate data under a null hypothesis. The permutation test is a viable resampling based alternative to this. To use a proper bootstrap you must make some assumptions about the sampling distri... | Computing p-value using bootstrap with R | There are numerous ways of calculating bootstrap CIs and p-values. The main issue is that it is impossible for the bootstrap to generate data under a null hypothesis. The permutation test is a viable | Computing p-value using bootstrap with R
There are numerous ways of calculating bootstrap CIs and p-values. The main issue is that it is impossible for the bootstrap to generate data under a null hypothesis. The permutation test is a viable resampling based alternative to this. To use a proper bootstrap you must make s... | Computing p-value using bootstrap with R
There are numerous ways of calculating bootstrap CIs and p-values. The main issue is that it is impossible for the bootstrap to generate data under a null hypothesis. The permutation test is a viable |
6,216 | Computing p-value using bootstrap with R | The answer of Elvis relies on permutations but in my opinion it does not make clear what is wrong with the original bootstrap approach. Let me discuss a solution based solely on bootstrap.
The crucial problem of your original simulation is that bootstrap always provides you with the TRUE distribution of the test statis... | Computing p-value using bootstrap with R | The answer of Elvis relies on permutations but in my opinion it does not make clear what is wrong with the original bootstrap approach. Let me discuss a solution based solely on bootstrap.
The crucial | Computing p-value using bootstrap with R
The answer of Elvis relies on permutations but in my opinion it does not make clear what is wrong with the original bootstrap approach. Let me discuss a solution based solely on bootstrap.
The crucial problem of your original simulation is that bootstrap always provides you with... | Computing p-value using bootstrap with R
The answer of Elvis relies on permutations but in my opinion it does not make clear what is wrong with the original bootstrap approach. Let me discuss a solution based solely on bootstrap.
The crucial |
6,217 | How to derive the least square estimator for multiple linear regression? | The derivation in matrix notation
Starting from $y= Xb +\epsilon $, which really is just the same as
$\begin{bmatrix}
y_{1} \\
y_{2} \\
\vdots \\
y_{N}
\end{bmatrix}
=
\begin{bmatrix}
x_{11} & x_{12} & \cdots & x_{1K} \\
x_{21} & x_{22} & \cdots & x_{2K} \\
\vdots & \ddots & \ddots & \vdots \\
x_{N1} & x_{N2} & \cdots ... | How to derive the least square estimator for multiple linear regression? | The derivation in matrix notation
Starting from $y= Xb +\epsilon $, which really is just the same as
$\begin{bmatrix}
y_{1} \\
y_{2} \\
\vdots \\
y_{N}
\end{bmatrix}
=
\begin{bmatrix}
x_{11} & x_{12} | How to derive the least square estimator for multiple linear regression?
The derivation in matrix notation
Starting from $y= Xb +\epsilon $, which really is just the same as
$\begin{bmatrix}
y_{1} \\
y_{2} \\
\vdots \\
y_{N}
\end{bmatrix}
=
\begin{bmatrix}
x_{11} & x_{12} & \cdots & x_{1K} \\
x_{21} & x_{22} & \cdots &... | How to derive the least square estimator for multiple linear regression?
The derivation in matrix notation
Starting from $y= Xb +\epsilon $, which really is just the same as
$\begin{bmatrix}
y_{1} \\
y_{2} \\
\vdots \\
y_{N}
\end{bmatrix}
=
\begin{bmatrix}
x_{11} & x_{12} |
6,218 | How to derive the least square estimator for multiple linear regression? | It is possible to estimate just one coefficient in a multiple regression without estimating the others.
The estimate of $\beta_1$ is obtained by removing the effects of $x_2$ from the other variables and then regressing the residuals of $y$ against the residuals of $x_1$. This is explained and illustrated How exactly ... | How to derive the least square estimator for multiple linear regression? | It is possible to estimate just one coefficient in a multiple regression without estimating the others.
The estimate of $\beta_1$ is obtained by removing the effects of $x_2$ from the other variables | How to derive the least square estimator for multiple linear regression?
It is possible to estimate just one coefficient in a multiple regression without estimating the others.
The estimate of $\beta_1$ is obtained by removing the effects of $x_2$ from the other variables and then regressing the residuals of $y$ agains... | How to derive the least square estimator for multiple linear regression?
It is possible to estimate just one coefficient in a multiple regression without estimating the others.
The estimate of $\beta_1$ is obtained by removing the effects of $x_2$ from the other variables |
6,219 | How to derive the least square estimator for multiple linear regression? | The ordinary least squares estimate of $\beta$ is a linear function of the response variable. Simply put, the OLS estimate of the coefficients, the $\beta$'s, can be written using only the dependent variable ($Y_i$'s) and the independent variables ($X_{ki}$'s).
To explain this fact for a general regression model, you ... | How to derive the least square estimator for multiple linear regression? | The ordinary least squares estimate of $\beta$ is a linear function of the response variable. Simply put, the OLS estimate of the coefficients, the $\beta$'s, can be written using only the dependent v | How to derive the least square estimator for multiple linear regression?
The ordinary least squares estimate of $\beta$ is a linear function of the response variable. Simply put, the OLS estimate of the coefficients, the $\beta$'s, can be written using only the dependent variable ($Y_i$'s) and the independent variables... | How to derive the least square estimator for multiple linear regression?
The ordinary least squares estimate of $\beta$ is a linear function of the response variable. Simply put, the OLS estimate of the coefficients, the $\beta$'s, can be written using only the dependent v |
6,220 | How to derive the least square estimator for multiple linear regression? | One small minor note on theory vs. practice. Mathematically $\beta_0, \beta_1, \beta_2 ... \beta_n$ can be estimated with the following formula:
$$ \hat{\beta} = (X'X)^{-1} X'Y$$
where $X$ is the original input data and $Y$ is the variable that we want to estimate. This follows from minimizing the error. I will proov... | How to derive the least square estimator for multiple linear regression? | One small minor note on theory vs. practice. Mathematically $\beta_0, \beta_1, \beta_2 ... \beta_n$ can be estimated with the following formula:
$$ \hat{\beta} = (X'X)^{-1} X'Y$$
where $X$ is the ori | How to derive the least square estimator for multiple linear regression?
One small minor note on theory vs. practice. Mathematically $\beta_0, \beta_1, \beta_2 ... \beta_n$ can be estimated with the following formula:
$$ \hat{\beta} = (X'X)^{-1} X'Y$$
where $X$ is the original input data and $Y$ is the variable that w... | How to derive the least square estimator for multiple linear regression?
One small minor note on theory vs. practice. Mathematically $\beta_0, \beta_1, \beta_2 ... \beta_n$ can be estimated with the following formula:
$$ \hat{\beta} = (X'X)^{-1} X'Y$$
where $X$ is the ori |
6,221 | How to derive the least square estimator for multiple linear regression? | A simple derivation can be done just by using the geometric interpretation of LR.
Linear regression can be interpreted as the projection of $Y$ onto the column space $X$. Thus, the error, $\hat{\epsilon}$ is orthogonal to the column space of $X$.
Therefore, the inner product between $X'$ and the error must be 0, i.e.,... | How to derive the least square estimator for multiple linear regression? | A simple derivation can be done just by using the geometric interpretation of LR.
Linear regression can be interpreted as the projection of $Y$ onto the column space $X$. Thus, the error, $\hat{\epsi | How to derive the least square estimator for multiple linear regression?
A simple derivation can be done just by using the geometric interpretation of LR.
Linear regression can be interpreted as the projection of $Y$ onto the column space $X$. Thus, the error, $\hat{\epsilon}$ is orthogonal to the column space of $X$.... | How to derive the least square estimator for multiple linear regression?
A simple derivation can be done just by using the geometric interpretation of LR.
Linear regression can be interpreted as the projection of $Y$ onto the column space $X$. Thus, the error, $\hat{\epsi |
6,222 | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic | I'm not sure that multicollinearity is what's going on here. It certainly could be, but from the information given I can't conclude that, and I don't want to start there. My first guess is that this might be a multiple comparisons issue. That is, if you run enough tests, something will show up, even if there's nothin... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi | I'm not sure that multicollinearity is what's going on here. It certainly could be, but from the information given I can't conclude that, and I don't want to start there. My first guess is that this | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic
I'm not sure that multicollinearity is what's going on here. It certainly could be, but from the information given I can't conclude that, and I don't want to start there. My first guess is that ... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi
I'm not sure that multicollinearity is what's going on here. It certainly could be, but from the information given I can't conclude that, and I don't want to start there. My first guess is that this |
6,223 | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic | I would like to suggest that this phenomenon (of a non-significant overall test despite a significant individual variable) can be understood as a kind of aggregate "masking effect" and that although it conceivably could arise from multicollinear explanatory variables, it need not do that at all. It also turns out not ... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi | I would like to suggest that this phenomenon (of a non-significant overall test despite a significant individual variable) can be understood as a kind of aggregate "masking effect" and that although i | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic
I would like to suggest that this phenomenon (of a non-significant overall test despite a significant individual variable) can be understood as a kind of aggregate "masking effect" and that altho... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi
I would like to suggest that this phenomenon (of a non-significant overall test despite a significant individual variable) can be understood as a kind of aggregate "masking effect" and that although i |
6,224 | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic | You frequently have this happen when you have a high degree of collinearity among your explanatory variables. The ANOVA F is a joint test that all the regressors are jointly uninformative. When your Xs contain similar information, the model cannot attribute the explanatory power to one regressor or another, but their c... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi | You frequently have this happen when you have a high degree of collinearity among your explanatory variables. The ANOVA F is a joint test that all the regressors are jointly uninformative. When your X | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic
You frequently have this happen when you have a high degree of collinearity among your explanatory variables. The ANOVA F is a joint test that all the regressors are jointly uninformative. When y... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi
You frequently have this happen when you have a high degree of collinearity among your explanatory variables. The ANOVA F is a joint test that all the regressors are jointly uninformative. When your X |
6,225 | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic | The example in whuber's answer is very to the point (+1), to which I want to elaborate the rationale behind it from the theoretical perspective. For a better exposition, suppose the number of regressors is $2$ and the number of observations is $n$, so the model can be written as:
\begin{align}
y_i = \beta_0 + \beta_1X... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi | The example in whuber's answer is very to the point (+1), to which I want to elaborate the rationale behind it from the theoretical perspective. For a better exposition, suppose the number of regress | Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic
The example in whuber's answer is very to the point (+1), to which I want to elaborate the rationale behind it from the theoretical perspective. For a better exposition, suppose the number of re... | Significance contradiction in linear regression: significant t-test for a coefficient vs non-signifi
The example in whuber's answer is very to the point (+1), to which I want to elaborate the rationale behind it from the theoretical perspective. For a better exposition, suppose the number of regress |
6,226 | Confidence interval for median | Here is an illustration on a classical R dataset:
> x = faithful$waiting
> bootmed = apply(matrix(sample(x, rep=TRUE, 10^4*length(x)), nrow=10^4), 1, median)
> quantile(bootmed, c(.025, 0.975))
2.5% 97.5%
73.5 77
which gives a (73.5, 77) confidence interval on the median.
(Note: Corrected version, thanks t... | Confidence interval for median | Here is an illustration on a classical R dataset:
> x = faithful$waiting
> bootmed = apply(matrix(sample(x, rep=TRUE, 10^4*length(x)), nrow=10^4), 1, median)
> quantile(bootmed, c(.025, 0.975))
| Confidence interval for median
Here is an illustration on a classical R dataset:
> x = faithful$waiting
> bootmed = apply(matrix(sample(x, rep=TRUE, 10^4*length(x)), nrow=10^4), 1, median)
> quantile(bootmed, c(.025, 0.975))
2.5% 97.5%
73.5 77
which gives a (73.5, 77) confidence interval on the median.
(No... | Confidence interval for median
Here is an illustration on a classical R dataset:
> x = faithful$waiting
> bootmed = apply(matrix(sample(x, rep=TRUE, 10^4*length(x)), nrow=10^4), 1, median)
> quantile(bootmed, c(.025, 0.975))
|
6,227 | Confidence interval for median | Another approach is based on quantiles of the binomial distribution.
e.g.:
> x=faithful$waiting
> sort(x)[qbinom(c(.025,.975), length(x), 0.5)]
[1] 73 77 | Confidence interval for median | Another approach is based on quantiles of the binomial distribution.
e.g.:
> x=faithful$waiting
> sort(x)[qbinom(c(.025,.975), length(x), 0.5)]
[1] 73 77 | Confidence interval for median
Another approach is based on quantiles of the binomial distribution.
e.g.:
> x=faithful$waiting
> sort(x)[qbinom(c(.025,.975), length(x), 0.5)]
[1] 73 77 | Confidence interval for median
Another approach is based on quantiles of the binomial distribution.
e.g.:
> x=faithful$waiting
> sort(x)[qbinom(c(.025,.975), length(x), 0.5)]
[1] 73 77 |
6,228 | Confidence interval for median | Check out bootstrap resampling. Search R help for the boot function. Depending on your data with resampling you can estimate confidence intervals for just about anything. | Confidence interval for median | Check out bootstrap resampling. Search R help for the boot function. Depending on your data with resampling you can estimate confidence intervals for just about anything. | Confidence interval for median
Check out bootstrap resampling. Search R help for the boot function. Depending on your data with resampling you can estimate confidence intervals for just about anything. | Confidence interval for median
Check out bootstrap resampling. Search R help for the boot function. Depending on your data with resampling you can estimate confidence intervals for just about anything. |
6,229 | Confidence interval for median | And there are other approaches:
One is based on Wilcoxon Rank Sum test applied for one sample with continuity correction. In R this can be supplied as:
wilcox.test(x,conf.level=0.95,alternative="two.sided",correct=TRUE)
And there is the David Olive's CI for median discussed here:
CI for Median | Confidence interval for median | And there are other approaches:
One is based on Wilcoxon Rank Sum test applied for one sample with continuity correction. In R this can be supplied as:
wilcox.test(x,conf.level=0.95,alternative="two.s | Confidence interval for median
And there are other approaches:
One is based on Wilcoxon Rank Sum test applied for one sample with continuity correction. In R this can be supplied as:
wilcox.test(x,conf.level=0.95,alternative="two.sided",correct=TRUE)
And there is the David Olive's CI for median discussed here:
CI for ... | Confidence interval for median
And there are other approaches:
One is based on Wilcoxon Rank Sum test applied for one sample with continuity correction. In R this can be supplied as:
wilcox.test(x,conf.level=0.95,alternative="two.s |
6,230 | Confidence interval for median | The result based on the qbinom approach isn't correct for small samples. Suppose that x has 10 components. Then qbinom(c(.025,.975),10,.5) gives 2 and 8. The resulting interval doesn't treat order statistics at the lower tail symmetrically with those from the upper tail; you should get either 2 and 9, or 3 and 8. T... | Confidence interval for median | The result based on the qbinom approach isn't correct for small samples. Suppose that x has 10 components. Then qbinom(c(.025,.975),10,.5) gives 2 and 8. The resulting interval doesn't treat order | Confidence interval for median
The result based on the qbinom approach isn't correct for small samples. Suppose that x has 10 components. Then qbinom(c(.025,.975),10,.5) gives 2 and 8. The resulting interval doesn't treat order statistics at the lower tail symmetrically with those from the upper tail; you should get... | Confidence interval for median
The result based on the qbinom approach isn't correct for small samples. Suppose that x has 10 components. Then qbinom(c(.025,.975),10,.5) gives 2 and 8. The resulting interval doesn't treat order |
6,231 | Polynomial regression using scikit-learn | Given data $\mathbf{x}$, a column vector, and $\mathbf{y}$, the target vector, you can perform polynomial regression by appending polynomials of $\mathbf{x}$. For example, consider if
$$ \mathbf{x} = \begin{bmatrix}
2 \\[0.3em]
-1 \\[0.3em]
\frac{1}{3}
\end{bmatrix}$$
Using just t... | Polynomial regression using scikit-learn | Given data $\mathbf{x}$, a column vector, and $\mathbf{y}$, the target vector, you can perform polynomial regression by appending polynomials of $\mathbf{x}$. For example, consider if
$$ \mathbf{x} = | Polynomial regression using scikit-learn
Given data $\mathbf{x}$, a column vector, and $\mathbf{y}$, the target vector, you can perform polynomial regression by appending polynomials of $\mathbf{x}$. For example, consider if
$$ \mathbf{x} = \begin{bmatrix}
2 \\[0.3em]
-1 \\[0.3em]
\frac{1}{3} ... | Polynomial regression using scikit-learn
Given data $\mathbf{x}$, a column vector, and $\mathbf{y}$, the target vector, you can perform polynomial regression by appending polynomials of $\mathbf{x}$. For example, consider if
$$ \mathbf{x} = |
6,232 | Polynomial regression using scikit-learn | Theory
Polynomial regression is a special case of linear regression. With the main idea of how do you select your features. Looking at the multivariate regression with 2 variables: x1 and x2. Linear regression will look like this: y = a1 * x1 + a2 * x2.
Now you want to have a polynomial regression (let's make 2 degree ... | Polynomial regression using scikit-learn | Theory
Polynomial regression is a special case of linear regression. With the main idea of how do you select your features. Looking at the multivariate regression with 2 variables: x1 and x2. Linear r | Polynomial regression using scikit-learn
Theory
Polynomial regression is a special case of linear regression. With the main idea of how do you select your features. Looking at the multivariate regression with 2 variables: x1 and x2. Linear regression will look like this: y = a1 * x1 + a2 * x2.
Now you want to have a po... | Polynomial regression using scikit-learn
Theory
Polynomial regression is a special case of linear regression. With the main idea of how do you select your features. Looking at the multivariate regression with 2 variables: x1 and x2. Linear r |
6,233 | Polynomial regression using scikit-learn | In case you are using a multivariate regression and not just a univariate regression, do not forget the cross terms. For instance if you have two variables $x_1$ and $x_2$, and you want polynomials up to power 2, you should use $y = a_1x_1 + a_2x_2 + a_3x_1^2 + a_4x_2^2 + a_5x_1x_2$ where the last term ($a_5x_1x_2$) is... | Polynomial regression using scikit-learn | In case you are using a multivariate regression and not just a univariate regression, do not forget the cross terms. For instance if you have two variables $x_1$ and $x_2$, and you want polynomials up | Polynomial regression using scikit-learn
In case you are using a multivariate regression and not just a univariate regression, do not forget the cross terms. For instance if you have two variables $x_1$ and $x_2$, and you want polynomials up to power 2, you should use $y = a_1x_1 + a_2x_2 + a_3x_1^2 + a_4x_2^2 + a_5x_1... | Polynomial regression using scikit-learn
In case you are using a multivariate regression and not just a univariate regression, do not forget the cross terms. For instance if you have two variables $x_1$ and $x_2$, and you want polynomials up |
6,234 | Polynomial regression using scikit-learn | Using a similar approach to @Cam.Davidson.Pilon, I wrote a couple functions to help demo this approach in Python. It can be expanded by adding more terms in the np.concatenate vectors. The output for the y_pred would not change, but getting the coefficients, regr.coef_[0][2], would need to be included.
from sklearn imp... | Polynomial regression using scikit-learn | Using a similar approach to @Cam.Davidson.Pilon, I wrote a couple functions to help demo this approach in Python. It can be expanded by adding more terms in the np.concatenate vectors. The output for | Polynomial regression using scikit-learn
Using a similar approach to @Cam.Davidson.Pilon, I wrote a couple functions to help demo this approach in Python. It can be expanded by adding more terms in the np.concatenate vectors. The output for the y_pred would not change, but getting the coefficients, regr.coef_[0][2], wo... | Polynomial regression using scikit-learn
Using a similar approach to @Cam.Davidson.Pilon, I wrote a couple functions to help demo this approach in Python. It can be expanded by adding more terms in the np.concatenate vectors. The output for |
6,235 | How to decide which glm family to use? | GLM families comprise a link function as well as a mean-variance relationship. For Poisson GLMs, the link function is a log, and the mean-variance relationship is the identity. Despite the warnings that most statistical software gives you, it's completely reasonable to model a relationship in continuous data in which t... | How to decide which glm family to use? | GLM families comprise a link function as well as a mean-variance relationship. For Poisson GLMs, the link function is a log, and the mean-variance relationship is the identity. Despite the warnings th | How to decide which glm family to use?
GLM families comprise a link function as well as a mean-variance relationship. For Poisson GLMs, the link function is a log, and the mean-variance relationship is the identity. Despite the warnings that most statistical software gives you, it's completely reasonable to model a rel... | How to decide which glm family to use?
GLM families comprise a link function as well as a mean-variance relationship. For Poisson GLMs, the link function is a log, and the mean-variance relationship is the identity. Despite the warnings th |
6,236 | How to decide which glm family to use? | Generalized linear model is defined in terms of linear predictor
$$
\eta = \boldsymbol{X} \beta
$$
that is passed through the link function $g$:
$$ g(E(Y\,|\,\boldsymbol{X})) = \eta $$
It models the relation between the dependent variable $Y$ and independent variables $\boldsymbol{X} = X_1,X_2,\dots,X_k$. More precisel... | How to decide which glm family to use? | Generalized linear model is defined in terms of linear predictor
$$
\eta = \boldsymbol{X} \beta
$$
that is passed through the link function $g$:
$$ g(E(Y\,|\,\boldsymbol{X})) = \eta $$
It models the r | How to decide which glm family to use?
Generalized linear model is defined in terms of linear predictor
$$
\eta = \boldsymbol{X} \beta
$$
that is passed through the link function $g$:
$$ g(E(Y\,|\,\boldsymbol{X})) = \eta $$
It models the relation between the dependent variable $Y$ and independent variables $\boldsymbol... | How to decide which glm family to use?
Generalized linear model is defined in terms of linear predictor
$$
\eta = \boldsymbol{X} \beta
$$
that is passed through the link function $g$:
$$ g(E(Y\,|\,\boldsymbol{X})) = \eta $$
It models the r |
6,237 | How to decide which glm family to use? | This is a somewhat broad question, you are asking for how to do modelling, and there are entire books dedicated to that. For example, when dealing with count data, consider the following:
In addition to choosing a distribution, you have to choose a link function. With count data you could try poisson or negative bino... | How to decide which glm family to use? | This is a somewhat broad question, you are asking for how to do modelling, and there are entire books dedicated to that. For example, when dealing with count data, consider the following:
In addition | How to decide which glm family to use?
This is a somewhat broad question, you are asking for how to do modelling, and there are entire books dedicated to that. For example, when dealing with count data, consider the following:
In addition to choosing a distribution, you have to choose a link function. With count data... | How to decide which glm family to use?
This is a somewhat broad question, you are asking for how to do modelling, and there are entire books dedicated to that. For example, when dealing with count data, consider the following:
In addition |
6,238 | Regression to the mean vs gambler's fallacy | I think the confusion can be resolved by considering that the concept of "regression to the mean" really has nothing to do with the past. It's merely the tautological observation that at each iteration of an experiment we expect the average outcome. So if we previously had an above average outcome then we expect a wo... | Regression to the mean vs gambler's fallacy | I think the confusion can be resolved by considering that the concept of "regression to the mean" really has nothing to do with the past. It's merely the tautological observation that at each iterati | Regression to the mean vs gambler's fallacy
I think the confusion can be resolved by considering that the concept of "regression to the mean" really has nothing to do with the past. It's merely the tautological observation that at each iteration of an experiment we expect the average outcome. So if we previously had ... | Regression to the mean vs gambler's fallacy
I think the confusion can be resolved by considering that the concept of "regression to the mean" really has nothing to do with the past. It's merely the tautological observation that at each iterati |
6,239 | Regression to the mean vs gambler's fallacy | If you were to find yourself in such a position, as a rational person (and assuming a fair coin), your best bet would be to just guess. If you were to find yourself in such a position as a superstitious gambler, your best bet would be to look at the prior events and try to justify your reasoning about the past - e.g. "... | Regression to the mean vs gambler's fallacy | If you were to find yourself in such a position, as a rational person (and assuming a fair coin), your best bet would be to just guess. If you were to find yourself in such a position as a superstitio | Regression to the mean vs gambler's fallacy
If you were to find yourself in such a position, as a rational person (and assuming a fair coin), your best bet would be to just guess. If you were to find yourself in such a position as a superstitious gambler, your best bet would be to look at the prior events and try to ju... | Regression to the mean vs gambler's fallacy
If you were to find yourself in such a position, as a rational person (and assuming a fair coin), your best bet would be to just guess. If you were to find yourself in such a position as a superstitio |
6,240 | Regression to the mean vs gambler's fallacy | Here's a simple example: you've decided to toss a total of 200 coins. So far you've tossed 100 of them and you've gotten extremely lucky: 100% came up heads (incredible, I know, but let's just keep things simple).
Conditional on 100 heads in the 100 first tosses, you expect to have 150 heads total at the end of the g... | Regression to the mean vs gambler's fallacy | Here's a simple example: you've decided to toss a total of 200 coins. So far you've tossed 100 of them and you've gotten extremely lucky: 100% came up heads (incredible, I know, but let's just keep | Regression to the mean vs gambler's fallacy
Here's a simple example: you've decided to toss a total of 200 coins. So far you've tossed 100 of them and you've gotten extremely lucky: 100% came up heads (incredible, I know, but let's just keep things simple).
Conditional on 100 heads in the 100 first tosses, you expect... | Regression to the mean vs gambler's fallacy
Here's a simple example: you've decided to toss a total of 200 coins. So far you've tossed 100 of them and you've gotten extremely lucky: 100% came up heads (incredible, I know, but let's just keep |
6,241 | Regression to the mean vs gambler's fallacy | I always try to remember that regression toward the mean isn't a compensatory mechanism for observing outliers.
There's no cause-and-effect relationship between having an outstanding gambling run, then going 50-50 after that. It's just a helpful way to remember that, when you're sampling from a distribution, you're mo... | Regression to the mean vs gambler's fallacy | I always try to remember that regression toward the mean isn't a compensatory mechanism for observing outliers.
There's no cause-and-effect relationship between having an outstanding gambling run, th | Regression to the mean vs gambler's fallacy
I always try to remember that regression toward the mean isn't a compensatory mechanism for observing outliers.
There's no cause-and-effect relationship between having an outstanding gambling run, then going 50-50 after that. It's just a helpful way to remember that, when yo... | Regression to the mean vs gambler's fallacy
I always try to remember that regression toward the mean isn't a compensatory mechanism for observing outliers.
There's no cause-and-effect relationship between having an outstanding gambling run, th |
6,242 | Regression to the mean vs gambler's fallacy | The key is that we don't have any information that will help us with the next event (gambler's fallacy), because the next event isn't dependent on the previous event. We can make a reasonable guess about how a series of trials will go. This reasonable guess is the average aka our expected mean result. So when we watch ... | Regression to the mean vs gambler's fallacy | The key is that we don't have any information that will help us with the next event (gambler's fallacy), because the next event isn't dependent on the previous event. We can make a reasonable guess ab | Regression to the mean vs gambler's fallacy
The key is that we don't have any information that will help us with the next event (gambler's fallacy), because the next event isn't dependent on the previous event. We can make a reasonable guess about how a series of trials will go. This reasonable guess is the average aka... | Regression to the mean vs gambler's fallacy
The key is that we don't have any information that will help us with the next event (gambler's fallacy), because the next event isn't dependent on the previous event. We can make a reasonable guess ab |
6,243 | Regression to the mean vs gambler's fallacy | Are students with higher grades who score worse on retest cheaters?
The question received a substantial edit since the last of six answers.
The edited question contains an example of regression to the mean in the context
of student scores on a $100$ question true-false test and an retest for the
top performers on an eq... | Regression to the mean vs gambler's fallacy | Are students with higher grades who score worse on retest cheaters?
The question received a substantial edit since the last of six answers.
The edited question contains an example of regression to the | Regression to the mean vs gambler's fallacy
Are students with higher grades who score worse on retest cheaters?
The question received a substantial edit since the last of six answers.
The edited question contains an example of regression to the mean in the context
of student scores on a $100$ question true-false test a... | Regression to the mean vs gambler's fallacy
Are students with higher grades who score worse on retest cheaters?
The question received a substantial edit since the last of six answers.
The edited question contains an example of regression to the |
6,244 | Regression to the mean vs gambler's fallacy | According to the gambler's fallacy shouldn't it be expected the same
probability for the scoring and not necessarily more likely close to 50?
No. You trapped in Gambler's fallacy.
Assuming large enough number of question asked in the second time, the ratio of their success will still remain the same for high scorers f... | Regression to the mean vs gambler's fallacy | According to the gambler's fallacy shouldn't it be expected the same
probability for the scoring and not necessarily more likely close to 50?
No. You trapped in Gambler's fallacy.
Assuming large enou | Regression to the mean vs gambler's fallacy
According to the gambler's fallacy shouldn't it be expected the same
probability for the scoring and not necessarily more likely close to 50?
No. You trapped in Gambler's fallacy.
Assuming large enough number of question asked in the second time, the ratio of their success w... | Regression to the mean vs gambler's fallacy
According to the gambler's fallacy shouldn't it be expected the same
probability for the scoring and not necessarily more likely close to 50?
No. You trapped in Gambler's fallacy.
Assuming large enou |
6,245 | Regression to the mean vs gambler's fallacy | I could be wrong but I have always thought the difference to be in the assumption of independence.
In the Gambler's fallacy the issue is the misunderstanding of independence. Sure over some large N number of coin tosses you will be around a 50-50 split, but if by chance you are not then the thought that your next T to... | Regression to the mean vs gambler's fallacy | I could be wrong but I have always thought the difference to be in the assumption of independence.
In the Gambler's fallacy the issue is the misunderstanding of independence. Sure over some large N n | Regression to the mean vs gambler's fallacy
I could be wrong but I have always thought the difference to be in the assumption of independence.
In the Gambler's fallacy the issue is the misunderstanding of independence. Sure over some large N number of coin tosses you will be around a 50-50 split, but if by chance you ... | Regression to the mean vs gambler's fallacy
I could be wrong but I have always thought the difference to be in the assumption of independence.
In the Gambler's fallacy the issue is the misunderstanding of independence. Sure over some large N n |
6,246 | Regression to the mean vs gambler's fallacy | Thanks your answers I think I could understand the difference between the Regression to the mean and Gambler's fallacy. Even more, I built a database to help me illustrate in the "real" case.
I built this situation: I collected 1000 students and I put them to do a test randomly answering questions .
The test score rang... | Regression to the mean vs gambler's fallacy | Thanks your answers I think I could understand the difference between the Regression to the mean and Gambler's fallacy. Even more, I built a database to help me illustrate in the "real" case.
I built | Regression to the mean vs gambler's fallacy
Thanks your answers I think I could understand the difference between the Regression to the mean and Gambler's fallacy. Even more, I built a database to help me illustrate in the "real" case.
I built this situation: I collected 1000 students and I put them to do a test random... | Regression to the mean vs gambler's fallacy
Thanks your answers I think I could understand the difference between the Regression to the mean and Gambler's fallacy. Even more, I built a database to help me illustrate in the "real" case.
I built |
6,247 | Regression to the mean vs gambler's fallacy | They are saying the same thing. You were mostly confused because no single experiment in the coin flip example has extreme result (H/T 50/50). Change it to "flipping ten fair coins at the same time in every experiment", and gamblers want to get all of them right. Then an extreme measurement would be that you happen to ... | Regression to the mean vs gambler's fallacy | They are saying the same thing. You were mostly confused because no single experiment in the coin flip example has extreme result (H/T 50/50). Change it to "flipping ten fair coins at the same time in | Regression to the mean vs gambler's fallacy
They are saying the same thing. You were mostly confused because no single experiment in the coin flip example has extreme result (H/T 50/50). Change it to "flipping ten fair coins at the same time in every experiment", and gamblers want to get all of them right. Then an extr... | Regression to the mean vs gambler's fallacy
They are saying the same thing. You were mostly confused because no single experiment in the coin flip example has extreme result (H/T 50/50). Change it to "flipping ten fair coins at the same time in |
6,248 | Regression to the mean vs gambler's fallacy | Let X and Y be two i.i.d. uniform random variables on [0,1]. Suppose we observe them one after another.
Gambler's Fallacy:
P( Y | X ) != P( Y )
This is, of course, nonsense because X and Y are independent.
Regression to the mean:
P( Y < X | X = 1) != P( Y < X )
This is true: LHS is 1, LHS < 1 | Regression to the mean vs gambler's fallacy | Let X and Y be two i.i.d. uniform random variables on [0,1]. Suppose we observe them one after another.
Gambler's Fallacy:
P( Y | X ) != P( Y )
This is, of course, nonsense because X and Y are indepe | Regression to the mean vs gambler's fallacy
Let X and Y be two i.i.d. uniform random variables on [0,1]. Suppose we observe them one after another.
Gambler's Fallacy:
P( Y | X ) != P( Y )
This is, of course, nonsense because X and Y are independent.
Regression to the mean:
P( Y < X | X = 1) != P( Y < X )
This is true:... | Regression to the mean vs gambler's fallacy
Let X and Y be two i.i.d. uniform random variables on [0,1]. Suppose we observe them one after another.
Gambler's Fallacy:
P( Y | X ) != P( Y )
This is, of course, nonsense because X and Y are indepe |
6,249 | Regression to the mean vs gambler's fallacy | Regression to the mean is basically just a special case (or corollary) of the Gambler's fallacy. The confusion easily arises from looking at the wrong variable.
Gambler's fallacy rule advises: the best prediction of the next event is the expected value, the history does not matter.
Example: you have 5 tails in a row, t... | Regression to the mean vs gambler's fallacy | Regression to the mean is basically just a special case (or corollary) of the Gambler's fallacy. The confusion easily arises from looking at the wrong variable.
Gambler's fallacy rule advises: the bes | Regression to the mean vs gambler's fallacy
Regression to the mean is basically just a special case (or corollary) of the Gambler's fallacy. The confusion easily arises from looking at the wrong variable.
Gambler's fallacy rule advises: the best prediction of the next event is the expected value, the history does not m... | Regression to the mean vs gambler's fallacy
Regression to the mean is basically just a special case (or corollary) of the Gambler's fallacy. The confusion easily arises from looking at the wrong variable.
Gambler's fallacy rule advises: the bes |
6,250 | Regression to the mean vs gambler's fallacy | I’m going to try to simplify.
After flipping 10 heads;
Gambler’s fallacy says that the next flip is more likely to be tails.
Regression to the mean says the next flip is 50/50, BUT the following series of tosses should go back to an even distribution.
In other words: RTTM isn’t making a specific occurrence prediction... | Regression to the mean vs gambler's fallacy | I’m going to try to simplify.
After flipping 10 heads;
Gambler’s fallacy says that the next flip is more likely to be tails.
Regression to the mean says the next flip is 50/50, BUT the following seri | Regression to the mean vs gambler's fallacy
I’m going to try to simplify.
After flipping 10 heads;
Gambler’s fallacy says that the next flip is more likely to be tails.
Regression to the mean says the next flip is 50/50, BUT the following series of tosses should go back to an even distribution.
In other words: RTTM i... | Regression to the mean vs gambler's fallacy
I’m going to try to simplify.
After flipping 10 heads;
Gambler’s fallacy says that the next flip is more likely to be tails.
Regression to the mean says the next flip is 50/50, BUT the following seri |
6,251 | Regression to the mean vs gambler's fallacy | A random walk will depart from the starting point increasingly as a measure of distance in time and decreasingly so in proportion to the total distance traveled. There is no controversy therein. For example, gambling on coin tosses will exaggerate the total amount won or lost with time, but the relative amount will ten... | Regression to the mean vs gambler's fallacy | A random walk will depart from the starting point increasingly as a measure of distance in time and decreasingly so in proportion to the total distance traveled. There is no controversy therein. For e | Regression to the mean vs gambler's fallacy
A random walk will depart from the starting point increasingly as a measure of distance in time and decreasingly so in proportion to the total distance traveled. There is no controversy therein. For example, gambling on coin tosses will exaggerate the total amount won or lost... | Regression to the mean vs gambler's fallacy
A random walk will depart from the starting point increasingly as a measure of distance in time and decreasingly so in proportion to the total distance traveled. There is no controversy therein. For e |
6,252 | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$? | Georges Monette and I introduced the GVIF in the paper "Generalized collinearity diagnostics," JASA 87:178-183, 1992 (link). As we explained, the GVIF represents the squared ratio of hypervolumes of the joint-confidence ellipsoid for a subset of coefficients to the "utopian" ellipsoid that would be obtained if the regr... | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df} | Georges Monette and I introduced the GVIF in the paper "Generalized collinearity diagnostics," JASA 87:178-183, 1992 (link). As we explained, the GVIF represents the squared ratio of hypervolumes of t | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$?
Georges Monette and I introduced the GVIF in the paper "Generalized collinearity diagnostics," JASA 87:178-183, 1992 (link). As we explained, the GVIF represents the squared ratio of hypervolumes of the joint-confid... | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df}
Georges Monette and I introduced the GVIF in the paper "Generalized collinearity diagnostics," JASA 87:178-183, 1992 (link). As we explained, the GVIF represents the squared ratio of hypervolumes of t |
6,253 | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$? | I ran into exactly the same question and tried to work my way through. See my detailed answer below.
First of all, I found 4 options producing similar VIF values in R:
• corvif command from the AED package,
• vif command from the car package,
• vif command from the rms package,
• vif command from the DAAG packa... | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df} | I ran into exactly the same question and tried to work my way through. See my detailed answer below.
First of all, I found 4 options producing similar VIF values in R:
• corvif command from the AED | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$?
I ran into exactly the same question and tried to work my way through. See my detailed answer below.
First of all, I found 4 options producing similar VIF values in R:
• corvif command from the AED package,
• vi... | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df}
I ran into exactly the same question and tried to work my way through. See my detailed answer below.
First of all, I found 4 options producing similar VIF values in R:
• corvif command from the AED |
6,254 | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$? | Fox & Monette (original citation for GVIF, GVIF^1/2df) suggest taking GVIF to the power of 1/2df makes the value of the GVIF comparable across different number of parameters. "It is analagous to taking the square root of the usual variance-inflation factor" ( from An R and S-Plus Companion to Applied Regression by John... | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df} | Fox & Monette (original citation for GVIF, GVIF^1/2df) suggest taking GVIF to the power of 1/2df makes the value of the GVIF comparable across different number of parameters. "It is analagous to takin | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$?
Fox & Monette (original citation for GVIF, GVIF^1/2df) suggest taking GVIF to the power of 1/2df makes the value of the GVIF comparable across different number of parameters. "It is analagous to taking the square ro... | Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df}
Fox & Monette (original citation for GVIF, GVIF^1/2df) suggest taking GVIF to the power of 1/2df makes the value of the GVIF comparable across different number of parameters. "It is analagous to takin |
6,255 | Looking for a good and complete probability and statistics book | If you are searching for proofs, I have been working for some time on a free stats textbook that collects lots of proofs of elementary and less elementary facts that are difficult to find in probability and statistics books (because they are scattered here and there). You can have a look at it at http://www.statlect.co... | Looking for a good and complete probability and statistics book | If you are searching for proofs, I have been working for some time on a free stats textbook that collects lots of proofs of elementary and less elementary facts that are difficult to find in probabili | Looking for a good and complete probability and statistics book
If you are searching for proofs, I have been working for some time on a free stats textbook that collects lots of proofs of elementary and less elementary facts that are difficult to find in probability and statistics books (because they are scattered here... | Looking for a good and complete probability and statistics book
If you are searching for proofs, I have been working for some time on a free stats textbook that collects lots of proofs of elementary and less elementary facts that are difficult to find in probabili |
6,256 | Looking for a good and complete probability and statistics book | If you want to read probability as a story, read the best book ever by Feller. I am also guessing that you do not want to go to the level of measure theoretic definition of probabilities which has specialized books. another beginner level book is from Ross. Other specialized applications have specialized books. so more... | Looking for a good and complete probability and statistics book | If you want to read probability as a story, read the best book ever by Feller. I am also guessing that you do not want to go to the level of measure theoretic definition of probabilities which has spe | Looking for a good and complete probability and statistics book
If you want to read probability as a story, read the best book ever by Feller. I am also guessing that you do not want to go to the level of measure theoretic definition of probabilities which has specialized books. another beginner level book is from Ross... | Looking for a good and complete probability and statistics book
If you want to read probability as a story, read the best book ever by Feller. I am also guessing that you do not want to go to the level of measure theoretic definition of probabilities which has spe |
6,257 | Looking for a good and complete probability and statistics book | I would recommend two books not mentioned, as well as several already mentioned.
The first is E.T. Jaynes "Probability: The Language of Science." It is polemic and he is a very partisan author, but it is very good.
The second is Leonard Jimmie Savage's "The Foundations of Statistics." You will probably be very surpri... | Looking for a good and complete probability and statistics book | I would recommend two books not mentioned, as well as several already mentioned.
The first is E.T. Jaynes "Probability: The Language of Science." It is polemic and he is a very partisan author, but i | Looking for a good and complete probability and statistics book
I would recommend two books not mentioned, as well as several already mentioned.
The first is E.T. Jaynes "Probability: The Language of Science." It is polemic and he is a very partisan author, but it is very good.
The second is Leonard Jimmie Savage's "T... | Looking for a good and complete probability and statistics book
I would recommend two books not mentioned, as well as several already mentioned.
The first is E.T. Jaynes "Probability: The Language of Science." It is polemic and he is a very partisan author, but i |
6,258 | Looking for a good and complete probability and statistics book | Finding a single, comprehensive book will be very difficult. If you're asking because you want to do some self-study, get a couple of used texts instead of a single new one. You can get classics for $3-10 dollars if you look around online.
Feller's "Introduction to Probability" is great for its completeness and expos... | Looking for a good and complete probability and statistics book | Finding a single, comprehensive book will be very difficult. If you're asking because you want to do some self-study, get a couple of used texts instead of a single new one. You can get classics for | Looking for a good and complete probability and statistics book
Finding a single, comprehensive book will be very difficult. If you're asking because you want to do some self-study, get a couple of used texts instead of a single new one. You can get classics for $3-10 dollars if you look around online.
Feller's "Intr... | Looking for a good and complete probability and statistics book
Finding a single, comprehensive book will be very difficult. If you're asking because you want to do some self-study, get a couple of used texts instead of a single new one. You can get classics for |
6,259 | Looking for a good and complete probability and statistics book | For the probability side I like Probability and Random Processes by Grimmett & Stirzaker. It has a nice way of giving intuitive explanations whilst still being fairly rigorous and providing some proofs at least.
For the Statistics side I've had Theory of Statistics by Schervish on my wish list for a while now but not ... | Looking for a good and complete probability and statistics book | For the probability side I like Probability and Random Processes by Grimmett & Stirzaker. It has a nice way of giving intuitive explanations whilst still being fairly rigorous and providing some proo | Looking for a good and complete probability and statistics book
For the probability side I like Probability and Random Processes by Grimmett & Stirzaker. It has a nice way of giving intuitive explanations whilst still being fairly rigorous and providing some proofs at least.
For the Statistics side I've had Theory of ... | Looking for a good and complete probability and statistics book
For the probability side I like Probability and Random Processes by Grimmett & Stirzaker. It has a nice way of giving intuitive explanations whilst still being fairly rigorous and providing some proo |
6,260 | Looking for a good and complete probability and statistics book | I recommend Probability Theory and Mathematical Statistics by Marek Fisz, because:
It contains most of the common proof, but without making the book too difficult as an introduction book
It is quite theoretical, but still contain enough well-designed examples to illustrate points
Exercises are meaningful. Some of the... | Looking for a good and complete probability and statistics book | I recommend Probability Theory and Mathematical Statistics by Marek Fisz, because:
It contains most of the common proof, but without making the book too difficult as an introduction book
It is quite | Looking for a good and complete probability and statistics book
I recommend Probability Theory and Mathematical Statistics by Marek Fisz, because:
It contains most of the common proof, but without making the book too difficult as an introduction book
It is quite theoretical, but still contain enough well-designed exam... | Looking for a good and complete probability and statistics book
I recommend Probability Theory and Mathematical Statistics by Marek Fisz, because:
It contains most of the common proof, but without making the book too difficult as an introduction book
It is quite |
6,261 | Looking for a good and complete probability and statistics book | As noted by many others, there is no single good text for any scientific subject simply because any given authors or group of authors use a set of assumptions regarding the readers' level of understanding and diversity of knowns and unknowns in the user's brain. Said this, my suggestion for someone knows basics in calc... | Looking for a good and complete probability and statistics book | As noted by many others, there is no single good text for any scientific subject simply because any given authors or group of authors use a set of assumptions regarding the readers' level of understan | Looking for a good and complete probability and statistics book
As noted by many others, there is no single good text for any scientific subject simply because any given authors or group of authors use a set of assumptions regarding the readers' level of understanding and diversity of knowns and unknowns in the user's ... | Looking for a good and complete probability and statistics book
As noted by many others, there is no single good text for any scientific subject simply because any given authors or group of authors use a set of assumptions regarding the readers' level of understan |
6,262 | Looking for a good and complete probability and statistics book | You can read Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes book. It provides clear examples and exercises with "additional questions" at the end of each chapter which really help improve learning and there is a logical progression from one idea to another. | Looking for a good and complete probability and statistics book | You can read Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes book. It provides clear examples and exercises with "additional questions" at the end of each c | Looking for a good and complete probability and statistics book
You can read Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes book. It provides clear examples and exercises with "additional questions" at the end of each chapter which really help improve learning and there is a... | Looking for a good and complete probability and statistics book
You can read Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes book. It provides clear examples and exercises with "additional questions" at the end of each c |
6,263 | What does the logit value actually mean? | The logit $L$ of a probability $p$ is defined as
$$L = \ln\frac{p}{1-p}$$
The term $\frac{p}{1-p}$ is called odds. The natural logarithm of the odds is known as log-odds or logit.
The inverse function is
$$p = \frac{1}{1+e^{-L}}$$
Probabilities range from zero to one, i.e., $p\in[0,1]$, whereas logits can be any real n... | What does the logit value actually mean? | The logit $L$ of a probability $p$ is defined as
$$L = \ln\frac{p}{1-p}$$
The term $\frac{p}{1-p}$ is called odds. The natural logarithm of the odds is known as log-odds or logit.
The inverse function | What does the logit value actually mean?
The logit $L$ of a probability $p$ is defined as
$$L = \ln\frac{p}{1-p}$$
The term $\frac{p}{1-p}$ is called odds. The natural logarithm of the odds is known as log-odds or logit.
The inverse function is
$$p = \frac{1}{1+e^{-L}}$$
Probabilities range from zero to one, i.e., $p\i... | What does the logit value actually mean?
The logit $L$ of a probability $p$ is defined as
$$L = \ln\frac{p}{1-p}$$
The term $\frac{p}{1-p}$ is called odds. The natural logarithm of the odds is known as log-odds or logit.
The inverse function |
6,264 | What does the logit value actually mean? | To add a more modern (but not very deep) perspective, consider how it's used in deep learning (ha, pun intended...):
logit is referred to the output of a function (e.g. a Neural Net) just before it's normalization (which we usually use the softmax). This is also known as the code. So if for label $y$ we have score $f_y... | What does the logit value actually mean? | To add a more modern (but not very deep) perspective, consider how it's used in deep learning (ha, pun intended...):
logit is referred to the output of a function (e.g. a Neural Net) just before it's | What does the logit value actually mean?
To add a more modern (but not very deep) perspective, consider how it's used in deep learning (ha, pun intended...):
logit is referred to the output of a function (e.g. a Neural Net) just before it's normalization (which we usually use the softmax). This is also known as the cod... | What does the logit value actually mean?
To add a more modern (but not very deep) perspective, consider how it's used in deep learning (ha, pun intended...):
logit is referred to the output of a function (e.g. a Neural Net) just before it's |
6,265 | What does the logit value actually mean? | Could you maybe specify your model and give a screenshot of the output, then I could give you an detailed answer, but as a first try.... you may want to check out also the following examples on these websites:
http://www.ats.ucla.edu/stat/stata/seminars/stata_logistic/default.htm
http://www.ats.ucla.edu/stat/stata/dae/... | What does the logit value actually mean? | Could you maybe specify your model and give a screenshot of the output, then I could give you an detailed answer, but as a first try.... you may want to check out also the following examples on these | What does the logit value actually mean?
Could you maybe specify your model and give a screenshot of the output, then I could give you an detailed answer, but as a first try.... you may want to check out also the following examples on these websites:
http://www.ats.ucla.edu/stat/stata/seminars/stata_logistic/default.ht... | What does the logit value actually mean?
Could you maybe specify your model and give a screenshot of the output, then I could give you an detailed answer, but as a first try.... you may want to check out also the following examples on these |
6,266 | Why is it that my colleagues and I learned opposite definitions for test and validation sets? | For machine learning, I've predominantly seen the usage OP describes, but I've also encountered lots of confusion coming from this usage.
Historically, I guess what happened (at least in my field, analytical chemistry) is that as models became more complex, at some point people noticed that independent data is needed ... | Why is it that my colleagues and I learned opposite definitions for test and validation sets? | For machine learning, I've predominantly seen the usage OP describes, but I've also encountered lots of confusion coming from this usage.
Historically, I guess what happened (at least in my field, an | Why is it that my colleagues and I learned opposite definitions for test and validation sets?
For machine learning, I've predominantly seen the usage OP describes, but I've also encountered lots of confusion coming from this usage.
Historically, I guess what happened (at least in my field, analytical chemistry) is tha... | Why is it that my colleagues and I learned opposite definitions for test and validation sets?
For machine learning, I've predominantly seen the usage OP describes, but I've also encountered lots of confusion coming from this usage.
Historically, I guess what happened (at least in my field, an |
6,267 | Why is it that my colleagues and I learned opposite definitions for test and validation sets? | Apparently, the terms are used ambiguously, but I always seen them used as that there are three (or more) sets of data: train set used for training the model, validation set for assessing the performance of the model when tuning it, and held-out test set that you use at the very end to assess the performance of the mod... | Why is it that my colleagues and I learned opposite definitions for test and validation sets? | Apparently, the terms are used ambiguously, but I always seen them used as that there are three (or more) sets of data: train set used for training the model, validation set for assessing the performa | Why is it that my colleagues and I learned opposite definitions for test and validation sets?
Apparently, the terms are used ambiguously, but I always seen them used as that there are three (or more) sets of data: train set used for training the model, validation set for assessing the performance of the model when tuni... | Why is it that my colleagues and I learned opposite definitions for test and validation sets?
Apparently, the terms are used ambiguously, but I always seen them used as that there are three (or more) sets of data: train set used for training the model, validation set for assessing the performa |
6,268 | Why is it that my colleagues and I learned opposite definitions for test and validation sets? | I was taught that you have a train/test split for tuning then you have a validation set to 'validate' that you haven't overfitted your test split. If you have a small dataset then you just have your train/test split, I would never call it a train/validation split because I think of validation as the final step to 'val... | Why is it that my colleagues and I learned opposite definitions for test and validation sets? | I was taught that you have a train/test split for tuning then you have a validation set to 'validate' that you haven't overfitted your test split. If you have a small dataset then you just have your | Why is it that my colleagues and I learned opposite definitions for test and validation sets?
I was taught that you have a train/test split for tuning then you have a validation set to 'validate' that you haven't overfitted your test split. If you have a small dataset then you just have your train/test split, I would ... | Why is it that my colleagues and I learned opposite definitions for test and validation sets?
I was taught that you have a train/test split for tuning then you have a validation set to 'validate' that you haven't overfitted your test split. If you have a small dataset then you just have your |
6,269 | What is the relationship between orthogonal, correlation and independence? | Independence is a statistical concept. Two random variables $X$ and $Y$ are statistically independent if their joint distribution is the product of the marginal distributions, i.e.
$$
f(x, y) = f(x) f(y)
$$
if each variable has a density $f$, or more generally
$$
F(x, y) = F(x) F(y)
$$
where $F$ denotes each random var... | What is the relationship between orthogonal, correlation and independence? | Independence is a statistical concept. Two random variables $X$ and $Y$ are statistically independent if their joint distribution is the product of the marginal distributions, i.e.
$$
f(x, y) = f(x) f | What is the relationship between orthogonal, correlation and independence?
Independence is a statistical concept. Two random variables $X$ and $Y$ are statistically independent if their joint distribution is the product of the marginal distributions, i.e.
$$
f(x, y) = f(x) f(y)
$$
if each variable has a density $f$, or... | What is the relationship between orthogonal, correlation and independence?
Independence is a statistical concept. Two random variables $X$ and $Y$ are statistically independent if their joint distribution is the product of the marginal distributions, i.e.
$$
f(x, y) = f(x) f |
6,270 | What is the relationship between orthogonal, correlation and independence? | Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y].
Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead to uncorrelated, (non-)orthogonal and (un)correlated can happen at the same time.
I am being the TA of probability this semester, so I m... | What is the relationship between orthogonal, correlation and independence? | Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y].
Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead to uncorrelated, | What is the relationship between orthogonal, correlation and independence?
Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y].
Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead to uncorrelated, (non-)orthogonal and (un)correlated can happe... | What is the relationship between orthogonal, correlation and independence?
Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y].
Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead to uncorrelated, |
6,271 | What is the relationship between orthogonal, correlation and independence? | Here is my intuitive view: Stating that x and y are uncorrelated/orthogonal are both ways of saying that knowledge of the value of x or y does not enable a prediction of the other -- x and y are independent of each other -- assuming that any relationship is linear.
The correlation coefficient provides an indication... | What is the relationship between orthogonal, correlation and independence? | Here is my intuitive view: Stating that x and y are uncorrelated/orthogonal are both ways of saying that knowledge of the value of x or y does not enable a prediction of the other -- x and y are in | What is the relationship between orthogonal, correlation and independence?
Here is my intuitive view: Stating that x and y are uncorrelated/orthogonal are both ways of saying that knowledge of the value of x or y does not enable a prediction of the other -- x and y are independent of each other -- assuming that any ... | What is the relationship between orthogonal, correlation and independence?
Here is my intuitive view: Stating that x and y are uncorrelated/orthogonal are both ways of saying that knowledge of the value of x or y does not enable a prediction of the other -- x and y are in |
6,272 | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | There are some strong voices in the Econometrics community against the validity of the Ljung-Box $Q$-statistic for testing for autocorrelation based on the residuals from an autoregressive model (i.e. with lagged dependent variables in the regressor matrix), see particularly Maddala (2001) "Introduction to Econometrics... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | There are some strong voices in the Econometrics community against the validity of the Ljung-Box $Q$-statistic for testing for autocorrelation based on the residuals from an autoregressive model (i.e. | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
There are some strong voices in the Econometrics community against the validity of the Ljung-Box $Q$-statistic for testing for autocorrelation based on the residuals from an autoregressive model (i.e. with lagged dependent variables in the regressor matrix),... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
There are some strong voices in the Econometrics community against the validity of the Ljung-Box $Q$-statistic for testing for autocorrelation based on the residuals from an autoregressive model (i.e. |
6,273 | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | Conjecture
I don't know about any study comparing these tests. I had the suspicion that the Ljung-Box test is more appropriate in the context of time series models like ARIMA models, where the explanatory variables are lags of the dependent variables. The Breusch-Godfrey test could be more appropriate for a general reg... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | Conjecture
I don't know about any study comparing these tests. I had the suspicion that the Ljung-Box test is more appropriate in the context of time series models like ARIMA models, where the explana | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
Conjecture
I don't know about any study comparing these tests. I had the suspicion that the Ljung-Box test is more appropriate in the context of time series models like ARIMA models, where the explanatory variables are lags of the dependent variables. The Br... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
Conjecture
I don't know about any study comparing these tests. I had the suspicion that the Ljung-Box test is more appropriate in the context of time series models like ARIMA models, where the explana |
6,274 | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | Greene (Econometric Analysis, 7th Edition, p. 963, section 20.7.2):
"The essential difference between the Godfrey-Breusch [GB] and the
Box-Pierce [BP] tests is the use of partial correlations (controlling
for $X$ and the other variables) in the former and simple correlations
in the latter. Under the null hypoth... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | Greene (Econometric Analysis, 7th Edition, p. 963, section 20.7.2):
"The essential difference between the Godfrey-Breusch [GB] and the
Box-Pierce [BP] tests is the use of partial correlations (con | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
Greene (Econometric Analysis, 7th Edition, p. 963, section 20.7.2):
"The essential difference between the Godfrey-Breusch [GB] and the
Box-Pierce [BP] tests is the use of partial correlations (controlling
for $X$ and the other variables) in the former ... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
Greene (Econometric Analysis, 7th Edition, p. 963, section 20.7.2):
"The essential difference between the Godfrey-Breusch [GB] and the
Box-Pierce [BP] tests is the use of partial correlations (con |
6,275 | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | It seems that Box-Pierce and Ljung-Box tests are mainly univariate tests, but there are some assumptions behind the Breusch-Godfrey test when testing if linear structure is left behind on residuals of time series regression (MA or AR process).
Here is link to discussion:
http://www.stata.com/meeting/new-orleans13/a... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | It seems that Box-Pierce and Ljung-Box tests are mainly univariate tests, but there are some assumptions behind the Breusch-Godfrey test when testing if linear structure is left behind on residuals of | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
It seems that Box-Pierce and Ljung-Box tests are mainly univariate tests, but there are some assumptions behind the Breusch-Godfrey test when testing if linear structure is left behind on residuals of time series regression (MA or AR process).
Here is link... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
It seems that Box-Pierce and Ljung-Box tests are mainly univariate tests, but there are some assumptions behind the Breusch-Godfrey test when testing if linear structure is left behind on residuals of |
6,276 | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | The main difference between the tests is the following:
The Breusch-Godfrey test is as Lagrange Multiplier test derived from
the (correctly specified) likelihood function (and thus from
first principles).
The Ljung-Box test is based on second moments of the residuals of a stationary process (and thus of a comparative... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | The main difference between the tests is the following:
The Breusch-Godfrey test is as Lagrange Multiplier test derived from
the (correctly specified) likelihood function (and thus from
first princip | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
The main difference between the tests is the following:
The Breusch-Godfrey test is as Lagrange Multiplier test derived from
the (correctly specified) likelihood function (and thus from
first principles).
The Ljung-Box test is based on second moments of th... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
The main difference between the tests is the following:
The Breusch-Godfrey test is as Lagrange Multiplier test derived from
the (correctly specified) likelihood function (and thus from
first princip |
6,277 | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | Looking further in Hayashi (2000) pp 146-147:
..when the regressors are not strictly exogenous we need to modify the
Q statistics to restore its asymptotic distribution
Basically we only have to assume that that the errors do not depend on the lagged regressors and they are conditionally homoskedastic.
Modifying the ... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey | Looking further in Hayashi (2000) pp 146-147:
..when the regressors are not strictly exogenous we need to modify the
Q statistics to restore its asymptotic distribution
Basically we only have to ass | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
Looking further in Hayashi (2000) pp 146-147:
..when the regressors are not strictly exogenous we need to modify the
Q statistics to restore its asymptotic distribution
Basically we only have to assume that that the errors do not depend on the lagged regre... | Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey
Looking further in Hayashi (2000) pp 146-147:
..when the regressors are not strictly exogenous we need to modify the
Q statistics to restore its asymptotic distribution
Basically we only have to ass |
6,278 | Purpose of the link function in generalized linear model | A.J. Dobson pointed out the following things in her book:
Linear regression assumes that the conditional distribution of the response variable is normally distributed. Generalized linear models can have response variables with conditional distributions other than the Normal distribution – they may even be categorical ... | Purpose of the link function in generalized linear model | A.J. Dobson pointed out the following things in her book:
Linear regression assumes that the conditional distribution of the response variable is normally distributed. Generalized linear models can h | Purpose of the link function in generalized linear model
A.J. Dobson pointed out the following things in her book:
Linear regression assumes that the conditional distribution of the response variable is normally distributed. Generalized linear models can have response variables with conditional distributions other tha... | Purpose of the link function in generalized linear model
A.J. Dobson pointed out the following things in her book:
Linear regression assumes that the conditional distribution of the response variable is normally distributed. Generalized linear models can h |
6,279 | Purpose of the link function in generalized linear model | It may help you to read my answer here: Difference between logit and probit models, which discusses GLiM links somewhat extensively.
The basic way of explaining this issue is laid out clearly by @BlainWaan, and Wikipedia: The actual parameter (e.g., $p$ for a binomial response--i.e., logistic regression) cannot range ... | Purpose of the link function in generalized linear model | It may help you to read my answer here: Difference between logit and probit models, which discusses GLiM links somewhat extensively.
The basic way of explaining this issue is laid out clearly by @Blai | Purpose of the link function in generalized linear model
It may help you to read my answer here: Difference between logit and probit models, which discusses GLiM links somewhat extensively.
The basic way of explaining this issue is laid out clearly by @BlainWaan, and Wikipedia: The actual parameter (e.g., $p$ for a bi... | Purpose of the link function in generalized linear model
It may help you to read my answer here: Difference between logit and probit models, which discusses GLiM links somewhat extensively.
The basic way of explaining this issue is laid out clearly by @Blai |
6,280 | Good methods for density plots of non-negative variables in R? | An alternative is the approach of Kooperberg and colleagues, based on estimating the density using splines to approximate the log-density of the data. I'll show an example using the data from @whuber's answer, which will allow for a comparison of approaches.
set.seed(17)
x <- rexp(1000)
You'll need the logspline packa... | Good methods for density plots of non-negative variables in R? | An alternative is the approach of Kooperberg and colleagues, based on estimating the density using splines to approximate the log-density of the data. I'll show an example using the data from @whuber' | Good methods for density plots of non-negative variables in R?
An alternative is the approach of Kooperberg and colleagues, based on estimating the density using splines to approximate the log-density of the data. I'll show an example using the data from @whuber's answer, which will allow for a comparison of approaches... | Good methods for density plots of non-negative variables in R?
An alternative is the approach of Kooperberg and colleagues, based on estimating the density using splines to approximate the log-density of the data. I'll show an example using the data from @whuber' |
6,281 | Good methods for density plots of non-negative variables in R? | One solution, borrowed from approaches to edge-weighting of spatial statistics, is to truncate the density on the left at zero but to up-weight the data that are closest to zero. The idea is that each value $x$ is "spread" into a kernel of unit total area centered at $x$; any part of the kernel that would spill over i... | Good methods for density plots of non-negative variables in R? | One solution, borrowed from approaches to edge-weighting of spatial statistics, is to truncate the density on the left at zero but to up-weight the data that are closest to zero. The idea is that eac | Good methods for density plots of non-negative variables in R?
One solution, borrowed from approaches to edge-weighting of spatial statistics, is to truncate the density on the left at zero but to up-weight the data that are closest to zero. The idea is that each value $x$ is "spread" into a kernel of unit total area ... | Good methods for density plots of non-negative variables in R?
One solution, borrowed from approaches to edge-weighting of spatial statistics, is to truncate the density on the left at zero but to up-weight the data that are closest to zero. The idea is that eac |
6,282 | Good methods for density plots of non-negative variables in R? | To compare distributions by groups (which you say is the goal in one of your comments) why not something simpler? Parallel box plots work nicely if N is large; parallel strip plots work if N is small (and both show outliers well, which you say is a problem in your data). | Good methods for density plots of non-negative variables in R? | To compare distributions by groups (which you say is the goal in one of your comments) why not something simpler? Parallel box plots work nicely if N is large; parallel strip plots work if N is small | Good methods for density plots of non-negative variables in R?
To compare distributions by groups (which you say is the goal in one of your comments) why not something simpler? Parallel box plots work nicely if N is large; parallel strip plots work if N is small (and both show outliers well, which you say is a problem ... | Good methods for density plots of non-negative variables in R?
To compare distributions by groups (which you say is the goal in one of your comments) why not something simpler? Parallel box plots work nicely if N is large; parallel strip plots work if N is small |
6,283 | Good methods for density plots of non-negative variables in R? | As Stéphane comments you can use from = 0 and, additionally, you can represent your values under the density curve with rug (x) | Good methods for density plots of non-negative variables in R? | As Stéphane comments you can use from = 0 and, additionally, you can represent your values under the density curve with rug (x) | Good methods for density plots of non-negative variables in R?
As Stéphane comments you can use from = 0 and, additionally, you can represent your values under the density curve with rug (x) | Good methods for density plots of non-negative variables in R?
As Stéphane comments you can use from = 0 and, additionally, you can represent your values under the density curve with rug (x) |
6,284 | Distribution of scalar products of two random unit vectors in $D$ dimensions | Because (as is well-known) a uniform distribution on the unit sphere $S^{D-1}$ is obtained by normalizing a $D$-variate normal distribution and the dot product $t$ of normalized vectors is their correlation coefficient, the answers to the three questions are:
$u= (t+1)/2$ has a Beta$((D-1)/2,(D-1)/2)$ distribution.
... | Distribution of scalar products of two random unit vectors in $D$ dimensions | Because (as is well-known) a uniform distribution on the unit sphere $S^{D-1}$ is obtained by normalizing a $D$-variate normal distribution and the dot product $t$ of normalized vectors is their corr | Distribution of scalar products of two random unit vectors in $D$ dimensions
Because (as is well-known) a uniform distribution on the unit sphere $S^{D-1}$ is obtained by normalizing a $D$-variate normal distribution and the dot product $t$ of normalized vectors is their correlation coefficient, the answers to the thr... | Distribution of scalar products of two random unit vectors in $D$ dimensions
Because (as is well-known) a uniform distribution on the unit sphere $S^{D-1}$ is obtained by normalizing a $D$-variate normal distribution and the dot product $t$ of normalized vectors is their corr |
6,285 | Distribution of scalar products of two random unit vectors in $D$ dimensions | Let's find the distribution and then the variance follows by standard results. Consider the vector product and write it on it's cosine form, i.e. note that we have $$P(x'y\leq t)=P(|x||y|\cos\theta\leq t)=P(\cos\theta\leq t)=\mathbb{E}P(\cos\theta\leq t\mid y),$$ where $\theta$ is the angle between $x$ and $y$. In the ... | Distribution of scalar products of two random unit vectors in $D$ dimensions | Let's find the distribution and then the variance follows by standard results. Consider the vector product and write it on it's cosine form, i.e. note that we have $$P(x'y\leq t)=P(|x||y|\cos\theta\le | Distribution of scalar products of two random unit vectors in $D$ dimensions
Let's find the distribution and then the variance follows by standard results. Consider the vector product and write it on it's cosine form, i.e. note that we have $$P(x'y\leq t)=P(|x||y|\cos\theta\leq t)=P(\cos\theta\leq t)=\mathbb{E}P(\cos\t... | Distribution of scalar products of two random unit vectors in $D$ dimensions
Let's find the distribution and then the variance follows by standard results. Consider the vector product and write it on it's cosine form, i.e. note that we have $$P(x'y\leq t)=P(|x||y|\cos\theta\le |
6,286 | Distribution of scalar products of two random unit vectors in $D$ dimensions | To answer the first part of your question, denote $Z = \langle X,Y \rangle = \sum X_i Y_i$. Define
$$
f_{Z_i}(z_i) = \int_{-\infty}^\infty f_{Z_1,\ldots,Z_D}(z_1,\ldots,z_D) \: d z_i
$$
The product of the $i^{th}$ elements of $X$ and $Y$ denoted here as $Z_i$ will be distributed according to the joint distribution o... | Distribution of scalar products of two random unit vectors in $D$ dimensions | To answer the first part of your question, denote $Z = \langle X,Y \rangle = \sum X_i Y_i$. Define
$$
f_{Z_i}(z_i) = \int_{-\infty}^\infty f_{Z_1,\ldots,Z_D}(z_1,\ldots,z_D) \: d z_i
$$
The product | Distribution of scalar products of two random unit vectors in $D$ dimensions
To answer the first part of your question, denote $Z = \langle X,Y \rangle = \sum X_i Y_i$. Define
$$
f_{Z_i}(z_i) = \int_{-\infty}^\infty f_{Z_1,\ldots,Z_D}(z_1,\ldots,z_D) \: d z_i
$$
The product of the $i^{th}$ elements of $X$ and $Y$ de... | Distribution of scalar products of two random unit vectors in $D$ dimensions
To answer the first part of your question, denote $Z = \langle X,Y \rangle = \sum X_i Y_i$. Define
$$
f_{Z_i}(z_i) = \int_{-\infty}^\infty f_{Z_1,\ldots,Z_D}(z_1,\ldots,z_D) \: d z_i
$$
The product |
6,287 | Why do naive Bayesian classifiers perform so well? | This paper seems to prove (I can't follow the math) that bayes is good not only when features are independent, but also when dependencies of features from each other are similar between features:
In this paper, we propose a novel explanation on the
superb classification performance of naive Bayes. We
show that, es... | Why do naive Bayesian classifiers perform so well? | This paper seems to prove (I can't follow the math) that bayes is good not only when features are independent, but also when dependencies of features from each other are similar between features:
In | Why do naive Bayesian classifiers perform so well?
This paper seems to prove (I can't follow the math) that bayes is good not only when features are independent, but also when dependencies of features from each other are similar between features:
In this paper, we propose a novel explanation on the
superb classifica... | Why do naive Bayesian classifiers perform so well?
This paper seems to prove (I can't follow the math) that bayes is good not only when features are independent, but also when dependencies of features from each other are similar between features:
In |
6,288 | Why do naive Bayesian classifiers perform so well? | Most Machine Learning problems are easy!
See for example at John Langford's blog. What he's really saying is that ML makes problems easy, and this presents a problem for researchers in terms of whether they should try to apply methods to a wide range of simple problems or attack more difficult problems. However the by-... | Why do naive Bayesian classifiers perform so well? | Most Machine Learning problems are easy!
See for example at John Langford's blog. What he's really saying is that ML makes problems easy, and this presents a problem for researchers in terms of whethe | Why do naive Bayesian classifiers perform so well?
Most Machine Learning problems are easy!
See for example at John Langford's blog. What he's really saying is that ML makes problems easy, and this presents a problem for researchers in terms of whether they should try to apply methods to a wide range of simple problems... | Why do naive Bayesian classifiers perform so well?
Most Machine Learning problems are easy!
See for example at John Langford's blog. What he's really saying is that ML makes problems easy, and this presents a problem for researchers in terms of whethe |
6,289 | Why do naive Bayesian classifiers perform so well? | Having used Naive Bayesian Classifiers extensively in segmentation classification tools, my experience is consistent with published papers showing NBC to be comparable in accuracy to linear discriminant and CART/CHAID when all of the predictor variables are available.
(By accuracy both "hit rate" in predicting the cor... | Why do naive Bayesian classifiers perform so well? | Having used Naive Bayesian Classifiers extensively in segmentation classification tools, my experience is consistent with published papers showing NBC to be comparable in accuracy to linear discrimina | Why do naive Bayesian classifiers perform so well?
Having used Naive Bayesian Classifiers extensively in segmentation classification tools, my experience is consistent with published papers showing NBC to be comparable in accuracy to linear discriminant and CART/CHAID when all of the predictor variables are available. ... | Why do naive Bayesian classifiers perform so well?
Having used Naive Bayesian Classifiers extensively in segmentation classification tools, my experience is consistent with published papers showing NBC to be comparable in accuracy to linear discrimina |
6,290 | Good accuracy despite high loss value | I have experienced a similar issue.
I have trained my neural network binary classifier with a cross entropy loss. Here the result of the cross entropy as a function of epoch. Red is for the training set and blue is for the test set.
By showing the accuracy, I had the surprise to get a better accuracy for epoch 1000 co... | Good accuracy despite high loss value | I have experienced a similar issue.
I have trained my neural network binary classifier with a cross entropy loss. Here the result of the cross entropy as a function of epoch. Red is for the training s | Good accuracy despite high loss value
I have experienced a similar issue.
I have trained my neural network binary classifier with a cross entropy loss. Here the result of the cross entropy as a function of epoch. Red is for the training set and blue is for the test set.
By showing the accuracy, I had the surprise to g... | Good accuracy despite high loss value
I have experienced a similar issue.
I have trained my neural network binary classifier with a cross entropy loss. Here the result of the cross entropy as a function of epoch. Red is for the training s |
6,291 | Good accuracy despite high loss value | One important thing to note as well is that the cross entropy is not a bounded loss. Which means that a single very wrong prediction can potentially make your loss "blow up". In that sense it is possible that there are one or a few outliers that are classified extremely badly and that are making the loss explode, but a... | Good accuracy despite high loss value | One important thing to note as well is that the cross entropy is not a bounded loss. Which means that a single very wrong prediction can potentially make your loss "blow up". In that sense it is possi | Good accuracy despite high loss value
One important thing to note as well is that the cross entropy is not a bounded loss. Which means that a single very wrong prediction can potentially make your loss "blow up". In that sense it is possible that there are one or a few outliers that are classified extremely badly and t... | Good accuracy despite high loss value
One important thing to note as well is that the cross entropy is not a bounded loss. Which means that a single very wrong prediction can potentially make your loss "blow up". In that sense it is possi |
6,292 | Good accuracy despite high loss value | ahstat gives very good illustrations.
Inspired by these illustrations, i conclude to 2 possible reasons.
1. Model is too simple to extract required features for prediction. In your Illustration 1, it's a manifold problem and need to one more layer to get 100% accuracy.
2. Data has too many noisy label.(compare Illust... | Good accuracy despite high loss value | ahstat gives very good illustrations.
Inspired by these illustrations, i conclude to 2 possible reasons.
1. Model is too simple to extract required features for prediction. In your Illustration 1, i | Good accuracy despite high loss value
ahstat gives very good illustrations.
Inspired by these illustrations, i conclude to 2 possible reasons.
1. Model is too simple to extract required features for prediction. In your Illustration 1, it's a manifold problem and need to one more layer to get 100% accuracy.
2. Data ha... | Good accuracy despite high loss value
ahstat gives very good illustrations.
Inspired by these illustrations, i conclude to 2 possible reasons.
1. Model is too simple to extract required features for prediction. In your Illustration 1, i |
6,293 | Good accuracy despite high loss value | In categorical cross entropy case accuracy measures true positive i.e accuracy is discrete values, while the logloss of softmax loss so to speak is a continuous variable that measures the models performance against false negatives. A wrong prediction affects accuracy slightly but penalizes the loss disproportionately. ... | Good accuracy despite high loss value | In categorical cross entropy case accuracy measures true positive i.e accuracy is discrete values, while the logloss of softmax loss so to speak is a continuous variable that measures the models perfo | Good accuracy despite high loss value
In categorical cross entropy case accuracy measures true positive i.e accuracy is discrete values, while the logloss of softmax loss so to speak is a continuous variable that measures the models performance against false negatives. A wrong prediction affects accuracy slightly but p... | Good accuracy despite high loss value
In categorical cross entropy case accuracy measures true positive i.e accuracy is discrete values, while the logloss of softmax loss so to speak is a continuous variable that measures the models perfo |
6,294 | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model? | Let the data be $\mathbf{x}=(x_1, \ldots, x_n)$. Write $F(\mathbf{x})$ for the empirical distribution. By definition, for any function $f$,
$$\mathbb{E}_{F(\mathbf{x})}[f(X)] = \frac{1}{n}\sum_{i=1}^n f(x_i).$$
Let the model $M$ have density $e^{f(x)}$ where $f$ is defined on the support of the model. The cross-entro... | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model? | Let the data be $\mathbf{x}=(x_1, \ldots, x_n)$. Write $F(\mathbf{x})$ for the empirical distribution. By definition, for any function $f$,
$$\mathbb{E}_{F(\mathbf{x})}[f(X)] = \frac{1}{n}\sum_{i=1}^ | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model?
Let the data be $\mathbf{x}=(x_1, \ldots, x_n)$. Write $F(\mathbf{x})$ for the empirical distribution. By definition, for any function $f$,
$$\mathbb{E}_{F(\mathbf{x})}[f(X)] = \frac{1}{n}\sum_{i=1}^n f(x_i).$$
Let the... | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model?
Let the data be $\mathbf{x}=(x_1, \ldots, x_n)$. Write $F(\mathbf{x})$ for the empirical distribution. By definition, for any function $f$,
$$\mathbb{E}_{F(\mathbf{x})}[f(X)] = \frac{1}{n}\sum_{i=1}^ |
6,295 | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model? | For readers of the Deep Learning book, I would like to add to the excellent accepted answer that the authors explain their statement in detail in section 5.5.1 namely the Example: Linear Regression as Maximum Likelihood.
There, they list exactly the constraint mentioned in the accepted answer:
$p(y | x) = \mathcal{N}... | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model? | For readers of the Deep Learning book, I would like to add to the excellent accepted answer that the authors explain their statement in detail in section 5.5.1 namely the Example: Linear Regression as | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model?
For readers of the Deep Learning book, I would like to add to the excellent accepted answer that the authors explain their statement in detail in section 5.5.1 namely the Example: Linear Regression as Maximum Likelihood... | Why is mean squared error the cross-entropy between the empirical distribution and a Gaussian model?
For readers of the Deep Learning book, I would like to add to the excellent accepted answer that the authors explain their statement in detail in section 5.5.1 namely the Example: Linear Regression as |
6,296 | Which search range for determining SVM optimal C and gamma parameters? | Check out A practical guide to SVM Classification for some pointers, particularly page 5.
We recommend a "grid-search" on $C$ and $\gamma$ using cross-validation. Various pairs of $(C,\gamma)$ values are tried and the one with the best cross-validation accuracy is
picked. We found that trying exponentially growing ... | Which search range for determining SVM optimal C and gamma parameters? | Check out A practical guide to SVM Classification for some pointers, particularly page 5.
We recommend a "grid-search" on $C$ and $\gamma$ using cross-validation. Various pairs of $(C,\gamma)$ value | Which search range for determining SVM optimal C and gamma parameters?
Check out A practical guide to SVM Classification for some pointers, particularly page 5.
We recommend a "grid-search" on $C$ and $\gamma$ using cross-validation. Various pairs of $(C,\gamma)$ values are tried and the one with the best cross-valid... | Which search range for determining SVM optimal C and gamma parameters?
Check out A practical guide to SVM Classification for some pointers, particularly page 5.
We recommend a "grid-search" on $C$ and $\gamma$ using cross-validation. Various pairs of $(C,\gamma)$ value |
6,297 | Which search range for determining SVM optimal C and gamma parameters? | Check out section 2.3.2 of this paper by Chapelle and Zien. They have a nice heuristic to select a good search range for $\sigma$ of the RBF kernel and $C$ for the SVM. I quote
To determine good values of the remaining free parameters (eg, by CV),
it is important to search on the right scale. We therefore fix defaul... | Which search range for determining SVM optimal C and gamma parameters? | Check out section 2.3.2 of this paper by Chapelle and Zien. They have a nice heuristic to select a good search range for $\sigma$ of the RBF kernel and $C$ for the SVM. I quote
To determine good valu | Which search range for determining SVM optimal C and gamma parameters?
Check out section 2.3.2 of this paper by Chapelle and Zien. They have a nice heuristic to select a good search range for $\sigma$ of the RBF kernel and $C$ for the SVM. I quote
To determine good values of the remaining free parameters (eg, by CV),
... | Which search range for determining SVM optimal C and gamma parameters?
Check out section 2.3.2 of this paper by Chapelle and Zien. They have a nice heuristic to select a good search range for $\sigma$ of the RBF kernel and $C$ for the SVM. I quote
To determine good valu |
6,298 | How to interpret OOB and confusion matrix for random forest? | The confusion matrix is calculated at a specific point determined by the cutoff on the votes. Depending on your needs, i.e., better precision (reduce false positives) or better sensitivity (reduce false negatives) you may prefer a different cutoff.
For this purpose I recommend plotting (i) a ROC curve, (ii) a recall-p... | How to interpret OOB and confusion matrix for random forest? | The confusion matrix is calculated at a specific point determined by the cutoff on the votes. Depending on your needs, i.e., better precision (reduce false positives) or better sensitivity (reduce fal | How to interpret OOB and confusion matrix for random forest?
The confusion matrix is calculated at a specific point determined by the cutoff on the votes. Depending on your needs, i.e., better precision (reduce false positives) or better sensitivity (reduce false negatives) you may prefer a different cutoff.
For this ... | How to interpret OOB and confusion matrix for random forest?
The confusion matrix is calculated at a specific point determined by the cutoff on the votes. Depending on your needs, i.e., better precision (reduce false positives) or better sensitivity (reduce fal |
6,299 | How to interpret OOB and confusion matrix for random forest? | Your set is sharply unbalanced -- RF usually fails in this scenario (i.e. predicts well only the bigger class).
You should try balancing your set either by sampling the "0" class only to have about the same size as "1" class or by playing with classwt parameter. | How to interpret OOB and confusion matrix for random forest? | Your set is sharply unbalanced -- RF usually fails in this scenario (i.e. predicts well only the bigger class).
You should try balancing your set either by sampling the "0" class only to have about t | How to interpret OOB and confusion matrix for random forest?
Your set is sharply unbalanced -- RF usually fails in this scenario (i.e. predicts well only the bigger class).
You should try balancing your set either by sampling the "0" class only to have about the same size as "1" class or by playing with classwt parame... | How to interpret OOB and confusion matrix for random forest?
Your set is sharply unbalanced -- RF usually fails in this scenario (i.e. predicts well only the bigger class).
You should try balancing your set either by sampling the "0" class only to have about t |
6,300 | How to interpret OOB and confusion matrix for random forest? | Based on your confusion matrix, you've got 5,908 data points and the vast, vast majority of them are of type 0 ('employee stayed'). The classifier can therefore get away with being "lazy" and picking the majority class unless it's absolutely certain that an example belongs to the other class. Note that your overall er... | How to interpret OOB and confusion matrix for random forest? | Based on your confusion matrix, you've got 5,908 data points and the vast, vast majority of them are of type 0 ('employee stayed'). The classifier can therefore get away with being "lazy" and picking | How to interpret OOB and confusion matrix for random forest?
Based on your confusion matrix, you've got 5,908 data points and the vast, vast majority of them are of type 0 ('employee stayed'). The classifier can therefore get away with being "lazy" and picking the majority class unless it's absolutely certain that an ... | How to interpret OOB and confusion matrix for random forest?
Based on your confusion matrix, you've got 5,908 data points and the vast, vast majority of them are of type 0 ('employee stayed'). The classifier can therefore get away with being "lazy" and picking |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.