idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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49,601 | Probability of two people meeting | The side of the square is one, so its surface $= 1 * 1 = 1$.
The side of the upper white square-cornered triangle is $1 - w_1$, so its surface is $(1-w_1)*(1-w_1)/2$.
Similarly with the bottom triangle.
So: the surface of the gray area = square - two white triangles = formula $P2$.
Finally note that each 'point' in the... | Probability of two people meeting | The side of the square is one, so its surface $= 1 * 1 = 1$.
The side of the upper white square-cornered triangle is $1 - w_1$, so its surface is $(1-w_1)*(1-w_1)/2$.
Similarly with the bottom triangl | Probability of two people meeting
The side of the square is one, so its surface $= 1 * 1 = 1$.
The side of the upper white square-cornered triangle is $1 - w_1$, so its surface is $(1-w_1)*(1-w_1)/2$.
Similarly with the bottom triangle.
So: the surface of the gray area = square - two white triangles = formula $P2$.
Fin... | Probability of two people meeting
The side of the square is one, so its surface $= 1 * 1 = 1$.
The side of the upper white square-cornered triangle is $1 - w_1$, so its surface is $(1-w_1)*(1-w_1)/2$.
Similarly with the bottom triangl |
49,602 | Probability of two people meeting | First of all this is a very good example of application of geometric probability. It's related to continuous distribution.
The idea behind taking the 1×1 square is as below. Imagine a square with both axes as time.let the time be 1 hour each.this means the area is now 1hour ×1 hour.Let the 2 people be A and B . If A a... | Probability of two people meeting | First of all this is a very good example of application of geometric probability. It's related to continuous distribution.
The idea behind taking the 1×1 square is as below. Imagine a square with both | Probability of two people meeting
First of all this is a very good example of application of geometric probability. It's related to continuous distribution.
The idea behind taking the 1×1 square is as below. Imagine a square with both axes as time.let the time be 1 hour each.this means the area is now 1hour ×1 hour.Let... | Probability of two people meeting
First of all this is a very good example of application of geometric probability. It's related to continuous distribution.
The idea behind taking the 1×1 square is as below. Imagine a square with both |
49,603 | Probability of two people meeting | Beside the geometric interpretation, the probability that the two people meet in the hour is given by the probability that the second person arrives in a suitable interval ($\pm 10$ minutes) conditioned to the time of arrival of the first person:
$$p(meet) = p(y \in \Delta T_x | x) \cdot p(x) = p(y \in \Delta T_x) \cd... | Probability of two people meeting | Beside the geometric interpretation, the probability that the two people meet in the hour is given by the probability that the second person arrives in a suitable interval ($\pm 10$ minutes) condition | Probability of two people meeting
Beside the geometric interpretation, the probability that the two people meet in the hour is given by the probability that the second person arrives in a suitable interval ($\pm 10$ minutes) conditioned to the time of arrival of the first person:
$$p(meet) = p(y \in \Delta T_x | x) \cd... | Probability of two people meeting
Beside the geometric interpretation, the probability that the two people meet in the hour is given by the probability that the second person arrives in a suitable interval ($\pm 10$ minutes) condition |
49,604 | Probability of two people meeting | First of all, we can see how many different ways the first person can arrive
i.e.,
if he comes at 3pm then he goes again at 3 10 pm, similarly
3 01 pm to 3 11 pm
3 02 pm to 3 12 pm ...................and so on
...
...
...
3 50 pm to 4 00 pm
Therefore, he can arrive in 51 ways if we calculate ... | Probability of two people meeting | First of all, we can see how many different ways the first person can arrive
i.e.,
if he comes at 3pm then he goes again at 3 10 pm, similarly
3 01 pm to 3 11 pm
3 02 pm to 3 12 pm . | Probability of two people meeting
First of all, we can see how many different ways the first person can arrive
i.e.,
if he comes at 3pm then he goes again at 3 10 pm, similarly
3 01 pm to 3 11 pm
3 02 pm to 3 12 pm ...................and so on
...
...
...
3 50 pm to 4 00 pm
Therefore, he can ... | Probability of two people meeting
First of all, we can see how many different ways the first person can arrive
i.e.,
if he comes at 3pm then he goes again at 3 10 pm, similarly
3 01 pm to 3 11 pm
3 02 pm to 3 12 pm . |
49,605 | How to understand the plotting of the cox.zph function in R? | When interpreting the output of cox.zph it is just as much (or even more) the "flatness" of the line, as it is the straightness of the line, that is important. If the line is straight but slanted upward it implies non-proportionality in the form of a rising hazard ratio over time. See Therneau and Gramsch's text in the... | How to understand the plotting of the cox.zph function in R? | When interpreting the output of cox.zph it is just as much (or even more) the "flatness" of the line, as it is the straightness of the line, that is important. If the line is straight but slanted upwa | How to understand the plotting of the cox.zph function in R?
When interpreting the output of cox.zph it is just as much (or even more) the "flatness" of the line, as it is the straightness of the line, that is important. If the line is straight but slanted upward it implies non-proportionality in the form of a rising h... | How to understand the plotting of the cox.zph function in R?
When interpreting the output of cox.zph it is just as much (or even more) the "flatness" of the line, as it is the straightness of the line, that is important. If the line is straight but slanted upwa |
49,606 | How to understand the plotting of the cox.zph function in R? | The curve is a natural spline fit (by default, with 4 degrees of freedom) of the time varying estimates of beta (the log of the hazard ratio). If that line is fairly flat and straight, then proportionality is supported. The dashed lines are confidence intervals at two standard errors. See the help pages for cox.zph ... | How to understand the plotting of the cox.zph function in R? | The curve is a natural spline fit (by default, with 4 degrees of freedom) of the time varying estimates of beta (the log of the hazard ratio). If that line is fairly flat and straight, then proportio | How to understand the plotting of the cox.zph function in R?
The curve is a natural spline fit (by default, with 4 degrees of freedom) of the time varying estimates of beta (the log of the hazard ratio). If that line is fairly flat and straight, then proportionality is supported. The dashed lines are confidence inter... | How to understand the plotting of the cox.zph function in R?
The curve is a natural spline fit (by default, with 4 degrees of freedom) of the time varying estimates of beta (the log of the hazard ratio). If that line is fairly flat and straight, then proportio |
49,607 | What is the most computationally efficient way to sample from an unnormalized density? | First of all, $P(\theta,D)=P(D|\theta)P(\theta)$ and not $P(\theta|D)$. Perhaps it is a type since you refer to it as an un-normalized version. Secondly, you may not need to run two rejection sampling algorithms since the prior $P(\theta)$ can usually be sampled directly and then you can reject it with $P(D|\theta)$. W... | What is the most computationally efficient way to sample from an unnormalized density? | First of all, $P(\theta,D)=P(D|\theta)P(\theta)$ and not $P(\theta|D)$. Perhaps it is a type since you refer to it as an un-normalized version. Secondly, you may not need to run two rejection sampling | What is the most computationally efficient way to sample from an unnormalized density?
First of all, $P(\theta,D)=P(D|\theta)P(\theta)$ and not $P(\theta|D)$. Perhaps it is a type since you refer to it as an un-normalized version. Secondly, you may not need to run two rejection sampling algorithms since the prior $P(\t... | What is the most computationally efficient way to sample from an unnormalized density?
First of all, $P(\theta,D)=P(D|\theta)P(\theta)$ and not $P(\theta|D)$. Perhaps it is a type since you refer to it as an un-normalized version. Secondly, you may not need to run two rejection sampling |
49,608 | What is the most computationally efficient way to sample from an unnormalized density? | It all depends on three aspects of your system:
the number of modes
dimensionality
the correlation structure of $\theta$
If you expect all parameters to have a unique solution, and your posterior to be unimodal, sampling is quite easy with all the methods you just cited, and I wouldn't really bother looking further, ... | What is the most computationally efficient way to sample from an unnormalized density? | It all depends on three aspects of your system:
the number of modes
dimensionality
the correlation structure of $\theta$
If you expect all parameters to have a unique solution, and your posterior to | What is the most computationally efficient way to sample from an unnormalized density?
It all depends on three aspects of your system:
the number of modes
dimensionality
the correlation structure of $\theta$
If you expect all parameters to have a unique solution, and your posterior to be unimodal, sampling is quite e... | What is the most computationally efficient way to sample from an unnormalized density?
It all depends on three aspects of your system:
the number of modes
dimensionality
the correlation structure of $\theta$
If you expect all parameters to have a unique solution, and your posterior to |
49,609 | How to quantify correlation stability? | You might want to compare constant conditional correlation with dynamic conditional correlation. In R, the ccgarch package will be helpful. In Matlab, Kevin Sheppard has an implementation of DCC. | How to quantify correlation stability? | You might want to compare constant conditional correlation with dynamic conditional correlation. In R, the ccgarch package will be helpful. In Matlab, Kevin Sheppard has an implementation of DCC. | How to quantify correlation stability?
You might want to compare constant conditional correlation with dynamic conditional correlation. In R, the ccgarch package will be helpful. In Matlab, Kevin Sheppard has an implementation of DCC. | How to quantify correlation stability?
You might want to compare constant conditional correlation with dynamic conditional correlation. In R, the ccgarch package will be helpful. In Matlab, Kevin Sheppard has an implementation of DCC. |
49,610 | How to quantify correlation stability? | You could start with a simple 'rolling' analysis of the correlation to see how stable it is over time. Here is an example in R:
#Get Data
require(quantmod)
getSymbols(c('SPY','EEM'))
#Rolling Correlation (30 days)
require(PerformanceAnalytics)
chart.RollingCorrelation(Cl(SPY), Cl(EEM), width=30) | How to quantify correlation stability? | You could start with a simple 'rolling' analysis of the correlation to see how stable it is over time. Here is an example in R:
#Get Data
require(quantmod)
getSymbols(c('SPY','EEM'))
#Rolling Correl | How to quantify correlation stability?
You could start with a simple 'rolling' analysis of the correlation to see how stable it is over time. Here is an example in R:
#Get Data
require(quantmod)
getSymbols(c('SPY','EEM'))
#Rolling Correlation (30 days)
require(PerformanceAnalytics)
chart.RollingCorrelation(Cl(SPY), C... | How to quantify correlation stability?
You could start with a simple 'rolling' analysis of the correlation to see how stable it is over time. Here is an example in R:
#Get Data
require(quantmod)
getSymbols(c('SPY','EEM'))
#Rolling Correl |
49,611 | How does "ward" clustering (in R's hclust function) work? | The distance between two clusters is calculated using the Lance-Williams update formula, see the Wikipedia entry. It holds that:
$$
2/3*\text{abs}(2-3)+2/3*\text{abs}(1-3)-1/3*1 = 1.666667
$$ | How does "ward" clustering (in R's hclust function) work? | The distance between two clusters is calculated using the Lance-Williams update formula, see the Wikipedia entry. It holds that:
$$
2/3*\text{abs}(2-3)+2/3*\text{abs}(1-3)-1/3*1 = 1.666667
$$ | How does "ward" clustering (in R's hclust function) work?
The distance between two clusters is calculated using the Lance-Williams update formula, see the Wikipedia entry. It holds that:
$$
2/3*\text{abs}(2-3)+2/3*\text{abs}(1-3)-1/3*1 = 1.666667
$$ | How does "ward" clustering (in R's hclust function) work?
The distance between two clusters is calculated using the Lance-Williams update formula, see the Wikipedia entry. It holds that:
$$
2/3*\text{abs}(2-3)+2/3*\text{abs}(1-3)-1/3*1 = 1.666667
$$ |
49,612 | How does "ward" clustering (in R's hclust function) work? | It is in fact (in words) the absolute distance from the extreme value to the overall mean, plus two times the absolute distance from the mean of the two moderate values to the overall mean, minus a third of the absolute distance from one of the moderate values to mean of the two moderate values, minus a third of the ab... | How does "ward" clustering (in R's hclust function) work? | It is in fact (in words) the absolute distance from the extreme value to the overall mean, plus two times the absolute distance from the mean of the two moderate values to the overall mean, minus a th | How does "ward" clustering (in R's hclust function) work?
It is in fact (in words) the absolute distance from the extreme value to the overall mean, plus two times the absolute distance from the mean of the two moderate values to the overall mean, minus a third of the absolute distance from one of the moderate values t... | How does "ward" clustering (in R's hclust function) work?
It is in fact (in words) the absolute distance from the extreme value to the overall mean, plus two times the absolute distance from the mean of the two moderate values to the overall mean, minus a th |
49,613 | How to simplify a stretched exponential fit? | The first thing to do, if possible, is to take care of the heteroscedasticity. Notice how the spread of the residuals consistently increases with the fit: in fact, the spread seems to increase almost quadratically with larger fit.
A standard cure is to return to the original response ($log(xy)$) and apply a strong tra... | How to simplify a stretched exponential fit? | The first thing to do, if possible, is to take care of the heteroscedasticity. Notice how the spread of the residuals consistently increases with the fit: in fact, the spread seems to increase almost | How to simplify a stretched exponential fit?
The first thing to do, if possible, is to take care of the heteroscedasticity. Notice how the spread of the residuals consistently increases with the fit: in fact, the spread seems to increase almost quadratically with larger fit.
A standard cure is to return to the origina... | How to simplify a stretched exponential fit?
The first thing to do, if possible, is to take care of the heteroscedasticity. Notice how the spread of the residuals consistently increases with the fit: in fact, the spread seems to increase almost |
49,614 | X-mean algorithm BIC calculation question | Let the clusters be indexed by $j = 1, \ldots, K$ with $K_j \gt 0$ points in cluster $j$. Let $\mu_j$ (no parentheses around the subscript) designate the mean of cluster $j$. Then, because by definition $\mu_{(i)}$ is the mean of whichever cluster $x_i$ belongs to, we can group the terms in the summation by cluster:
... | X-mean algorithm BIC calculation question | Let the clusters be indexed by $j = 1, \ldots, K$ with $K_j \gt 0$ points in cluster $j$. Let $\mu_j$ (no parentheses around the subscript) designate the mean of cluster $j$. Then, because by defini | X-mean algorithm BIC calculation question
Let the clusters be indexed by $j = 1, \ldots, K$ with $K_j \gt 0$ points in cluster $j$. Let $\mu_j$ (no parentheses around the subscript) designate the mean of cluster $j$. Then, because by definition $\mu_{(i)}$ is the mean of whichever cluster $x_i$ belongs to, we can gro... | X-mean algorithm BIC calculation question
Let the clusters be indexed by $j = 1, \ldots, K$ with $K_j \gt 0$ points in cluster $j$. Let $\mu_j$ (no parentheses around the subscript) designate the mean of cluster $j$. Then, because by defini |
49,615 | Interpret t-values when not assuming normal distribution of the error term | If the residuals are not normal (and note that this applies to the theoretical residuals rather than the observed residuals), but not overly skewed or with outliers then the Central Limit Theorem applies and the inference on the slopes (t-tests, confidence intervals) will be approximately correct. The quality of the a... | Interpret t-values when not assuming normal distribution of the error term | If the residuals are not normal (and note that this applies to the theoretical residuals rather than the observed residuals), but not overly skewed or with outliers then the Central Limit Theorem appl | Interpret t-values when not assuming normal distribution of the error term
If the residuals are not normal (and note that this applies to the theoretical residuals rather than the observed residuals), but not overly skewed or with outliers then the Central Limit Theorem applies and the inference on the slopes (t-tests,... | Interpret t-values when not assuming normal distribution of the error term
If the residuals are not normal (and note that this applies to the theoretical residuals rather than the observed residuals), but not overly skewed or with outliers then the Central Limit Theorem appl |
49,616 | Interpret t-values when not assuming normal distribution of the error term | If the errors are not normally distributed, asymptotic results can be used. Suppose your model is
$$y_i=x_i'\beta+\varepsilon_i$$
where $(y_i,x_i',\varepsilon_i)$, $i=1,...,n$ is an iid sample. Assume
\begin{align*}
E(\varepsilon_i|x_i)&=0 \\
E(\varepsilon_i^2|x_i)&=\sigma^2
\end{align*}
and
$$rank(Ex_ix_i')=K,$$
whe... | Interpret t-values when not assuming normal distribution of the error term | If the errors are not normally distributed, asymptotic results can be used. Suppose your model is
$$y_i=x_i'\beta+\varepsilon_i$$
where $(y_i,x_i',\varepsilon_i)$, $i=1,...,n$ is an iid sample. Assume | Interpret t-values when not assuming normal distribution of the error term
If the errors are not normally distributed, asymptotic results can be used. Suppose your model is
$$y_i=x_i'\beta+\varepsilon_i$$
where $(y_i,x_i',\varepsilon_i)$, $i=1,...,n$ is an iid sample. Assume
\begin{align*}
E(\varepsilon_i|x_i)&=0 \\
E... | Interpret t-values when not assuming normal distribution of the error term
If the errors are not normally distributed, asymptotic results can be used. Suppose your model is
$$y_i=x_i'\beta+\varepsilon_i$$
where $(y_i,x_i',\varepsilon_i)$, $i=1,...,n$ is an iid sample. Assume |
49,617 | How to combine two independent repeated experiments with different success probabilities? | Interesting problem.
Let's first generalize it and simplify the notation. There are two multinomial distributions, one with probabilities $(p_1, p_2, \ldots, p_n)$ = $(2/(n+1), 1/(n+1), \ldots, 1/(n+1))$ and the other with probabilities $(q_1,q_2, \ldots, q_n)$ = $(3/(2n+1), 2/(2n+1), \ldots, 2/(2n+1))$. The probabil... | How to combine two independent repeated experiments with different success probabilities? | Interesting problem.
Let's first generalize it and simplify the notation. There are two multinomial distributions, one with probabilities $(p_1, p_2, \ldots, p_n)$ = $(2/(n+1), 1/(n+1), \ldots, 1/(n+ | How to combine two independent repeated experiments with different success probabilities?
Interesting problem.
Let's first generalize it and simplify the notation. There are two multinomial distributions, one with probabilities $(p_1, p_2, \ldots, p_n)$ = $(2/(n+1), 1/(n+1), \ldots, 1/(n+1))$ and the other with probab... | How to combine two independent repeated experiments with different success probabilities?
Interesting problem.
Let's first generalize it and simplify the notation. There are two multinomial distributions, one with probabilities $(p_1, p_2, \ldots, p_n)$ = $(2/(n+1), 1/(n+1), \ldots, 1/(n+ |
49,618 | How to tell the "closeness" of two variables | Solution
When you assume the residuals (vertical deviations in a graph of $n$ data) are independently and identically distributed with some normal distribution of zero mean, the estimate of the slope will have a Student t distribution with $n-2$ degrees of freedom, scaled by the standard error. Because the theoretical... | How to tell the "closeness" of two variables | Solution
When you assume the residuals (vertical deviations in a graph of $n$ data) are independently and identically distributed with some normal distribution of zero mean, the estimate of the slope | How to tell the "closeness" of two variables
Solution
When you assume the residuals (vertical deviations in a graph of $n$ data) are independently and identically distributed with some normal distribution of zero mean, the estimate of the slope will have a Student t distribution with $n-2$ degrees of freedom, scaled by... | How to tell the "closeness" of two variables
Solution
When you assume the residuals (vertical deviations in a graph of $n$ data) are independently and identically distributed with some normal distribution of zero mean, the estimate of the slope |
49,619 | Getting an average measurement based on two raters for cases where data is missing for one rater | The idea above sounds rather like single imputation. This is a better idea when faced with missing data than either list-wise or pair-wise deletion. However, its still not a good approach.
A better approach could be multiple imputation. Essentially, you simulate from 3-10 datasets conditional on your observed data. Yo... | Getting an average measurement based on two raters for cases where data is missing for one rater | The idea above sounds rather like single imputation. This is a better idea when faced with missing data than either list-wise or pair-wise deletion. However, its still not a good approach.
A better a | Getting an average measurement based on two raters for cases where data is missing for one rater
The idea above sounds rather like single imputation. This is a better idea when faced with missing data than either list-wise or pair-wise deletion. However, its still not a good approach.
A better approach could be multip... | Getting an average measurement based on two raters for cases where data is missing for one rater
The idea above sounds rather like single imputation. This is a better idea when faced with missing data than either list-wise or pair-wise deletion. However, its still not a good approach.
A better a |
49,620 | What is the pull distribution? | I think this CDF public analysis note can be a good answer.
or the ps file from CDF. | What is the pull distribution? | I think this CDF public analysis note can be a good answer.
or the ps file from CDF. | What is the pull distribution?
I think this CDF public analysis note can be a good answer.
or the ps file from CDF. | What is the pull distribution?
I think this CDF public analysis note can be a good answer.
or the ps file from CDF. |
49,621 | Can anyone explain quantile maximum probability estimation (QMPE)? | I'm late to the party but it seems this question still needs an answer, and, surprising to me, I don't see any other questions on this topic. So I'll go ahead and offer this.
To summarize, the QMPE approach is to formulate a likelihood function in terms of the quantiles of the observed data and not the observed data th... | Can anyone explain quantile maximum probability estimation (QMPE)? | I'm late to the party but it seems this question still needs an answer, and, surprising to me, I don't see any other questions on this topic. So I'll go ahead and offer this.
To summarize, the QMPE ap | Can anyone explain quantile maximum probability estimation (QMPE)?
I'm late to the party but it seems this question still needs an answer, and, surprising to me, I don't see any other questions on this topic. So I'll go ahead and offer this.
To summarize, the QMPE approach is to formulate a likelihood function in terms... | Can anyone explain quantile maximum probability estimation (QMPE)?
I'm late to the party but it seems this question still needs an answer, and, surprising to me, I don't see any other questions on this topic. So I'll go ahead and offer this.
To summarize, the QMPE ap |
49,622 | Can anyone explain quantile maximum probability estimation (QMPE)? | Just a small suggestion:
Have you checked out the Newcastle Cognition Lab's page on QMPE?
It has source code, a getting started guide, and a few other resources. | Can anyone explain quantile maximum probability estimation (QMPE)? | Just a small suggestion:
Have you checked out the Newcastle Cognition Lab's page on QMPE?
It has source code, a getting started guide, and a few other resources. | Can anyone explain quantile maximum probability estimation (QMPE)?
Just a small suggestion:
Have you checked out the Newcastle Cognition Lab's page on QMPE?
It has source code, a getting started guide, and a few other resources. | Can anyone explain quantile maximum probability estimation (QMPE)?
Just a small suggestion:
Have you checked out the Newcastle Cognition Lab's page on QMPE?
It has source code, a getting started guide, and a few other resources. |
49,623 | Structural equation modeling for experimental design data | There is no simple yes or no answer. People constantly attempt to make inferences about causal relationships. The question is what assumptions you have to make, and how sensitive your inferences are to changing those assumptions.
The causal effects you can identify with the fewest assumptions are the effects of the... | Structural equation modeling for experimental design data | There is no simple yes or no answer. People constantly attempt to make inferences about causal relationships. The question is what assumptions you have to make, and how sensitive your inferences are | Structural equation modeling for experimental design data
There is no simple yes or no answer. People constantly attempt to make inferences about causal relationships. The question is what assumptions you have to make, and how sensitive your inferences are to changing those assumptions.
The causal effects you can i... | Structural equation modeling for experimental design data
There is no simple yes or no answer. People constantly attempt to make inferences about causal relationships. The question is what assumptions you have to make, and how sensitive your inferences are |
49,624 | Generating dependent time series from a given distribution? | You can use Markov chains. You will have a to specify a density $p(x_t|x_{t-1})$. Of course you will have to be able to sample from that marginal. Then just sample... | Generating dependent time series from a given distribution? | You can use Markov chains. You will have a to specify a density $p(x_t|x_{t-1})$. Of course you will have to be able to sample from that marginal. Then just sample... | Generating dependent time series from a given distribution?
You can use Markov chains. You will have a to specify a density $p(x_t|x_{t-1})$. Of course you will have to be able to sample from that marginal. Then just sample... | Generating dependent time series from a given distribution?
You can use Markov chains. You will have a to specify a density $p(x_t|x_{t-1})$. Of course you will have to be able to sample from that marginal. Then just sample... |
49,625 | Generating dependent time series from a given distribution? | One way is to use transformations of random variables. It's easy to generate dependent Gaussians; then transform them to uniform variates with the CDF of the gaussian, and then transform the uniform variates to your distribution with the inverse CDF of your distribution. | Generating dependent time series from a given distribution? | One way is to use transformations of random variables. It's easy to generate dependent Gaussians; then transform them to uniform variates with the CDF of the gaussian, and then transform the uniform | Generating dependent time series from a given distribution?
One way is to use transformations of random variables. It's easy to generate dependent Gaussians; then transform them to uniform variates with the CDF of the gaussian, and then transform the uniform variates to your distribution with the inverse CDF of your d... | Generating dependent time series from a given distribution?
One way is to use transformations of random variables. It's easy to generate dependent Gaussians; then transform them to uniform variates with the CDF of the gaussian, and then transform the uniform |
49,626 | Fast integration of a posterior distribution | How accurate does your posterior cdf need to be? You might consider replacing the continuous prior with a discrete approximation:
$p^*(\theta) \propto p(\theta) 1(\theta\in t_1, \dots, t_k)$
where $p(\theta)$ is your original continuous prior.
Then to compute the posterior you just calculate likelihood x prior
$p(\the... | Fast integration of a posterior distribution | How accurate does your posterior cdf need to be? You might consider replacing the continuous prior with a discrete approximation:
$p^*(\theta) \propto p(\theta) 1(\theta\in t_1, \dots, t_k)$
where $p( | Fast integration of a posterior distribution
How accurate does your posterior cdf need to be? You might consider replacing the continuous prior with a discrete approximation:
$p^*(\theta) \propto p(\theta) 1(\theta\in t_1, \dots, t_k)$
where $p(\theta)$ is your original continuous prior.
Then to compute the posterior y... | Fast integration of a posterior distribution
How accurate does your posterior cdf need to be? You might consider replacing the continuous prior with a discrete approximation:
$p^*(\theta) \propto p(\theta) 1(\theta\in t_1, \dots, t_k)$
where $p( |
49,627 | Fast integration of a posterior distribution | There may be a simpler approach, simply by applying the usual Beta conjugate to the binomial, and then requiring $\theta \in [\frac12,1]$. You can do this with an indicator function, for example as in
$$p(\theta) \propto \theta^{\alpha-1} {(1-\theta)}^{\beta-1} \mathbb{1}[{\tfrac12 \le \theta \le 1}]$$
Now apply your ... | Fast integration of a posterior distribution | There may be a simpler approach, simply by applying the usual Beta conjugate to the binomial, and then requiring $\theta \in [\frac12,1]$. You can do this with an indicator function, for example as in | Fast integration of a posterior distribution
There may be a simpler approach, simply by applying the usual Beta conjugate to the binomial, and then requiring $\theta \in [\frac12,1]$. You can do this with an indicator function, for example as in
$$p(\theta) \propto \theta^{\alpha-1} {(1-\theta)}^{\beta-1} \mathbb{1}[{... | Fast integration of a posterior distribution
There may be a simpler approach, simply by applying the usual Beta conjugate to the binomial, and then requiring $\theta \in [\frac12,1]$. You can do this with an indicator function, for example as in |
49,628 | Fast integration of a posterior distribution | You can always use Monte Carlo Integration or the Midpoint method. With Monte Carlo, you simply generate a bunch of points in your parameter space and see if they are in the area or volume or hyper-dimensional space you are trying to integrate.
From:
http://farside.ph.utexas.edu/teaching/329/lectures/node109.html
"Let ... | Fast integration of a posterior distribution | You can always use Monte Carlo Integration or the Midpoint method. With Monte Carlo, you simply generate a bunch of points in your parameter space and see if they are in the area or volume or hyper-di | Fast integration of a posterior distribution
You can always use Monte Carlo Integration or the Midpoint method. With Monte Carlo, you simply generate a bunch of points in your parameter space and see if they are in the area or volume or hyper-dimensional space you are trying to integrate.
From:
http://farside.ph.utexas... | Fast integration of a posterior distribution
You can always use Monte Carlo Integration or the Midpoint method. With Monte Carlo, you simply generate a bunch of points in your parameter space and see if they are in the area or volume or hyper-di |
49,629 | Resampling within a survey to account for missing data | Your question is above my pay grade, as it were, but I can suggest a first look at the R survey package, which might implement some of the routines that you'd use to answer your questions. | Resampling within a survey to account for missing data | Your question is above my pay grade, as it were, but I can suggest a first look at the R survey package, which might implement some of the routines that you'd use to answer your questions. | Resampling within a survey to account for missing data
Your question is above my pay grade, as it were, but I can suggest a first look at the R survey package, which might implement some of the routines that you'd use to answer your questions. | Resampling within a survey to account for missing data
Your question is above my pay grade, as it were, but I can suggest a first look at the R survey package, which might implement some of the routines that you'd use to answer your questions. |
49,630 | Resampling within a survey to account for missing data | Standard formulas for standard errors of a proportion would be suitable. With regards to your question about which companies the "n=100 sample" plan to use in the future, these standard errors would be based on n = 100. If this yields standard errors that are too large for your liking, then you need to increase your sa... | Resampling within a survey to account for missing data | Standard formulas for standard errors of a proportion would be suitable. With regards to your question about which companies the "n=100 sample" plan to use in the future, these standard errors would b | Resampling within a survey to account for missing data
Standard formulas for standard errors of a proportion would be suitable. With regards to your question about which companies the "n=100 sample" plan to use in the future, these standard errors would be based on n = 100. If this yields standard errors that are too l... | Resampling within a survey to account for missing data
Standard formulas for standard errors of a proportion would be suitable. With regards to your question about which companies the "n=100 sample" plan to use in the future, these standard errors would b |
49,631 | Comparing cosine similarities for tf-idf vectors for documents with different length | According to Wikipedia's article of tf-idf:
The term count in the given document is simply the number of times a given term appears in
that document. This count is usually normalized to prevent a bias towards longer documents
(which may have a higher term count regardless of the actual importance of that term in ... | Comparing cosine similarities for tf-idf vectors for documents with different length | According to Wikipedia's article of tf-idf:
The term count in the given document is simply the number of times a given term appears in
that document. This count is usually normalized to prevent a | Comparing cosine similarities for tf-idf vectors for documents with different length
According to Wikipedia's article of tf-idf:
The term count in the given document is simply the number of times a given term appears in
that document. This count is usually normalized to prevent a bias towards longer documents
(wh... | Comparing cosine similarities for tf-idf vectors for documents with different length
According to Wikipedia's article of tf-idf:
The term count in the given document is simply the number of times a given term appears in
that document. This count is usually normalized to prevent a |
49,632 | Comparing cosine similarities for tf-idf vectors for documents with different length | The cosine similarity is still a valid measure. Actually, this is the rule that tf-idf weights have different lengths for different documents, simply because they do not use exactly the same words. Notice that a missing word in a tf-idf vector is actually a word with a frequency of 0.
So you elongate both vectors to th... | Comparing cosine similarities for tf-idf vectors for documents with different length | The cosine similarity is still a valid measure. Actually, this is the rule that tf-idf weights have different lengths for different documents, simply because they do not use exactly the same words. No | Comparing cosine similarities for tf-idf vectors for documents with different length
The cosine similarity is still a valid measure. Actually, this is the rule that tf-idf weights have different lengths for different documents, simply because they do not use exactly the same words. Notice that a missing word in a tf-id... | Comparing cosine similarities for tf-idf vectors for documents with different length
The cosine similarity is still a valid measure. Actually, this is the rule that tf-idf weights have different lengths for different documents, simply because they do not use exactly the same words. No |
49,633 | Estimating speed from position updates with uncertain time intervals | Because you trust the GPS positions (and therefore the distances computed from them) but the times have errors, regress the times against the cumulative distances.
To account for acceleration and deceleration, consider a model of the form
$$\text{Time} = t = \beta_0 + \beta_1 X + \beta_2 X^2 + \varepsilon$$
where $X$ i... | Estimating speed from position updates with uncertain time intervals | Because you trust the GPS positions (and therefore the distances computed from them) but the times have errors, regress the times against the cumulative distances.
To account for acceleration and dece | Estimating speed from position updates with uncertain time intervals
Because you trust the GPS positions (and therefore the distances computed from them) but the times have errors, regress the times against the cumulative distances.
To account for acceleration and deceleration, consider a model of the form
$$\text{Time... | Estimating speed from position updates with uncertain time intervals
Because you trust the GPS positions (and therefore the distances computed from them) but the times have errors, regress the times against the cumulative distances.
To account for acceleration and dece |
49,634 | Principal components of spatial variables | Your idea about the "rasters" is not very clearly stated, but you might have a look at the paper by Borcard and Legendre (1994) and their later works on spatial eigenvector-based analyses to see if one of the approaches will fit to your problem.
Borcard, D., Legendre, P., (1994) Environmental control and spatial struct... | Principal components of spatial variables | Your idea about the "rasters" is not very clearly stated, but you might have a look at the paper by Borcard and Legendre (1994) and their later works on spatial eigenvector-based analyses to see if on | Principal components of spatial variables
Your idea about the "rasters" is not very clearly stated, but you might have a look at the paper by Borcard and Legendre (1994) and their later works on spatial eigenvector-based analyses to see if one of the approaches will fit to your problem.
Borcard, D., Legendre, P., (1994... | Principal components of spatial variables
Your idea about the "rasters" is not very clearly stated, but you might have a look at the paper by Borcard and Legendre (1994) and their later works on spatial eigenvector-based analyses to see if on |
49,635 | Is it possible to fit a multivariate regression model where the independent variable is latent? | Might we reformulate the question as: 'I have N M-variate observations which I assume to be generated by N corresponding P-variate latent variables i.e. for each case/row M observed numbers are generated by P unobserved numbers. I have an idea that this mapping is linear with an M x P matrix of coefficients and I want... | Is it possible to fit a multivariate regression model where the independent variable is latent? | Might we reformulate the question as: 'I have N M-variate observations which I assume to be generated by N corresponding P-variate latent variables i.e. for each case/row M observed numbers are genera | Is it possible to fit a multivariate regression model where the independent variable is latent?
Might we reformulate the question as: 'I have N M-variate observations which I assume to be generated by N corresponding P-variate latent variables i.e. for each case/row M observed numbers are generated by P unobserved numb... | Is it possible to fit a multivariate regression model where the independent variable is latent?
Might we reformulate the question as: 'I have N M-variate observations which I assume to be generated by N corresponding P-variate latent variables i.e. for each case/row M observed numbers are genera |
49,636 | Output layer of artificial neural networks when learning non-linear functions with limited value range | I am opposed to cutting values of, since this will lead to an undifferentiable transfer function and your gradient based training algorithm might screw up.
The sigmoid function at the output layer is fine: $\sigma(x) = \frac{1}{1 + e^{-x}}$. It will squash any output to lie within $(0, 1)$. So you can get arbitrarily c... | Output layer of artificial neural networks when learning non-linear functions with limited value ran | I am opposed to cutting values of, since this will lead to an undifferentiable transfer function and your gradient based training algorithm might screw up.
The sigmoid function at the output layer is | Output layer of artificial neural networks when learning non-linear functions with limited value range
I am opposed to cutting values of, since this will lead to an undifferentiable transfer function and your gradient based training algorithm might screw up.
The sigmoid function at the output layer is fine: $\sigma(x) ... | Output layer of artificial neural networks when learning non-linear functions with limited value ran
I am opposed to cutting values of, since this will lead to an undifferentiable transfer function and your gradient based training algorithm might screw up.
The sigmoid function at the output layer is |
49,637 | Output layer of artificial neural networks when learning non-linear functions with limited value range | If you use a logistic activation function in the output layer it will restrict the output to the range 0-1 as you require.
However if you have a regression problem with a restricted output range the sum-of-squares error metric may not be ideal and maybe a beta noise model might be more appropriate (c.f. beta regressi... | Output layer of artificial neural networks when learning non-linear functions with limited value ran | If you use a logistic activation function in the output layer it will restrict the output to the range 0-1 as you require.
However if you have a regression problem with a restricted output range the | Output layer of artificial neural networks when learning non-linear functions with limited value range
If you use a logistic activation function in the output layer it will restrict the output to the range 0-1 as you require.
However if you have a regression problem with a restricted output range the sum-of-squares e... | Output layer of artificial neural networks when learning non-linear functions with limited value ran
If you use a logistic activation function in the output layer it will restrict the output to the range 0-1 as you require.
However if you have a regression problem with a restricted output range the |
49,638 | Output layer of artificial neural networks when learning non-linear functions with limited value range | If you know an absolute range for the output, but there is no reason to expect it to have the non-linear characteristic of the typical logistic activation function (i.e. a value in the middle is just as likely as a value near 0 or 1), then you can just transform the output by dividing by the absolute maximum. If the m... | Output layer of artificial neural networks when learning non-linear functions with limited value ran | If you know an absolute range for the output, but there is no reason to expect it to have the non-linear characteristic of the typical logistic activation function (i.e. a value in the middle is just | Output layer of artificial neural networks when learning non-linear functions with limited value range
If you know an absolute range for the output, but there is no reason to expect it to have the non-linear characteristic of the typical logistic activation function (i.e. a value in the middle is just as likely as a va... | Output layer of artificial neural networks when learning non-linear functions with limited value ran
If you know an absolute range for the output, but there is no reason to expect it to have the non-linear characteristic of the typical logistic activation function (i.e. a value in the middle is just |
49,639 | Output layer of artificial neural networks when learning non-linear functions with limited value range | "Would it work to use the linear function and simply cut all values below 0 to 0, and values above 1 to 1?"
I believe in many cases the cut-off value should be the percentage split of the training data. Eg if your training data has 13% - 0's and 87% - 1's, then the cut-off would be 0.13; For example anything 0.13 and ... | Output layer of artificial neural networks when learning non-linear functions with limited value ran | "Would it work to use the linear function and simply cut all values below 0 to 0, and values above 1 to 1?"
I believe in many cases the cut-off value should be the percentage split of the training dat | Output layer of artificial neural networks when learning non-linear functions with limited value range
"Would it work to use the linear function and simply cut all values below 0 to 0, and values above 1 to 1?"
I believe in many cases the cut-off value should be the percentage split of the training data. Eg if your tra... | Output layer of artificial neural networks when learning non-linear functions with limited value ran
"Would it work to use the linear function and simply cut all values below 0 to 0, and values above 1 to 1?"
I believe in many cases the cut-off value should be the percentage split of the training dat |
49,640 | How to graphically compare predicted and actual values from multivariate regression in R? | In addition to @mpiktas's comment, you can also have a look at the rms package from Frank Harrell. The advantage is that it handles both LM and GLM for model fitting and prediction; see for example the plot.Predict() function. If you're planning to do serious job in regression modeling, this package and its companion H... | How to graphically compare predicted and actual values from multivariate regression in R? | In addition to @mpiktas's comment, you can also have a look at the rms package from Frank Harrell. The advantage is that it handles both LM and GLM for model fitting and prediction; see for example th | How to graphically compare predicted and actual values from multivariate regression in R?
In addition to @mpiktas's comment, you can also have a look at the rms package from Frank Harrell. The advantage is that it handles both LM and GLM for model fitting and prediction; see for example the plot.Predict() function. If ... | How to graphically compare predicted and actual values from multivariate regression in R?
In addition to @mpiktas's comment, you can also have a look at the rms package from Frank Harrell. The advantage is that it handles both LM and GLM for model fitting and prediction; see for example th |
49,641 | Probability calculation, system uptime, likelihood of occurence | Okay, so here is my answer that I promised. I initially thought it would be quickish, but my answer has become quite large, so at the begining, I state my general results first, and leave the gory details down the bottom for those who want to see it.
I must thank @terry felkrow for this fascinating question - if I cou... | Probability calculation, system uptime, likelihood of occurence | Okay, so here is my answer that I promised. I initially thought it would be quickish, but my answer has become quite large, so at the begining, I state my general results first, and leave the gory de | Probability calculation, system uptime, likelihood of occurence
Okay, so here is my answer that I promised. I initially thought it would be quickish, but my answer has become quite large, so at the begining, I state my general results first, and leave the gory details down the bottom for those who want to see it.
I mu... | Probability calculation, system uptime, likelihood of occurence
Okay, so here is my answer that I promised. I initially thought it would be quickish, but my answer has become quite large, so at the begining, I state my general results first, and leave the gory de |
49,642 | Predicting a semi-deterministic process | If you want to forecast time-series data, first you need to check whether it is stationary. Basically this means checking whether data has trends. If for example some time trend is present, you can concern yourself only with its forecast, because time-trends usually dominate everything else. For stationary time series ... | Predicting a semi-deterministic process | If you want to forecast time-series data, first you need to check whether it is stationary. Basically this means checking whether data has trends. If for example some time trend is present, you can co | Predicting a semi-deterministic process
If you want to forecast time-series data, first you need to check whether it is stationary. Basically this means checking whether data has trends. If for example some time trend is present, you can concern yourself only with its forecast, because time-trends usually dominate ever... | Predicting a semi-deterministic process
If you want to forecast time-series data, first you need to check whether it is stationary. Basically this means checking whether data has trends. If for example some time trend is present, you can co |
49,643 | Cluster data points by distance between clusters | Create a graph in which the points are nodes and two points are connected with an edge if and only if they lie within distance $d$ of each other. Stated in these terms, your criteria become
Every node in a cluster of two or more nodes is connected to at least one other node in that cluster.
No two points in any disjo... | Cluster data points by distance between clusters | Create a graph in which the points are nodes and two points are connected with an edge if and only if they lie within distance $d$ of each other. Stated in these terms, your criteria become
Every no | Cluster data points by distance between clusters
Create a graph in which the points are nodes and two points are connected with an edge if and only if they lie within distance $d$ of each other. Stated in these terms, your criteria become
Every node in a cluster of two or more nodes is connected to at least one other... | Cluster data points by distance between clusters
Create a graph in which the points are nodes and two points are connected with an edge if and only if they lie within distance $d$ of each other. Stated in these terms, your criteria become
Every no |
49,644 | Leave-one-out cross validation and boosted regression trees | It is hard to tell without data, but the set may be "too homogeneous" to make LOO work -- imagine you have a set $X$ and you duplicate all objects to make a set $X_d$ -- while BRT usually have very good accuracy on its train, it is pretty obvious that LOO on $X_d$ will probably give identical results to test-on-train.
... | Leave-one-out cross validation and boosted regression trees | It is hard to tell without data, but the set may be "too homogeneous" to make LOO work -- imagine you have a set $X$ and you duplicate all objects to make a set $X_d$ -- while BRT usually have very go | Leave-one-out cross validation and boosted regression trees
It is hard to tell without data, but the set may be "too homogeneous" to make LOO work -- imagine you have a set $X$ and you duplicate all objects to make a set $X_d$ -- while BRT usually have very good accuracy on its train, it is pretty obvious that LOO on $... | Leave-one-out cross validation and boosted regression trees
It is hard to tell without data, but the set may be "too homogeneous" to make LOO work -- imagine you have a set $X$ and you duplicate all objects to make a set $X_d$ -- while BRT usually have very go |
49,645 | Choosing the right threshold for a biometric trait authentication system | Generally, the cut-off value is chosen such as to maximize the compromise between sensitivity (Se) and specificity (Sp). You can generate a regular sequence of thresholds and plot the resulting ROC curve, as shown below, based on the DiagnosisMed R package.
Actually, the raw data looks like
test.values TP FN FP TN S... | Choosing the right threshold for a biometric trait authentication system | Generally, the cut-off value is chosen such as to maximize the compromise between sensitivity (Se) and specificity (Sp). You can generate a regular sequence of thresholds and plot the resulting ROC cu | Choosing the right threshold for a biometric trait authentication system
Generally, the cut-off value is chosen such as to maximize the compromise between sensitivity (Se) and specificity (Sp). You can generate a regular sequence of thresholds and plot the resulting ROC curve, as shown below, based on the DiagnosisMed ... | Choosing the right threshold for a biometric trait authentication system
Generally, the cut-off value is chosen such as to maximize the compromise between sensitivity (Se) and specificity (Sp). You can generate a regular sequence of thresholds and plot the resulting ROC cu |
49,646 | Generalization of the Signal-Noise ratio for non-Gaussian processes | I think signal to noise ratio is very common in signal processing regardless of the form of the noise distribution. It is like the reciprocal of the coefficient of variation not the ratio of two variances. | Generalization of the Signal-Noise ratio for non-Gaussian processes | I think signal to noise ratio is very common in signal processing regardless of the form of the noise distribution. It is like the reciprocal of the coefficient of variation not the ratio of two vari | Generalization of the Signal-Noise ratio for non-Gaussian processes
I think signal to noise ratio is very common in signal processing regardless of the form of the noise distribution. It is like the reciprocal of the coefficient of variation not the ratio of two variances. | Generalization of the Signal-Noise ratio for non-Gaussian processes
I think signal to noise ratio is very common in signal processing regardless of the form of the noise distribution. It is like the reciprocal of the coefficient of variation not the ratio of two vari |
49,647 | Generalization of the Signal-Noise ratio for non-Gaussian processes | Speaking from an engineering viewpoint, there are many different definitions of signal to noise ratio (see for example, this question on dsp.SE) depending on the application and the author, and the key property that they all share is that the performance parameters of interest (e.g. bit error rate) generally are monoto... | Generalization of the Signal-Noise ratio for non-Gaussian processes | Speaking from an engineering viewpoint, there are many different definitions of signal to noise ratio (see for example, this question on dsp.SE) depending on the application and the author, and the ke | Generalization of the Signal-Noise ratio for non-Gaussian processes
Speaking from an engineering viewpoint, there are many different definitions of signal to noise ratio (see for example, this question on dsp.SE) depending on the application and the author, and the key property that they all share is that the performan... | Generalization of the Signal-Noise ratio for non-Gaussian processes
Speaking from an engineering viewpoint, there are many different definitions of signal to noise ratio (see for example, this question on dsp.SE) depending on the application and the author, and the ke |
49,648 | How to test for parameter stationarity? | This problem is encountered in quality control/statistical process control settings. There's a large literature, as you have hinted, because different parameters as estimated in various ways from different forms of sampling different distributions can be expected to vary in different ways. The purpose is to detect th... | How to test for parameter stationarity? | This problem is encountered in quality control/statistical process control settings. There's a large literature, as you have hinted, because different parameters as estimated in various ways from dif | How to test for parameter stationarity?
This problem is encountered in quality control/statistical process control settings. There's a large literature, as you have hinted, because different parameters as estimated in various ways from different forms of sampling different distributions can be expected to vary in diff... | How to test for parameter stationarity?
This problem is encountered in quality control/statistical process control settings. There's a large literature, as you have hinted, because different parameters as estimated in various ways from dif |
49,649 | How to test for parameter stationarity? | This is a pretty general problem in time series analysis. I'd probably start by looking at some descriptive statistics like the cross-correlation to see if the samples are roughly independent over time. You could also test whether the correlation between successive samples is significant.
Or you could go the model-fitt... | How to test for parameter stationarity? | This is a pretty general problem in time series analysis. I'd probably start by looking at some descriptive statistics like the cross-correlation to see if the samples are roughly independent over tim | How to test for parameter stationarity?
This is a pretty general problem in time series analysis. I'd probably start by looking at some descriptive statistics like the cross-correlation to see if the samples are roughly independent over time. You could also test whether the correlation between successive samples is sig... | How to test for parameter stationarity?
This is a pretty general problem in time series analysis. I'd probably start by looking at some descriptive statistics like the cross-correlation to see if the samples are roughly independent over tim |
49,650 | From Marginal Exp-Norm Distributions to What Conditionals and Joint? | Would copulas be any use here? I don't know enough about them, or your problem, to be sure. | From Marginal Exp-Norm Distributions to What Conditionals and Joint? | Would copulas be any use here? I don't know enough about them, or your problem, to be sure. | From Marginal Exp-Norm Distributions to What Conditionals and Joint?
Would copulas be any use here? I don't know enough about them, or your problem, to be sure. | From Marginal Exp-Norm Distributions to What Conditionals and Joint?
Would copulas be any use here? I don't know enough about them, or your problem, to be sure. |
49,651 | Forecasting unemployment rate with plm | It is a known bug in plm package, when effect="individual" the pgmm crashes. The bug is fixed in plm version 1.2-7.
As for simulation, you need to calculate estimates of individual effects, since they are not estimated in GMM. At the current moment, the plm does not have the functions for predicting GMM model. I have... | Forecasting unemployment rate with plm | It is a known bug in plm package, when effect="individual" the pgmm crashes. The bug is fixed in plm version 1.2-7.
As for simulation, you need to calculate estimates of individual effects, since th | Forecasting unemployment rate with plm
It is a known bug in plm package, when effect="individual" the pgmm crashes. The bug is fixed in plm version 1.2-7.
As for simulation, you need to calculate estimates of individual effects, since they are not estimated in GMM. At the current moment, the plm does not have the fun... | Forecasting unemployment rate with plm
It is a known bug in plm package, when effect="individual" the pgmm crashes. The bug is fixed in plm version 1.2-7.
As for simulation, you need to calculate estimates of individual effects, since th |
49,652 | Are there any R functions which support Reversible Jump MCMC for a GLM or SGLM? [closed] | WinBUGS has support for RJMCMC with an addon. I've used it for GLMs, including those with an intrinsic CAR component. Not R, obviously, but through R2WinBUGS you can patch them together. | Are there any R functions which support Reversible Jump MCMC for a GLM or SGLM? [closed] | WinBUGS has support for RJMCMC with an addon. I've used it for GLMs, including those with an intrinsic CAR component. Not R, obviously, but through R2WinBUGS you can patch them together. | Are there any R functions which support Reversible Jump MCMC for a GLM or SGLM? [closed]
WinBUGS has support for RJMCMC with an addon. I've used it for GLMs, including those with an intrinsic CAR component. Not R, obviously, but through R2WinBUGS you can patch them together. | Are there any R functions which support Reversible Jump MCMC for a GLM or SGLM? [closed]
WinBUGS has support for RJMCMC with an addon. I've used it for GLMs, including those with an intrinsic CAR component. Not R, obviously, but through R2WinBUGS you can patch them together. |
49,653 | What are good references for dynamic pricing? | This article is highly cited:
"Yield Management at American Airlines" by Barry C. Smith et al.
Links:
JSTOR
free PDF 1, broken at 06.09.12
free PDF 2, broken at 02.01.18
free PDF 3 | What are good references for dynamic pricing? | This article is highly cited:
"Yield Management at American Airlines" by Barry C. Smith et al.
Links:
JSTOR
free PDF 1, broken at 06.09.12
free PDF 2, broken at 02.01.18
free PDF 3 | What are good references for dynamic pricing?
This article is highly cited:
"Yield Management at American Airlines" by Barry C. Smith et al.
Links:
JSTOR
free PDF 1, broken at 06.09.12
free PDF 2, broken at 02.01.18
free PDF 3 | What are good references for dynamic pricing?
This article is highly cited:
"Yield Management at American Airlines" by Barry C. Smith et al.
Links:
JSTOR
free PDF 1, broken at 06.09.12
free PDF 2, broken at 02.01.18
free PDF 3 |
49,654 | Learning parameters of a mixture of Gaussian using MLE | EM essentially solves the maximum likelihood problem and therefore has the same properties w.r.t. sample sizes. EM for Gaussian mixture models is known to converge asymptotically to a local maximum and exhibits first order convergence (see this paper).
BTW, there are some results which quantify how good the EM solution... | Learning parameters of a mixture of Gaussian using MLE | EM essentially solves the maximum likelihood problem and therefore has the same properties w.r.t. sample sizes. EM for Gaussian mixture models is known to converge asymptotically to a local maximum an | Learning parameters of a mixture of Gaussian using MLE
EM essentially solves the maximum likelihood problem and therefore has the same properties w.r.t. sample sizes. EM for Gaussian mixture models is known to converge asymptotically to a local maximum and exhibits first order convergence (see this paper).
BTW, there a... | Learning parameters of a mixture of Gaussian using MLE
EM essentially solves the maximum likelihood problem and therefore has the same properties w.r.t. sample sizes. EM for Gaussian mixture models is known to converge asymptotically to a local maximum an |
49,655 | Tangency portfolio in R | I haven't looked at your code yet, but here are two pointers:
Rmetrics has the tangencyPortfolio function in the fPortfolio package: http://help.rmetrics.org/fPortfolio/html/class-fPORTFOLIO.html
Here is a solution from David Ruppert's "Statistics and Finance" book: http://www.stat.tamu.edu/~ljin/Finance/chapter5/Fig5... | Tangency portfolio in R | I haven't looked at your code yet, but here are two pointers:
Rmetrics has the tangencyPortfolio function in the fPortfolio package: http://help.rmetrics.org/fPortfolio/html/class-fPORTFOLIO.html
Her | Tangency portfolio in R
I haven't looked at your code yet, but here are two pointers:
Rmetrics has the tangencyPortfolio function in the fPortfolio package: http://help.rmetrics.org/fPortfolio/html/class-fPORTFOLIO.html
Here is a solution from David Ruppert's "Statistics and Finance" book: http://www.stat.tamu.edu/~lj... | Tangency portfolio in R
I haven't looked at your code yet, but here are two pointers:
Rmetrics has the tangencyPortfolio function in the fPortfolio package: http://help.rmetrics.org/fPortfolio/html/class-fPORTFOLIO.html
Her |
49,656 | How to fit a negative binomial distribution in R while incorporating censoring [closed] | You can try gamlss.cens package. | How to fit a negative binomial distribution in R while incorporating censoring [closed] | You can try gamlss.cens package. | How to fit a negative binomial distribution in R while incorporating censoring [closed]
You can try gamlss.cens package. | How to fit a negative binomial distribution in R while incorporating censoring [closed]
You can try gamlss.cens package. |
49,657 | How to fit a negative binomial distribution in R while incorporating censoring [closed] | Another R package that seems to do what you want, is pscal. The associated vignette has lots of examples. | How to fit a negative binomial distribution in R while incorporating censoring [closed] | Another R package that seems to do what you want, is pscal. The associated vignette has lots of examples. | How to fit a negative binomial distribution in R while incorporating censoring [closed]
Another R package that seems to do what you want, is pscal. The associated vignette has lots of examples. | How to fit a negative binomial distribution in R while incorporating censoring [closed]
Another R package that seems to do what you want, is pscal. The associated vignette has lots of examples. |
49,658 | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised learning to learn based on user-ranked examples? | Supervised LLM training only gives the model positive examples, i.e. ones it should produce. It does not provide the negative ones, and a naive attempt to do so would probably fail due to the sheer volume of negatives in the space of possible outputs.
Indeed, you probably could somehow penalize the model for producing ... | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised | Supervised LLM training only gives the model positive examples, i.e. ones it should produce. It does not provide the negative ones, and a naive attempt to do so would probably fail due to the sheer vo | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised learning to learn based on user-ranked examples?
Supervised LLM training only gives the model positive examples, i.e. ones it should produce. It does not provide the negative ones, and a naive attempt to do so would pro... | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised
Supervised LLM training only gives the model positive examples, i.e. ones it should produce. It does not provide the negative ones, and a naive attempt to do so would probably fail due to the sheer vo |
49,659 | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised learning to learn based on user-ranked examples? | Your LLM will give you a categorical distribution as output, over which you can sample, and thus use RL to estimate the gradient...
What you are suggesting looks more like a GAN which instead of using a discriminator, you have a ordinal-NN, over which you take the gradient to maximize the ordinal output... however, thi... | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised | Your LLM will give you a categorical distribution as output, over which you can sample, and thus use RL to estimate the gradient...
What you are suggesting looks more like a GAN which instead of using | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised learning to learn based on user-ranked examples?
Your LLM will give you a categorical distribution as output, over which you can sample, and thus use RL to estimate the gradient...
What you are suggesting looks more lik... | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised
Your LLM will give you a categorical distribution as output, over which you can sample, and thus use RL to estimate the gradient...
What you are suggesting looks more like a GAN which instead of using |
49,660 | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised learning to learn based on user-ranked examples? | The paper LIMA: Less Is More for Alignment uploaded a few days ago to arXiv shows that fine-tuning with the standard supervised loss without any reinforcement learning works fine:
Large language models are trained in two stages: (1) unsupervised pretraining from raw text, to learn general-purpose representations, and ... | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised | The paper LIMA: Less Is More for Alignment uploaded a few days ago to arXiv shows that fine-tuning with the standard supervised loss without any reinforcement learning works fine:
Large language mode | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised learning to learn based on user-ranked examples?
The paper LIMA: Less Is More for Alignment uploaded a few days ago to arXiv shows that fine-tuning with the standard supervised loss without any reinforcement learning wo... | Why do language models like InstructGPT and LLM utilize reinforcement learning instead of supervised
The paper LIMA: Less Is More for Alignment uploaded a few days ago to arXiv shows that fine-tuning with the standard supervised loss without any reinforcement learning works fine:
Large language mode |
49,661 | Does Frequentist statistics still make sense when the experiment is not repeatable? | You have hit on the major challenge to the frequentist interpretation
As a preliminary observation, the usual examples of non-repeatable events used for this question relate to predictions of one-off things like the outcome of an election. Unlike your vase example, these are situations where the event of interest is n... | Does Frequentist statistics still make sense when the experiment is not repeatable? | You have hit on the major challenge to the frequentist interpretation
As a preliminary observation, the usual examples of non-repeatable events used for this question relate to predictions of one-off | Does Frequentist statistics still make sense when the experiment is not repeatable?
You have hit on the major challenge to the frequentist interpretation
As a preliminary observation, the usual examples of non-repeatable events used for this question relate to predictions of one-off things like the outcome of an electi... | Does Frequentist statistics still make sense when the experiment is not repeatable?
You have hit on the major challenge to the frequentist interpretation
As a preliminary observation, the usual examples of non-repeatable events used for this question relate to predictions of one-off |
49,662 | Does Frequentist statistics still make sense when the experiment is not repeatable? | Simple answer, yes the frequentist approach is still viable. We start with a (admittedly idealized) model. Take your vase example. Pre-sample, under the model we know that the confidence procedure with random sampling produces CIs covering the parameter 95% of the time. No actual repetitions are required. Also, if you ... | Does Frequentist statistics still make sense when the experiment is not repeatable? | Simple answer, yes the frequentist approach is still viable. We start with a (admittedly idealized) model. Take your vase example. Pre-sample, under the model we know that the confidence procedure wit | Does Frequentist statistics still make sense when the experiment is not repeatable?
Simple answer, yes the frequentist approach is still viable. We start with a (admittedly idealized) model. Take your vase example. Pre-sample, under the model we know that the confidence procedure with random sampling produces CIs cover... | Does Frequentist statistics still make sense when the experiment is not repeatable?
Simple answer, yes the frequentist approach is still viable. We start with a (admittedly idealized) model. Take your vase example. Pre-sample, under the model we know that the confidence procedure wit |
49,663 | Book recommendations for beginners about probability distributions | I am not familiar with any book that would meet your requirements, but there's a Harvard course Statistics 110 by Joe Blitzstein that focuses exactly on the intuitions behind the distributions and probability theory concepts. (It is freely available online.) | Book recommendations for beginners about probability distributions | I am not familiar with any book that would meet your requirements, but there's a Harvard course Statistics 110 by Joe Blitzstein that focuses exactly on the intuitions behind the distributions and pro | Book recommendations for beginners about probability distributions
I am not familiar with any book that would meet your requirements, but there's a Harvard course Statistics 110 by Joe Blitzstein that focuses exactly on the intuitions behind the distributions and probability theory concepts. (It is freely available onl... | Book recommendations for beginners about probability distributions
I am not familiar with any book that would meet your requirements, but there's a Harvard course Statistics 110 by Joe Blitzstein that focuses exactly on the intuitions behind the distributions and pro |
49,664 | Book recommendations for beginners about probability distributions | Blitzstein & Hwang's "Introduction to Probability" is in the same vein as the online course referenced by Tim but a lot more breadth. Highly recommended. | Book recommendations for beginners about probability distributions | Blitzstein & Hwang's "Introduction to Probability" is in the same vein as the online course referenced by Tim but a lot more breadth. Highly recommended. | Book recommendations for beginners about probability distributions
Blitzstein & Hwang's "Introduction to Probability" is in the same vein as the online course referenced by Tim but a lot more breadth. Highly recommended. | Book recommendations for beginners about probability distributions
Blitzstein & Hwang's "Introduction to Probability" is in the same vein as the online course referenced by Tim but a lot more breadth. Highly recommended. |
49,665 | justification for 'population prediction intervals'? | In the econometrics literature this is referred to as the method of Krinsky and Robb (1986, 1990, & 1991).
I think the argument goes as follows:
Assume we have consistently estimated the expectation and the covariance matrix of an asymptotically normal estimator $\hat{\Theta}$ of $\Theta$. Then, by the law of large num... | justification for 'population prediction intervals'? | In the econometrics literature this is referred to as the method of Krinsky and Robb (1986, 1990, & 1991).
I think the argument goes as follows:
Assume we have consistently estimated the expectation a | justification for 'population prediction intervals'?
In the econometrics literature this is referred to as the method of Krinsky and Robb (1986, 1990, & 1991).
I think the argument goes as follows:
Assume we have consistently estimated the expectation and the covariance matrix of an asymptotically normal estimator $\ha... | justification for 'population prediction intervals'?
In the econometrics literature this is referred to as the method of Krinsky and Robb (1986, 1990, & 1991).
I think the argument goes as follows:
Assume we have consistently estimated the expectation a |
49,666 | Biased coin game | Well, I've done a simulation where I used a simple criterion of saying the coin is biased if the current proportion is >0.55 else the coin is fair (middle between 0.5 and 0.6). Code in R:
res=replicate(1e3,{
k=sample(c(0.5,0.6),1)
s=sample(0:1,2e3,prob=c(1-k,k),replace=T)
tmp=cumsum(s)/seq_along(s)
ifelse(ifels... | Biased coin game | Well, I've done a simulation where I used a simple criterion of saying the coin is biased if the current proportion is >0.55 else the coin is fair (middle between 0.5 and 0.6). Code in R:
res=replicat | Biased coin game
Well, I've done a simulation where I used a simple criterion of saying the coin is biased if the current proportion is >0.55 else the coin is fair (middle between 0.5 and 0.6). Code in R:
res=replicate(1e3,{
k=sample(c(0.5,0.6),1)
s=sample(0:1,2e3,prob=c(1-k,k),replace=T)
tmp=cumsum(s)/seq_along(... | Biased coin game
Well, I've done a simulation where I used a simple criterion of saying the coin is biased if the current proportion is >0.55 else the coin is fair (middle between 0.5 and 0.6). Code in R:
res=replicat |
49,667 | Biased coin game | I'd keep track of the Bayes factor for the two hypotheses over time, and make a decision once the evidence passes a threshold.
Let $F$ be the event that the coin is fair and $B$ be the event that the coin is biased. Let $n$ be the number of coin tosses observed, and let $h, t$ be the observed number of heads and tails.... | Biased coin game | I'd keep track of the Bayes factor for the two hypotheses over time, and make a decision once the evidence passes a threshold.
Let $F$ be the event that the coin is fair and $B$ be the event that the | Biased coin game
I'd keep track of the Bayes factor for the two hypotheses over time, and make a decision once the evidence passes a threshold.
Let $F$ be the event that the coin is fair and $B$ be the event that the coin is biased. Let $n$ be the number of coin tosses observed, and let $h, t$ be the observed number of... | Biased coin game
I'd keep track of the Bayes factor for the two hypotheses over time, and make a decision once the evidence passes a threshold.
Let $F$ be the event that the coin is fair and $B$ be the event that the |
49,668 | Strange result with GLMM (binomial) | You construct a Wald confidence interval for the log odds of passing the test: $\hat{\theta} \pm z_{1-\alpha/2}\operatorname{SE}(\hat{\theta})$. This is based on the theory that the maximum likelihood estimator (MLE) is asymptotically Normal. However, since the probability of passing the test is very close to 1 (its up... | Strange result with GLMM (binomial) | You construct a Wald confidence interval for the log odds of passing the test: $\hat{\theta} \pm z_{1-\alpha/2}\operatorname{SE}(\hat{\theta})$. This is based on the theory that the maximum likelihood | Strange result with GLMM (binomial)
You construct a Wald confidence interval for the log odds of passing the test: $\hat{\theta} \pm z_{1-\alpha/2}\operatorname{SE}(\hat{\theta})$. This is based on the theory that the maximum likelihood estimator (MLE) is asymptotically Normal. However, since the probability of passing... | Strange result with GLMM (binomial)
You construct a Wald confidence interval for the log odds of passing the test: $\hat{\theta} \pm z_{1-\alpha/2}\operatorname{SE}(\hat{\theta})$. This is based on the theory that the maximum likelihood |
49,669 | Standardizing neural network inputs with a linear layer? | One way to do standardization is to subtract some value (e.g. the sample mean $\hat \mu$) and divide by another value (e.g. the sample standard deviation $\hat \sigma$):
$$
z = \frac{x - \hat \mu}{\hat \sigma}.
$$
When $X$ is a matrix, we can compute the columns' means and standard deviations; each is a vector. Then we... | Standardizing neural network inputs with a linear layer? | One way to do standardization is to subtract some value (e.g. the sample mean $\hat \mu$) and divide by another value (e.g. the sample standard deviation $\hat \sigma$):
$$
z = \frac{x - \hat \mu}{\ha | Standardizing neural network inputs with a linear layer?
One way to do standardization is to subtract some value (e.g. the sample mean $\hat \mu$) and divide by another value (e.g. the sample standard deviation $\hat \sigma$):
$$
z = \frac{x - \hat \mu}{\hat \sigma}.
$$
When $X$ is a matrix, we can compute the columns'... | Standardizing neural network inputs with a linear layer?
One way to do standardization is to subtract some value (e.g. the sample mean $\hat \mu$) and divide by another value (e.g. the sample standard deviation $\hat \sigma$):
$$
z = \frac{x - \hat \mu}{\ha |
49,670 | double-tail Bayesian "p value" à la MCMCglmm | You might find Reconnecting p-Value and Posterior Probability Under One- and Two-Sided Tests by Shi and Yin (2021) useful.
They show interesting connections between the two-sided posterior probability $\mathrm{{PoP}_2}$ and the (frequentist) p-value if flat or "non-informative" priors are used. In particular, $\mathrm{... | double-tail Bayesian "p value" à la MCMCglmm | You might find Reconnecting p-Value and Posterior Probability Under One- and Two-Sided Tests by Shi and Yin (2021) useful.
They show interesting connections between the two-sided posterior probability | double-tail Bayesian "p value" à la MCMCglmm
You might find Reconnecting p-Value and Posterior Probability Under One- and Two-Sided Tests by Shi and Yin (2021) useful.
They show interesting connections between the two-sided posterior probability $\mathrm{{PoP}_2}$ and the (frequentist) p-value if flat or "non-informati... | double-tail Bayesian "p value" à la MCMCglmm
You might find Reconnecting p-Value and Posterior Probability Under One- and Two-Sided Tests by Shi and Yin (2021) useful.
They show interesting connections between the two-sided posterior probability |
49,671 | Show that no two sets in the probability space with $\mathbb{P}(\{k\})=2^{-k!}$ are independent | The question outlines a rigorous proof -- but where does the idea come from?
It all becomes clear when you write the probabilities in binary: from the binary representation of one of these probabilities $\mathbb{P}(A)$ you can read off the elements of $A,$ at least when $1\notin A.$ Just look at positions $2, 6, 24, 1... | Show that no two sets in the probability space with $\mathbb{P}(\{k\})=2^{-k!}$ are independent | The question outlines a rigorous proof -- but where does the idea come from?
It all becomes clear when you write the probabilities in binary: from the binary representation of one of these probabiliti | Show that no two sets in the probability space with $\mathbb{P}(\{k\})=2^{-k!}$ are independent
The question outlines a rigorous proof -- but where does the idea come from?
It all becomes clear when you write the probabilities in binary: from the binary representation of one of these probabilities $\mathbb{P}(A)$ you c... | Show that no two sets in the probability space with $\mathbb{P}(\{k\})=2^{-k!}$ are independent
The question outlines a rigorous proof -- but where does the idea come from?
It all becomes clear when you write the probabilities in binary: from the binary representation of one of these probabiliti |
49,672 | References on data partitioning (cross-validation, train/val/test set construction) when data are non-IID | It really all boils down to two rules of thumb:
When splitting your data, leave out what you want to predict. If you want to generalize to new hospitals, rather than new patients at the same hospital, leave out one hospital at a time when doing CV — do not leave out one patient at a time, as this only tests your abili... | References on data partitioning (cross-validation, train/val/test set construction) when data are no | It really all boils down to two rules of thumb:
When splitting your data, leave out what you want to predict. If you want to generalize to new hospitals, rather than new patients at the same hospital | References on data partitioning (cross-validation, train/val/test set construction) when data are non-IID
It really all boils down to two rules of thumb:
When splitting your data, leave out what you want to predict. If you want to generalize to new hospitals, rather than new patients at the same hospital, leave out on... | References on data partitioning (cross-validation, train/val/test set construction) when data are no
It really all boils down to two rules of thumb:
When splitting your data, leave out what you want to predict. If you want to generalize to new hospitals, rather than new patients at the same hospital |
49,673 | How do I summarize the “contribution” of covariates in a GLM? | People do compare $R^2$ values, but for some GLMs there are approximations to $R^2$, but they are of limited value. A little more common is to compare deviance values (these are at least well defined). But comparing $R^2$ or deviance is more about statistical significance than the real importance of a variable.
I pre... | How do I summarize the “contribution” of covariates in a GLM? | People do compare $R^2$ values, but for some GLMs there are approximations to $R^2$, but they are of limited value. A little more common is to compare deviance values (these are at least well defined | How do I summarize the “contribution” of covariates in a GLM?
People do compare $R^2$ values, but for some GLMs there are approximations to $R^2$, but they are of limited value. A little more common is to compare deviance values (these are at least well defined). But comparing $R^2$ or deviance is more about statisti... | How do I summarize the “contribution” of covariates in a GLM?
People do compare $R^2$ values, but for some GLMs there are approximations to $R^2$, but they are of limited value. A little more common is to compare deviance values (these are at least well defined |
49,674 | Uniformly Most Powerful Test for Weibull Distribution | You've got $L=\frac{\theta_a^n}{\theta_0^n}\,exp\left({-\frac{\theta_a-\theta_0}
{\theta_0\theta_a}\sum_{i=1}^ny_i^m}\right)<k$, which is good. Now we take $log$ of both sides:
$$n log\left(\frac{\theta_a}{\theta_0}\right)+\left(\frac{\theta_0-\theta_a}{\theta_0\theta_a}\right)\sum_{i=1}^{n}{y_i^m} < log(k)$$
and so th... | Uniformly Most Powerful Test for Weibull Distribution | You've got $L=\frac{\theta_a^n}{\theta_0^n}\,exp\left({-\frac{\theta_a-\theta_0}
{\theta_0\theta_a}\sum_{i=1}^ny_i^m}\right)<k$, which is good. Now we take $log$ of both sides:
$$n log\left(\frac{\the | Uniformly Most Powerful Test for Weibull Distribution
You've got $L=\frac{\theta_a^n}{\theta_0^n}\,exp\left({-\frac{\theta_a-\theta_0}
{\theta_0\theta_a}\sum_{i=1}^ny_i^m}\right)<k$, which is good. Now we take $log$ of both sides:
$$n log\left(\frac{\theta_a}{\theta_0}\right)+\left(\frac{\theta_0-\theta_a}{\theta_0\the... | Uniformly Most Powerful Test for Weibull Distribution
You've got $L=\frac{\theta_a^n}{\theta_0^n}\,exp\left({-\frac{\theta_a-\theta_0}
{\theta_0\theta_a}\sum_{i=1}^ny_i^m}\right)<k$, which is good. Now we take $log$ of both sides:
$$n log\left(\frac{\the |
49,675 | Numbers of double-headed, double-tailed, and normal coins based on one toss per coin | This can be done using Bayes' Theorem. It requires you to have a (somewhat subjective) prior distribution for how many of each type of coin the bucket contains. For example, let $A$ be the event that the bucket contains 90 double-headed coins and 10 normal coins, and let $B$ be the event that you observe exactly 90 hea... | Numbers of double-headed, double-tailed, and normal coins based on one toss per coin | This can be done using Bayes' Theorem. It requires you to have a (somewhat subjective) prior distribution for how many of each type of coin the bucket contains. For example, let $A$ be the event that | Numbers of double-headed, double-tailed, and normal coins based on one toss per coin
This can be done using Bayes' Theorem. It requires you to have a (somewhat subjective) prior distribution for how many of each type of coin the bucket contains. For example, let $A$ be the event that the bucket contains 90 double-heade... | Numbers of double-headed, double-tailed, and normal coins based on one toss per coin
This can be done using Bayes' Theorem. It requires you to have a (somewhat subjective) prior distribution for how many of each type of coin the bucket contains. For example, let $A$ be the event that |
49,676 | Heteroscedasticity and non-normal errors are only an issue when predicting from a linear model - why? | I suspect that Gelman and Hill are either overstating the case concerning whether normality is an issue, or that their comments are taken out of context. While linearity (or more precisely, correct functional specification) is usually more important, there are cases of non-normality that indeed should be of great conce... | Heteroscedasticity and non-normal errors are only an issue when predicting from a linear model - why | I suspect that Gelman and Hill are either overstating the case concerning whether normality is an issue, or that their comments are taken out of context. While linearity (or more precisely, correct fu | Heteroscedasticity and non-normal errors are only an issue when predicting from a linear model - why?
I suspect that Gelman and Hill are either overstating the case concerning whether normality is an issue, or that their comments are taken out of context. While linearity (or more precisely, correct functional specifica... | Heteroscedasticity and non-normal errors are only an issue when predicting from a linear model - why
I suspect that Gelman and Hill are either overstating the case concerning whether normality is an issue, or that their comments are taken out of context. While linearity (or more precisely, correct fu |
49,677 | Estimate $E[X_1 | X_1>X_2>\cdots>X_k]$ with simulation | I have never heard of this algorithm by Geweke et al. but since it is a special case of importance sampling the fact that a single weight takes all the mass is indicative that the importance function is poorly suited for the target. Given that the integral is over the set$$\mathfrak H=\{x\in\mathbb R^k;~x_1>x_2>\cdots... | Estimate $E[X_1 | X_1>X_2>\cdots>X_k]$ with simulation | I have never heard of this algorithm by Geweke et al. but since it is a special case of importance sampling the fact that a single weight takes all the mass is indicative that the importance function | Estimate $E[X_1 | X_1>X_2>\cdots>X_k]$ with simulation
I have never heard of this algorithm by Geweke et al. but since it is a special case of importance sampling the fact that a single weight takes all the mass is indicative that the importance function is poorly suited for the target. Given that the integral is over... | Estimate $E[X_1 | X_1>X_2>\cdots>X_k]$ with simulation
I have never heard of this algorithm by Geweke et al. but since it is a special case of importance sampling the fact that a single weight takes all the mass is indicative that the importance function |
49,678 | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity | This is a visual answer: a careful consideration of the second figure shows what is going on. Everything else in this post is only a gloss on that figure.
In this figure of the $(x,y)$ plane, region $I$ (blue, top) consists of all $y$ values exceeding a quantile $Q_{90}(Y),$ region $II$ (red, right) consists of all $... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd | This is a visual answer: a careful consideration of the second figure shows what is going on. Everything else in this post is only a gloss on that figure.
In this figure of the $(x,y)$ plane, region | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity
This is a visual answer: a careful consideration of the second figure shows what is going on. Everything else in this post is only a gloss on that figure.
In this figure of the $(x,y)$ plane, region $I$ (blue, ... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd
This is a visual answer: a careful consideration of the second figure shows what is going on. Everything else in this post is only a gloss on that figure.
In this figure of the $(x,y)$ plane, region |
49,679 | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity | TLDR; Let's define $Q_X(0.9) = c$ as the reserved costs. And $2c$ will be the costs reserved for two variables $X$ and $Y$.
For the specific case in the question, the probability for $X+Y$ to exceed $2c$ is larger than 10%, namely 13.16%.
This is because the probability for $X$ and $Y$ to exceed $2c$ is already individ... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd | TLDR; Let's define $Q_X(0.9) = c$ as the reserved costs. And $2c$ will be the costs reserved for two variables $X$ and $Y$.
For the specific case in the question, the probability for $X+Y$ to exceed $ | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity
TLDR; Let's define $Q_X(0.9) = c$ as the reserved costs. And $2c$ will be the costs reserved for two variables $X$ and $Y$.
For the specific case in the question, the probability for $X+Y$ to exceed $2c$ is large... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd
TLDR; Let's define $Q_X(0.9) = c$ as the reserved costs. And $2c$ will be the costs reserved for two variables $X$ and $Y$.
For the specific case in the question, the probability for $X+Y$ to exceed $ |
49,680 | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity | As distributions get more right-tailed, the $90^{th}$ percentile of $X+Y$ approaches the $\frac{3}{\sqrt{10}}$th quantile of $X$, roughly the $95^{th}$ percentile. In other words, the top 10% of combined losses will come from roughly 5% in which the first loss is as high as possible, and 5% in which the second loss is ... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd | As distributions get more right-tailed, the $90^{th}$ percentile of $X+Y$ approaches the $\frac{3}{\sqrt{10}}$th quantile of $X$, roughly the $95^{th}$ percentile. In other words, the top 10% of combi | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity
As distributions get more right-tailed, the $90^{th}$ percentile of $X+Y$ approaches the $\frac{3}{\sqrt{10}}$th quantile of $X$, roughly the $95^{th}$ percentile. In other words, the top 10% of combined losses w... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd
As distributions get more right-tailed, the $90^{th}$ percentile of $X+Y$ approaches the $\frac{3}{\sqrt{10}}$th quantile of $X$, roughly the $95^{th}$ percentile. In other words, the top 10% of combi |
49,681 | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity | Using the business world example: Quantile measures of risk exclude worst-case scenarios. When a distribution is very fat-tailed, a measure such as $Q_{90}$ will exclude almost all bad scenarios and deceptively present an innocent-looking risk.
But when risks are summed, we are now looking at the risk of at-least-one-... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd | Using the business world example: Quantile measures of risk exclude worst-case scenarios. When a distribution is very fat-tailed, a measure such as $Q_{90}$ will exclude almost all bad scenarios and | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity
Using the business world example: Quantile measures of risk exclude worst-case scenarios. When a distribution is very fat-tailed, a measure such as $Q_{90}$ will exclude almost all bad scenarios and deceptively ... | What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadd
Using the business world example: Quantile measures of risk exclude worst-case scenarios. When a distribution is very fat-tailed, a measure such as $Q_{90}$ will exclude almost all bad scenarios and |
49,682 | Lavaan mediation + moderation + 2 X's | I simulated some irrelevant data:
library(lavaan)
dat <- as.data.frame(mvrnorm(5e2, rep(0, 6), matrix(.25, 6, 6) + .75 * diag(6)))
colnames(dat) <- c("X", "X2", "M1", "M2", "W", "Y")
dat$X2 <- dat$X ^ 2
head(dat)
# X X2 M1 M2 W Y
# 1 -1.2556613 1.57668526 0.9558917... | Lavaan mediation + moderation + 2 X's | I simulated some irrelevant data:
library(lavaan)
dat <- as.data.frame(mvrnorm(5e2, rep(0, 6), matrix(.25, 6, 6) + .75 * diag(6)))
colnames(dat) <- c("X", "X2", "M1", "M2", "W", "Y")
dat$X2 <- dat$X | Lavaan mediation + moderation + 2 X's
I simulated some irrelevant data:
library(lavaan)
dat <- as.data.frame(mvrnorm(5e2, rep(0, 6), matrix(.25, 6, 6) + .75 * diag(6)))
colnames(dat) <- c("X", "X2", "M1", "M2", "W", "Y")
dat$X2 <- dat$X ^ 2
head(dat)
# X X2 M1 M2 W ... | Lavaan mediation + moderation + 2 X's
I simulated some irrelevant data:
library(lavaan)
dat <- as.data.frame(mvrnorm(5e2, rep(0, 6), matrix(.25, 6, 6) + .75 * diag(6)))
colnames(dat) <- c("X", "X2", "M1", "M2", "W", "Y")
dat$X2 <- dat$X |
49,683 | Lavaan mediation + moderation + 2 X's | Moderation is basically the product of the IVs ($X_i$) with the moderator ($W$). Since you have two IVs, you have two products $X_1W$ and $W_2W$, you just have to do it once for each predictor $X_i$ on each outcome ($M_1,M_2,Y$), since you want the moderator on each of them.
I used the notation in the graph for the cod... | Lavaan mediation + moderation + 2 X's | Moderation is basically the product of the IVs ($X_i$) with the moderator ($W$). Since you have two IVs, you have two products $X_1W$ and $W_2W$, you just have to do it once for each predictor $X_i$ o | Lavaan mediation + moderation + 2 X's
Moderation is basically the product of the IVs ($X_i$) with the moderator ($W$). Since you have two IVs, you have two products $X_1W$ and $W_2W$, you just have to do it once for each predictor $X_i$ on each outcome ($M_1,M_2,Y$), since you want the moderator on each of them.
I used... | Lavaan mediation + moderation + 2 X's
Moderation is basically the product of the IVs ($X_i$) with the moderator ($W$). Since you have two IVs, you have two products $X_1W$ and $W_2W$, you just have to do it once for each predictor $X_i$ o |
49,684 | Are there any conjugate likelihood distributions for a Categorical Prior? | Any likelihood function will do this: Since $Z \sim \text{Cat}(\pi)$, it is a discrete random variable with some finite number of possible states. Regardless of the likelihood function, it will still be distributed over these same states a posteriori and so it will still have a categorical distribution. This merely r... | Are there any conjugate likelihood distributions for a Categorical Prior? | Any likelihood function will do this: Since $Z \sim \text{Cat}(\pi)$, it is a discrete random variable with some finite number of possible states. Regardless of the likelihood function, it will still | Are there any conjugate likelihood distributions for a Categorical Prior?
Any likelihood function will do this: Since $Z \sim \text{Cat}(\pi)$, it is a discrete random variable with some finite number of possible states. Regardless of the likelihood function, it will still be distributed over these same states a poste... | Are there any conjugate likelihood distributions for a Categorical Prior?
Any likelihood function will do this: Since $Z \sim \text{Cat}(\pi)$, it is a discrete random variable with some finite number of possible states. Regardless of the likelihood function, it will still |
49,685 | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$ | The obvious analogy here is to use independent estimators $Y_1,...,Y_c$ with expectations:
$$\mathbb{E}(Y_i) = X^{p_i}
\quad \quad \quad \sum p_i = k.$$
In theory this is possible so long as you have a method to construct the required estimators for this problem. The independence requirement will generally make it imp... | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$ | The obvious analogy here is to use independent estimators $Y_1,...,Y_c$ with expectations:
$$\mathbb{E}(Y_i) = X^{p_i}
\quad \quad \quad \sum p_i = k.$$
In theory this is possible so long as you have | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$
The obvious analogy here is to use independent estimators $Y_1,...,Y_c$ with expectations:
$$\mathbb{E}(Y_i) = X^{p_i}
\quad \quad \quad \sum p_i = k.$$
In theory this is possible so long as you have a method to construct the required estimators f... | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$
The obvious analogy here is to use independent estimators $Y_1,...,Y_c$ with expectations:
$$\mathbb{E}(Y_i) = X^{p_i}
\quad \quad \quad \sum p_i = k.$$
In theory this is possible so long as you have |
49,686 | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$ | To illustrate the point that the answer depends on the underlying statistical model: If $Y\sim\mathcal E(1/X)$, an exponential variable, then
$$\mathbb E[Y^k]= X^k\Gamma(k+1)$$
meaning that $Y^k/\Gamma(k+1)=Y^k/k!$ is an unbiased estimator of $X^k$, based on a single observation. This extends to Gamma variables, obviou... | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$ | To illustrate the point that the answer depends on the underlying statistical model: If $Y\sim\mathcal E(1/X)$, an exponential variable, then
$$\mathbb E[Y^k]= X^k\Gamma(k+1)$$
meaning that $Y^k/\Gamm | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$
To illustrate the point that the answer depends on the underlying statistical model: If $Y\sim\mathcal E(1/X)$, an exponential variable, then
$$\mathbb E[Y^k]= X^k\Gamma(k+1)$$
meaning that $Y^k/\Gamma(k+1)=Y^k/k!$ is an unbiased estimator of $X^k... | Unbiased estimator of $X^k$ given independent unbiased estimators of $X$
To illustrate the point that the answer depends on the underlying statistical model: If $Y\sim\mathcal E(1/X)$, an exponential variable, then
$$\mathbb E[Y^k]= X^k\Gamma(k+1)$$
meaning that $Y^k/\Gamm |
49,687 | Analysis for a design with variation among and within trees | Your model:
y ~ Sex*Side + (1 | Site) + (1 | Site:Tree)
makes sense to me conceptually. However with only 5 sites, this is rather few for fitting random intercepts, so I would suggest also fitting
y ~ Sex*Side + Site*Tree
Hopefully the inferences for Sex, Side and their interaction will be similar in both models.
You... | Analysis for a design with variation among and within trees | Your model:
y ~ Sex*Side + (1 | Site) + (1 | Site:Tree)
makes sense to me conceptually. However with only 5 sites, this is rather few for fitting random intercepts, so I would suggest also fitting
y | Analysis for a design with variation among and within trees
Your model:
y ~ Sex*Side + (1 | Site) + (1 | Site:Tree)
makes sense to me conceptually. However with only 5 sites, this is rather few for fitting random intercepts, so I would suggest also fitting
y ~ Sex*Side + Site*Tree
Hopefully the inferences for Sex, Si... | Analysis for a design with variation among and within trees
Your model:
y ~ Sex*Side + (1 | Site) + (1 | Site:Tree)
makes sense to me conceptually. However with only 5 sites, this is rather few for fitting random intercepts, so I would suggest also fitting
y |
49,688 | Comparisons between independent geometric random variables | By remembering how the geometric distribution arises, we can solve this problem with almost no calculation.
The problem can be seen as a competition
A geometric random variable $W$ models the number of failures in a sequence of independent Bernoulli trials before the first success is observed. Its parameter $p$ is the... | Comparisons between independent geometric random variables | By remembering how the geometric distribution arises, we can solve this problem with almost no calculation.
The problem can be seen as a competition
A geometric random variable $W$ models the number o | Comparisons between independent geometric random variables
By remembering how the geometric distribution arises, we can solve this problem with almost no calculation.
The problem can be seen as a competition
A geometric random variable $W$ models the number of failures in a sequence of independent Bernoulli trials befo... | Comparisons between independent geometric random variables
By remembering how the geometric distribution arises, we can solve this problem with almost no calculation.
The problem can be seen as a competition
A geometric random variable $W$ models the number o |
49,689 | Comparisons between independent geometric random variables | In accordance with whuber's suggestion, I am posting an extended version of some comments that I made on whuber's answer as a separate answer of my own.
The experiment consists of players A and B each (independently) tossing their individual coins that turn up Heads with probabilities $p_A$ and $p_B$ respectively. Repe... | Comparisons between independent geometric random variables | In accordance with whuber's suggestion, I am posting an extended version of some comments that I made on whuber's answer as a separate answer of my own.
The experiment consists of players A and B each | Comparisons between independent geometric random variables
In accordance with whuber's suggestion, I am posting an extended version of some comments that I made on whuber's answer as a separate answer of my own.
The experiment consists of players A and B each (independently) tossing their individual coins that turn up ... | Comparisons between independent geometric random variables
In accordance with whuber's suggestion, I am posting an extended version of some comments that I made on whuber's answer as a separate answer of my own.
The experiment consists of players A and B each |
49,690 | Comparisons between independent geometric random variables | As I indicated in a comment above there is a cited path to the solution available here courtesy of the Math forum on Stack Exchange on the topic 'Difference between two independent geometric distribution.
However, I have also found another route that is worthy of mention as it may have more broad applications (that is,... | Comparisons between independent geometric random variables | As I indicated in a comment above there is a cited path to the solution available here courtesy of the Math forum on Stack Exchange on the topic 'Difference between two independent geometric distribut | Comparisons between independent geometric random variables
As I indicated in a comment above there is a cited path to the solution available here courtesy of the Math forum on Stack Exchange on the topic 'Difference between two independent geometric distribution.
However, I have also found another route that is worthy ... | Comparisons between independent geometric random variables
As I indicated in a comment above there is a cited path to the solution available here courtesy of the Math forum on Stack Exchange on the topic 'Difference between two independent geometric distribut |
49,691 | How do I analyze bimodal distibuted data with a linear mixed model | I try to sum up what I‘ve learned from the comments to close the question:
Linear mixed effect models do not necessarily need normally distributed data; here is a link to another Post dealing with the same question
Not the data itself but the residuals of the model should be normally distributed
One of the most import... | How do I analyze bimodal distibuted data with a linear mixed model | I try to sum up what I‘ve learned from the comments to close the question:
Linear mixed effect models do not necessarily need normally distributed data; here is a link to another Post dealing with th | How do I analyze bimodal distibuted data with a linear mixed model
I try to sum up what I‘ve learned from the comments to close the question:
Linear mixed effect models do not necessarily need normally distributed data; here is a link to another Post dealing with the same question
Not the data itself but the residuals... | How do I analyze bimodal distibuted data with a linear mixed model
I try to sum up what I‘ve learned from the comments to close the question:
Linear mixed effect models do not necessarily need normally distributed data; here is a link to another Post dealing with th |
49,692 | Is there a hard distinction between hyperparameter vs parameter in machine learning? | That's a great question - I'm not sure what the best way to answer this, but in a statistical framework, I believe the differences are a bit more clearly cut. I'll be curious to see how others answer this from a purer ML/DL perspective.
I think one way in which they differ is that parameters (at last from a statistical... | Is there a hard distinction between hyperparameter vs parameter in machine learning? | That's a great question - I'm not sure what the best way to answer this, but in a statistical framework, I believe the differences are a bit more clearly cut. I'll be curious to see how others answer | Is there a hard distinction between hyperparameter vs parameter in machine learning?
That's a great question - I'm not sure what the best way to answer this, but in a statistical framework, I believe the differences are a bit more clearly cut. I'll be curious to see how others answer this from a purer ML/DL perspective... | Is there a hard distinction between hyperparameter vs parameter in machine learning?
That's a great question - I'm not sure what the best way to answer this, but in a statistical framework, I believe the differences are a bit more clearly cut. I'll be curious to see how others answer |
49,693 | K-mean clustering label problem | Unfortunately, you cannot do that. Firstly, because your old cluster assignments will not be the same as the new cluster assignments. You can only try to define a mapping afterwards (not saying this is easy), which may not be successful if the two runs significantly differ. | K-mean clustering label problem | Unfortunately, you cannot do that. Firstly, because your old cluster assignments will not be the same as the new cluster assignments. You can only try to define a mapping afterwards (not saying this i | K-mean clustering label problem
Unfortunately, you cannot do that. Firstly, because your old cluster assignments will not be the same as the new cluster assignments. You can only try to define a mapping afterwards (not saying this is easy), which may not be successful if the two runs significantly differ. | K-mean clustering label problem
Unfortunately, you cannot do that. Firstly, because your old cluster assignments will not be the same as the new cluster assignments. You can only try to define a mapping afterwards (not saying this i |
49,694 | Mixed ANOVA normality: which variables should be examined? (in universal and practical application with stats::aov) | TL;DR:
ANOVA pools information among all observations to get the best estimates of fixed effects, random effects, and error variance. If you want to examine normality of ANOVA residuals, doing so after all fixed and random effects are taken into account thus makes the most sense. Reliable ANOVA estimates don't require ... | Mixed ANOVA normality: which variables should be examined? (in universal and practical application w | TL;DR:
ANOVA pools information among all observations to get the best estimates of fixed effects, random effects, and error variance. If you want to examine normality of ANOVA residuals, doing so afte | Mixed ANOVA normality: which variables should be examined? (in universal and practical application with stats::aov)
TL;DR:
ANOVA pools information among all observations to get the best estimates of fixed effects, random effects, and error variance. If you want to examine normality of ANOVA residuals, doing so after al... | Mixed ANOVA normality: which variables should be examined? (in universal and practical application w
TL;DR:
ANOVA pools information among all observations to get the best estimates of fixed effects, random effects, and error variance. If you want to examine normality of ANOVA residuals, doing so afte |
49,695 | Who invented the "Histogram"? | The best I know of at the moment is by an article by Rufilanchas in 2017 [1]: in it, he says that Pearson, the first person to use the word (not the first who used such a diagram), used it in relation to how he believed that the vertical alignment of columns to represent frequency distributions is preferable to it alig... | Who invented the "Histogram"? | The best I know of at the moment is by an article by Rufilanchas in 2017 [1]: in it, he says that Pearson, the first person to use the word (not the first who used such a diagram), used it in relation | Who invented the "Histogram"?
The best I know of at the moment is by an article by Rufilanchas in 2017 [1]: in it, he says that Pearson, the first person to use the word (not the first who used such a diagram), used it in relation to how he believed that the vertical alignment of columns to represent frequency distribu... | Who invented the "Histogram"?
The best I know of at the moment is by an article by Rufilanchas in 2017 [1]: in it, he says that Pearson, the first person to use the word (not the first who used such a diagram), used it in relation |
49,696 | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields where little is known? | Doubly robust methods (Urminsky et al. "Using Double-Lasso Regression for Principled Variable Selection") have become very popular recently since they allow (see page 18, Concluding Remarks) "identifying which covariates to include and not include in analyses" (even if the number of variables is larger than the sample ... | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields whe | Doubly robust methods (Urminsky et al. "Using Double-Lasso Regression for Principled Variable Selection") have become very popular recently since they allow (see page 18, Concluding Remarks) "identify | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields where little is known?
Doubly robust methods (Urminsky et al. "Using Double-Lasso Regression for Principled Variable Selection") have become very popular recently since they allow (see page 18, Concluding Remarks) "identify... | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields whe
Doubly robust methods (Urminsky et al. "Using Double-Lasso Regression for Principled Variable Selection") have become very popular recently since they allow (see page 18, Concluding Remarks) "identify |
49,697 | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields where little is known? | Prediction models are about making good predictions. That's what you are optimizing (in terms of the metric you optimized your elastic net parameters for), when you go for your second option. Whatever hyperparameter settings help the model predict well as assessed by k-fold CV gets used and then you get some resulting ... | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields whe | Prediction models are about making good predictions. That's what you are optimizing (in terms of the metric you optimized your elastic net parameters for), when you go for your second option. Whatever | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields where little is known?
Prediction models are about making good predictions. That's what you are optimizing (in terms of the metric you optimized your elastic net parameters for), when you go for your second option. Whatever... | Do variable-selection methods (e.g. Elastic Net; Lasso) invalidate theory-based models in fields whe
Prediction models are about making good predictions. That's what you are optimizing (in terms of the metric you optimized your elastic net parameters for), when you go for your second option. Whatever |
49,698 | Multiple regression with mixed continuous/categorical variables: Dummy coding, scaling, regularization | We do standardization/normalization to put our features in $[0,1]$ or $[-1,1]$ range. Let suppose we are using min-max normalization to put the values in the range $[0,1]$. The answer of your question are as follows.
Should I standardize/scale my data WITH or WITHOUT dummy coded cat. variables?
There is no clear Yes/... | Multiple regression with mixed continuous/categorical variables: Dummy coding, scaling, regularizati | We do standardization/normalization to put our features in $[0,1]$ or $[-1,1]$ range. Let suppose we are using min-max normalization to put the values in the range $[0,1]$. The answer of your question | Multiple regression with mixed continuous/categorical variables: Dummy coding, scaling, regularization
We do standardization/normalization to put our features in $[0,1]$ or $[-1,1]$ range. Let suppose we are using min-max normalization to put the values in the range $[0,1]$. The answer of your question are as follows.
... | Multiple regression with mixed continuous/categorical variables: Dummy coding, scaling, regularizati
We do standardization/normalization to put our features in $[0,1]$ or $[-1,1]$ range. Let suppose we are using min-max normalization to put the values in the range $[0,1]$. The answer of your question |
49,699 | What can we say about P(X<Y and X<Z)? | Yes there can be a bound.
Since $Y$ and $Z$ are exchangable, denote
$$
P(X<Y<Z)=P(X<Z<Y)=p_1 \\
P(Y<X<Z)=P(Z<X<Y)=p_2 \\
P(Y<Z<X)=P(Z<Y<X)=p_3 \\
$$
So the target can be rewritten as $P(X<Y\text{ and }X<Z) = P(X<Y<Z) + P(X<Z<Y) = 2p_1$.
According to the permutations and the additional condition, $p_1,p_2,p_3$ satisfy t... | What can we say about P(X<Y and X<Z)? | Yes there can be a bound.
Since $Y$ and $Z$ are exchangable, denote
$$
P(X<Y<Z)=P(X<Z<Y)=p_1 \\
P(Y<X<Z)=P(Z<X<Y)=p_2 \\
P(Y<Z<X)=P(Z<Y<X)=p_3 \\
$$
So the target can be rewritten as $P(X<Y\text{ and | What can we say about P(X<Y and X<Z)?
Yes there can be a bound.
Since $Y$ and $Z$ are exchangable, denote
$$
P(X<Y<Z)=P(X<Z<Y)=p_1 \\
P(Y<X<Z)=P(Z<X<Y)=p_2 \\
P(Y<Z<X)=P(Z<Y<X)=p_3 \\
$$
So the target can be rewritten as $P(X<Y\text{ and }X<Z) = P(X<Y<Z) + P(X<Z<Y) = 2p_1$.
According to the permutations and the additio... | What can we say about P(X<Y and X<Z)?
Yes there can be a bound.
Since $Y$ and $Z$ are exchangable, denote
$$
P(X<Y<Z)=P(X<Z<Y)=p_1 \\
P(Y<X<Z)=P(Z<X<Y)=p_2 \\
P(Y<Z<X)=P(Z<Y<X)=p_3 \\
$$
So the target can be rewritten as $P(X<Y\text{ and |
49,700 | Formula of the Chebyshev's inequality for an asymmetric interval | What you are observing here is an idiosyncracy of the general Chebyshev inequality. Generally speaking, the inequality gets better as the midpoint of the interval gets closer to the mean $\mu$ and it also gets better as the length of the interval increases. However, if you hold one of the bounds constant and move the... | Formula of the Chebyshev's inequality for an asymmetric interval | What you are observing here is an idiosyncracy of the general Chebyshev inequality. Generally speaking, the inequality gets better as the midpoint of the interval gets closer to the mean $\mu$ and it | Formula of the Chebyshev's inequality for an asymmetric interval
What you are observing here is an idiosyncracy of the general Chebyshev inequality. Generally speaking, the inequality gets better as the midpoint of the interval gets closer to the mean $\mu$ and it also gets better as the length of the interval increas... | Formula of the Chebyshev's inequality for an asymmetric interval
What you are observing here is an idiosyncracy of the general Chebyshev inequality. Generally speaking, the inequality gets better as the midpoint of the interval gets closer to the mean $\mu$ and it |
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