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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47,301 | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test | The Streitberg-Röhmel shift algorithm is described in two manuscripts:
Streitberg B, Röhmel J (1986). "Exact Distributions for Permutation and Rank Tests: An Introduction to Some Recently Published Algorithms." Statistical Software Newsletter, 12(1), 10-17. ISSN 1609-3631.
Streitberg B, Röhmel J (1987). "Exakte Vertei... | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test | The Streitberg-Röhmel shift algorithm is described in two manuscripts:
Streitberg B, Röhmel J (1986). "Exact Distributions for Permutation and Rank Tests: An Introduction to Some Recently Published A | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test
The Streitberg-Röhmel shift algorithm is described in two manuscripts:
Streitberg B, Röhmel J (1986). "Exact Distributions for Permutation and Rank Tests: An Introduction to Some Recently Published Algorithms." Statistical Software Newsletter, 12(1),... | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test
The Streitberg-Röhmel shift algorithm is described in two manuscripts:
Streitberg B, Röhmel J (1986). "Exact Distributions for Permutation and Rank Tests: An Introduction to Some Recently Published A |
47,302 | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test | Actually, on this website you can find an implemented version of the Wilcoxon Rank-Sum test which provides the exact solution for data that involves ties and also for data without ties. In addition, quite big sample sizes can be solved (at the moment $A, B \le 200$).
(The reference is Marx, A.; Backes, C.; Meese, E.;... | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test | Actually, on this website you can find an implemented version of the Wilcoxon Rank-Sum test which provides the exact solution for data that involves ties and also for data without ties. In addition, q | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test
Actually, on this website you can find an implemented version of the Wilcoxon Rank-Sum test which provides the exact solution for data that involves ties and also for data without ties. In addition, quite big sample sizes can be solved (at the moment ... | Algorithm and R code for dealing with ties in Wilcoxon rank-sum test
Actually, on this website you can find an implemented version of the Wilcoxon Rank-Sum test which provides the exact solution for data that involves ties and also for data without ties. In addition, q |
47,303 | software library to compute KL divergence? | I ended up coding KL divergences and derivatives myself in Julia. I've released it as part of an existing open source project. Future readers may find the code at this page of the Celeste.jl project. | software library to compute KL divergence? | I ended up coding KL divergences and derivatives myself in Julia. I've released it as part of an existing open source project. Future readers may find the code at this page of the Celeste.jl project. | software library to compute KL divergence?
I ended up coding KL divergences and derivatives myself in Julia. I've released it as part of an existing open source project. Future readers may find the code at this page of the Celeste.jl project. | software library to compute KL divergence?
I ended up coding KL divergences and derivatives myself in Julia. I've released it as part of an existing open source project. Future readers may find the code at this page of the Celeste.jl project. |
47,304 | software library to compute KL divergence? | It's great that you came up with the solution (+1). I meant to post an answer to this question much earlier, but was busy traveling to my dissertation defense (which was successful :-). You are likely to be happy with your solution, but, in addition to possibility to compute KL divergences for certain distributions in ... | software library to compute KL divergence? | It's great that you came up with the solution (+1). I meant to post an answer to this question much earlier, but was busy traveling to my dissertation defense (which was successful :-). You are likely | software library to compute KL divergence?
It's great that you came up with the solution (+1). I meant to post an answer to this question much earlier, but was busy traveling to my dissertation defense (which was successful :-). You are likely to be happy with your solution, but, in addition to possibility to compute K... | software library to compute KL divergence?
It's great that you came up with the solution (+1). I meant to post an answer to this question much earlier, but was busy traveling to my dissertation defense (which was successful :-). You are likely |
47,305 | Is dimensionality reduction almost always useful for classification? | I think there are two ways to look at the question whether SVD/PCA helps in general.
Is it better to use PCA reduced data instead of the raw data?
Often yes, but there are situations where PCA is not needed.
I'd in addition consider how well the bilinear concept behind PCA fits with the data generation process. I wo... | Is dimensionality reduction almost always useful for classification? | I think there are two ways to look at the question whether SVD/PCA helps in general.
Is it better to use PCA reduced data instead of the raw data?
Often yes, but there are situations where PCA is not | Is dimensionality reduction almost always useful for classification?
I think there are two ways to look at the question whether SVD/PCA helps in general.
Is it better to use PCA reduced data instead of the raw data?
Often yes, but there are situations where PCA is not needed.
I'd in addition consider how well the bi... | Is dimensionality reduction almost always useful for classification?
I think there are two ways to look at the question whether SVD/PCA helps in general.
Is it better to use PCA reduced data instead of the raw data?
Often yes, but there are situations where PCA is not |
47,306 | Is dimensionality reduction almost always useful for classification? | Your intuition is correct. Performing a singular value decomposition in order to use the derived scores in a classifier has a positive influence in a classifier's overall performance in most cases. That is because through SVD one will effectively regularise and/or filter out modes of irrelevant variation (aka. noise). ... | Is dimensionality reduction almost always useful for classification? | Your intuition is correct. Performing a singular value decomposition in order to use the derived scores in a classifier has a positive influence in a classifier's overall performance in most cases. Th | Is dimensionality reduction almost always useful for classification?
Your intuition is correct. Performing a singular value decomposition in order to use the derived scores in a classifier has a positive influence in a classifier's overall performance in most cases. That is because through SVD one will effectively regu... | Is dimensionality reduction almost always useful for classification?
Your intuition is correct. Performing a singular value decomposition in order to use the derived scores in a classifier has a positive influence in a classifier's overall performance in most cases. Th |
47,307 | A continuous generalization of the binary bandit | Disclosure: I know almost nothing about bandits. Still, my suggestion seems like a natuaral generalization of the case you presented. It does not consider the experimental design step in detail (since I don't know what people ususally consider as a loss function in this scenario), so might fail in this respect.
Let me ... | A continuous generalization of the binary bandit | Disclosure: I know almost nothing about bandits. Still, my suggestion seems like a natuaral generalization of the case you presented. It does not consider the experimental design step in detail (since | A continuous generalization of the binary bandit
Disclosure: I know almost nothing about bandits. Still, my suggestion seems like a natuaral generalization of the case you presented. It does not consider the experimental design step in detail (since I don't know what people ususally consider as a loss function in this ... | A continuous generalization of the binary bandit
Disclosure: I know almost nothing about bandits. Still, my suggestion seems like a natuaral generalization of the case you presented. It does not consider the experimental design step in detail (since |
47,308 | A continuous generalization of the binary bandit | This problem is tackled by the Dearden paper on Bayesian Q-Learning. He considers a normal model for "returns" (future rewards) like @yair's solution. He also considers another term called the "value of information": "the expected improvement in future decision quality that might arise from the information acquired b... | A continuous generalization of the binary bandit | This problem is tackled by the Dearden paper on Bayesian Q-Learning. He considers a normal model for "returns" (future rewards) like @yair's solution. He also considers another term called the "valu | A continuous generalization of the binary bandit
This problem is tackled by the Dearden paper on Bayesian Q-Learning. He considers a normal model for "returns" (future rewards) like @yair's solution. He also considers another term called the "value of information": "the expected improvement in future decision quality... | A continuous generalization of the binary bandit
This problem is tackled by the Dearden paper on Bayesian Q-Learning. He considers a normal model for "returns" (future rewards) like @yair's solution. He also considers another term called the "valu |
47,309 | Nonlinear total least squares / Deming regression in R | There is a technique called "Orthogonal Distance Regression" that does this. An implementation in R was recently released:
http://www.r-bloggers.com/introducing-orthogonal-nonlinear-least-squares-regression-in-r/ | Nonlinear total least squares / Deming regression in R | There is a technique called "Orthogonal Distance Regression" that does this. An implementation in R was recently released:
http://www.r-bloggers.com/introducing-orthogonal-nonlinear-least-squares-re | Nonlinear total least squares / Deming regression in R
There is a technique called "Orthogonal Distance Regression" that does this. An implementation in R was recently released:
http://www.r-bloggers.com/introducing-orthogonal-nonlinear-least-squares-regression-in-r/ | Nonlinear total least squares / Deming regression in R
There is a technique called "Orthogonal Distance Regression" that does this. An implementation in R was recently released:
http://www.r-bloggers.com/introducing-orthogonal-nonlinear-least-squares-re |
47,310 | Are different p-values for chi-squared and z test expected for testing difference in proportions? | Very simple: both the z test and the contingency table $\chi^{2}$ test are two tailed tests, but you have got the one-sided $p$-value for your z test statistic. That is for $H_{0}: p_{1} - p_{2} = 0$, the $p$-value = $P(|Z| \ge |z|)$, but your reported $p$-value is only $P(Z \le z)$.
Notice that $0.4013 \times 2 \appro... | Are different p-values for chi-squared and z test expected for testing difference in proportions? | Very simple: both the z test and the contingency table $\chi^{2}$ test are two tailed tests, but you have got the one-sided $p$-value for your z test statistic. That is for $H_{0}: p_{1} - p_{2} = 0$, | Are different p-values for chi-squared and z test expected for testing difference in proportions?
Very simple: both the z test and the contingency table $\chi^{2}$ test are two tailed tests, but you have got the one-sided $p$-value for your z test statistic. That is for $H_{0}: p_{1} - p_{2} = 0$, the $p$-value = $P(|Z... | Are different p-values for chi-squared and z test expected for testing difference in proportions?
Very simple: both the z test and the contingency table $\chi^{2}$ test are two tailed tests, but you have got the one-sided $p$-value for your z test statistic. That is for $H_{0}: p_{1} - p_{2} = 0$, |
47,311 | Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed? | The Kolmogorov-Smirnov test can be used to test with a null of any fully specified continuous distribution.
Since the statistic is only a function of the largest difference in cdf, if you use a probability integral transform on the data, that won't change the test statistic but turns it into a test against uniformity. ... | Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed? | The Kolmogorov-Smirnov test can be used to test with a null of any fully specified continuous distribution.
Since the statistic is only a function of the largest difference in cdf, if you use a probab | Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed?
The Kolmogorov-Smirnov test can be used to test with a null of any fully specified continuous distribution.
Since the statistic is only a function of the largest difference in cdf, if you use a probability integral transform on the data, t... | Can I use Kolmogorov Smirnov test to check if my data are uniformly distributed?
The Kolmogorov-Smirnov test can be used to test with a null of any fully specified continuous distribution.
Since the statistic is only a function of the largest difference in cdf, if you use a probab |
47,312 | Comparing two means using permutation test and bootstrapping with the boot() function in R | While permutations tests, randomization tests and bootstrapping all fall under the class of resampling procedures, they differ in some important ways.
In particular, a permutation test differs in several respects from bootstrapping; you seem to think they're the same thing.
Some of these differences will make it essent... | Comparing two means using permutation test and bootstrapping with the boot() function in R | While permutations tests, randomization tests and bootstrapping all fall under the class of resampling procedures, they differ in some important ways.
In particular, a permutation test differs in seve | Comparing two means using permutation test and bootstrapping with the boot() function in R
While permutations tests, randomization tests and bootstrapping all fall under the class of resampling procedures, they differ in some important ways.
In particular, a permutation test differs in several respects from bootstrappi... | Comparing two means using permutation test and bootstrapping with the boot() function in R
While permutations tests, randomization tests and bootstrapping all fall under the class of resampling procedures, they differ in some important ways.
In particular, a permutation test differs in seve |
47,313 | Why are inf and sup used in the definition of minimax estimators? | It is possible that the set of values $R(\theta,\hat{\delta})$ is an open set. Therefore, supremum/infimum is more general than maximum/minimum. Suppose, $ \{R(\theta,\hat{\delta}): \theta \in \Theta\}=\{x: 0<x<1\}$ where $\Theta$ is the parameter space. This has no maximum, but it has a supremum of 1. | Why are inf and sup used in the definition of minimax estimators? | It is possible that the set of values $R(\theta,\hat{\delta})$ is an open set. Therefore, supremum/infimum is more general than maximum/minimum. Suppose, $ \{R(\theta,\hat{\delta}): \theta \in \Theta\ | Why are inf and sup used in the definition of minimax estimators?
It is possible that the set of values $R(\theta,\hat{\delta})$ is an open set. Therefore, supremum/infimum is more general than maximum/minimum. Suppose, $ \{R(\theta,\hat{\delta}): \theta \in \Theta\}=\{x: 0<x<1\}$ where $\Theta$ is the parameter space.... | Why are inf and sup used in the definition of minimax estimators?
It is possible that the set of values $R(\theta,\hat{\delta})$ is an open set. Therefore, supremum/infimum is more general than maximum/minimum. Suppose, $ \{R(\theta,\hat{\delta}): \theta \in \Theta\ |
47,314 | How to convert sport odds into percentage? | The odds you have are in decimal format, which the bookmaker calculates as:
$$
d_E = \frac{1}{p_E + o_E}
$$
where $d_E$ is the decimal odds for event $E$, $p_E$ is the bookmakers estimated probability of event $E$, and $o_E$ is the over-round which the bookmaker adds to the decimal odds for event $E$. The over-round ef... | How to convert sport odds into percentage? | The odds you have are in decimal format, which the bookmaker calculates as:
$$
d_E = \frac{1}{p_E + o_E}
$$
where $d_E$ is the decimal odds for event $E$, $p_E$ is the bookmakers estimated probability | How to convert sport odds into percentage?
The odds you have are in decimal format, which the bookmaker calculates as:
$$
d_E = \frac{1}{p_E + o_E}
$$
where $d_E$ is the decimal odds for event $E$, $p_E$ is the bookmakers estimated probability of event $E$, and $o_E$ is the over-round which the bookmaker adds to the de... | How to convert sport odds into percentage?
The odds you have are in decimal format, which the bookmaker calculates as:
$$
d_E = \frac{1}{p_E + o_E}
$$
where $d_E$ is the decimal odds for event $E$, $p_E$ is the bookmakers estimated probability |
47,315 | How to convert sport odds into percentage? | If the odds describe real events, you most likely got them from some betting site.
You are searching for overround. If your implied probabilities do not add up to 1 but are greater 1, then the bookmaker makes a sure profit of all above 1.
A simple way to work is to re-normalize, i.e. divide every inverse odd again by ... | How to convert sport odds into percentage? | If the odds describe real events, you most likely got them from some betting site.
You are searching for overround. If your implied probabilities do not add up to 1 but are greater 1, then the bookmak | How to convert sport odds into percentage?
If the odds describe real events, you most likely got them from some betting site.
You are searching for overround. If your implied probabilities do not add up to 1 but are greater 1, then the bookmaker makes a sure profit of all above 1.
A simple way to work is to re-normali... | How to convert sport odds into percentage?
If the odds describe real events, you most likely got them from some betting site.
You are searching for overround. If your implied probabilities do not add up to 1 but are greater 1, then the bookmak |
47,316 | How to convert sport odds into percentage? | If you just want to estimate the probabilities, it seems indeed reasonable to just devide each percentage by 1.04.
However, if you want to find out more about the true percentages that the bookkeeper uses, you can do something more.
Let's assume that the bookkeeper does not want to accept a negative expected value for ... | How to convert sport odds into percentage? | If you just want to estimate the probabilities, it seems indeed reasonable to just devide each percentage by 1.04.
However, if you want to find out more about the true percentages that the bookkeeper | How to convert sport odds into percentage?
If you just want to estimate the probabilities, it seems indeed reasonable to just devide each percentage by 1.04.
However, if you want to find out more about the true percentages that the bookkeeper uses, you can do something more.
Let's assume that the bookkeeper does not wa... | How to convert sport odds into percentage?
If you just want to estimate the probabilities, it seems indeed reasonable to just devide each percentage by 1.04.
However, if you want to find out more about the true percentages that the bookkeeper |
47,317 | How to convert sport odds into percentage? | I think they are odds against. i.e.
2.5 = (Prob(away team wins) + Prob(draw)) / Prob (Home team wins)
You can compute P(Away team wins) + Prob(draw) by taking 1/(2.5+1).
If you do that for all 3, you can P(W) = 0.285, P(D) = 0.235, P(L) = 0.25.
They do not sum up to 1, probably because the odds are rigged. But you can... | How to convert sport odds into percentage? | I think they are odds against. i.e.
2.5 = (Prob(away team wins) + Prob(draw)) / Prob (Home team wins)
You can compute P(Away team wins) + Prob(draw) by taking 1/(2.5+1).
If you do that for all 3, you | How to convert sport odds into percentage?
I think they are odds against. i.e.
2.5 = (Prob(away team wins) + Prob(draw)) / Prob (Home team wins)
You can compute P(Away team wins) + Prob(draw) by taking 1/(2.5+1).
If you do that for all 3, you can P(W) = 0.285, P(D) = 0.235, P(L) = 0.25.
They do not sum up to 1, probab... | How to convert sport odds into percentage?
I think they are odds against. i.e.
2.5 = (Prob(away team wins) + Prob(draw)) / Prob (Home team wins)
You can compute P(Away team wins) + Prob(draw) by taking 1/(2.5+1).
If you do that for all 3, you |
47,318 | How to convert sport odds into percentage? | There is a major issue with the odds that are offered in this scenario. Where did they come from?
Suppose I bet \$1 on the home team. With odds of 2.5, I would win \$2.50 and get my \$1 back, for a collection of \$3.50. So, let's look at the chart below:
Winner - Odds - Payback on $1
Home - 2.5 - $3.5
Draw - 3.... | How to convert sport odds into percentage? | There is a major issue with the odds that are offered in this scenario. Where did they come from?
Suppose I bet \$1 on the home team. With odds of 2.5, I would win \$2.50 and get my \$1 back, for a | How to convert sport odds into percentage?
There is a major issue with the odds that are offered in this scenario. Where did they come from?
Suppose I bet \$1 on the home team. With odds of 2.5, I would win \$2.50 and get my \$1 back, for a collection of \$3.50. So, let's look at the chart below:
Winner - Odds - Pay... | How to convert sport odds into percentage?
There is a major issue with the odds that are offered in this scenario. Where did they come from?
Suppose I bet \$1 on the home team. With odds of 2.5, I would win \$2.50 and get my \$1 back, for a |
47,319 | Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Cholesky decomposition of $\Sigma$ | By the chain rule,
$\frac{\partial x^{T}A^{T}y}{\partial \Sigma_{i,j}}=
\mbox{tr} \left( \left( \frac{\partial x^{T}A^{T}y}{\partial A^{T}} \right)^{T} \frac{\partial A^{T}}{\partial \Sigma_{i,j} } \right) $.
This chain rule formulation is described in many references on matrix calculus, such as The Matrix Cookbook ... | Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Chole | By the chain rule,
$\frac{\partial x^{T}A^{T}y}{\partial \Sigma_{i,j}}=
\mbox{tr} \left( \left( \frac{\partial x^{T}A^{T}y}{\partial A^{T}} \right)^{T} \frac{\partial A^{T}}{\partial \Sigma_{i,j} } \ | Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Cholesky decomposition of $\Sigma$
By the chain rule,
$\frac{\partial x^{T}A^{T}y}{\partial \Sigma_{i,j}}=
\mbox{tr} \left( \left( \frac{\partial x^{T}A^{T}y}{\partial A^{T}} \right)^{T} \frac{\partial A^{T}}{\partial \Sigma... | Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Chole
By the chain rule,
$\frac{\partial x^{T}A^{T}y}{\partial \Sigma_{i,j}}=
\mbox{tr} \left( \left( \frac{\partial x^{T}A^{T}y}{\partial A^{T}} \right)^{T} \frac{\partial A^{T}}{\partial \Sigma_{i,j} } \ |
47,320 | Why doesn't a non-linear kernel improve accuracy in high dimensions compared to a linear kernel? | The motivation to use kernel functions is to map the data onto a (typically higher dimensional) feature space in which it is easier to separate the data linearly. If the input space is high dimensional, the data is typically already (nearly) separable, so there is no need to map to an even higher dimensional feature sp... | Why doesn't a non-linear kernel improve accuracy in high dimensions compared to a linear kernel? | The motivation to use kernel functions is to map the data onto a (typically higher dimensional) feature space in which it is easier to separate the data linearly. If the input space is high dimensiona | Why doesn't a non-linear kernel improve accuracy in high dimensions compared to a linear kernel?
The motivation to use kernel functions is to map the data onto a (typically higher dimensional) feature space in which it is easier to separate the data linearly. If the input space is high dimensional, the data is typicall... | Why doesn't a non-linear kernel improve accuracy in high dimensions compared to a linear kernel?
The motivation to use kernel functions is to map the data onto a (typically higher dimensional) feature space in which it is easier to separate the data linearly. If the input space is high dimensiona |
47,321 | Why does Slice sampler use the log of the density? | The slice sampler does not "sample from the log-density". It can, however, use the log density in the calculations to obtain a dependent sequence of observations from the density.
The basic idea of a slice sampler is in terms of the density itself, but for various reasons (computational accuracy, primarily) it's usuall... | Why does Slice sampler use the log of the density? | The slice sampler does not "sample from the log-density". It can, however, use the log density in the calculations to obtain a dependent sequence of observations from the density.
The basic idea of a | Why does Slice sampler use the log of the density?
The slice sampler does not "sample from the log-density". It can, however, use the log density in the calculations to obtain a dependent sequence of observations from the density.
The basic idea of a slice sampler is in terms of the density itself, but for various reas... | Why does Slice sampler use the log of the density?
The slice sampler does not "sample from the log-density". It can, however, use the log density in the calculations to obtain a dependent sequence of observations from the density.
The basic idea of a |
47,322 | The order of Data Centering and Data Transformation | If logarithms of predictors, generically $x$, are helpful, and centring variables on their mean is helpful, would it help to centre before transforming?
Once you have subtracted the mean from a variable, then necessarily at least one value is now negative and logarithms can't (usefully) be calculated (setting aside co... | The order of Data Centering and Data Transformation | If logarithms of predictors, generically $x$, are helpful, and centring variables on their mean is helpful, would it help to centre before transforming?
Once you have subtracted the mean from a varia | The order of Data Centering and Data Transformation
If logarithms of predictors, generically $x$, are helpful, and centring variables on their mean is helpful, would it help to centre before transforming?
Once you have subtracted the mean from a variable, then necessarily at least one value is now negative and logarit... | The order of Data Centering and Data Transformation
If logarithms of predictors, generically $x$, are helpful, and centring variables on their mean is helpful, would it help to centre before transforming?
Once you have subtracted the mean from a varia |
47,323 | The order of Data Centering and Data Transformation | This is not a question with a straightforward answer. There are deep issues involved.
If logarithm of a variable, say X, is improving the model, then X is an important variable itself as a "level". For example, stock prices are not important as levels (of course this is debatable), because they are recalculated after ... | The order of Data Centering and Data Transformation | This is not a question with a straightforward answer. There are deep issues involved.
If logarithm of a variable, say X, is improving the model, then X is an important variable itself as a "level". F | The order of Data Centering and Data Transformation
This is not a question with a straightforward answer. There are deep issues involved.
If logarithm of a variable, say X, is improving the model, then X is an important variable itself as a "level". For example, stock prices are not important as levels (of course this... | The order of Data Centering and Data Transformation
This is not a question with a straightforward answer. There are deep issues involved.
If logarithm of a variable, say X, is improving the model, then X is an important variable itself as a "level". F |
47,324 | Odds vs. Probabilities (Confusion) | A probability lies between 0 and 1; I presume you're familiar enough with it that we don't need to define probability, but please clarify if you do require a basic definition. [So if I say something like "The probability of at least two heads in three tosses of a coin is 1/2" or "the probability that I miss the bus tom... | Odds vs. Probabilities (Confusion) | A probability lies between 0 and 1; I presume you're familiar enough with it that we don't need to define probability, but please clarify if you do require a basic definition. [So if I say something l | Odds vs. Probabilities (Confusion)
A probability lies between 0 and 1; I presume you're familiar enough with it that we don't need to define probability, but please clarify if you do require a basic definition. [So if I say something like "The probability of at least two heads in three tosses of a coin is 1/2" or "the ... | Odds vs. Probabilities (Confusion)
A probability lies between 0 and 1; I presume you're familiar enough with it that we don't need to define probability, but please clarify if you do require a basic definition. [So if I say something l |
47,325 | Odds vs. Probabilities (Confusion) | Odds ratio is best understood in the gambling context. If you are throwing a dice, and the winning side is 6, then they say you have 5/1 chance to win, i.e. for every one winning chance there are 5 chances to lose. If the wining sides are 2 and 3, then your odds ratio is 2/1.
Now, you can see how the odds ratio is rela... | Odds vs. Probabilities (Confusion) | Odds ratio is best understood in the gambling context. If you are throwing a dice, and the winning side is 6, then they say you have 5/1 chance to win, i.e. for every one winning chance there are 5 ch | Odds vs. Probabilities (Confusion)
Odds ratio is best understood in the gambling context. If you are throwing a dice, and the winning side is 6, then they say you have 5/1 chance to win, i.e. for every one winning chance there are 5 chances to lose. If the wining sides are 2 and 3, then your odds ratio is 2/1.
Now, you... | Odds vs. Probabilities (Confusion)
Odds ratio is best understood in the gambling context. If you are throwing a dice, and the winning side is 6, then they say you have 5/1 chance to win, i.e. for every one winning chance there are 5 ch |
47,326 | Is it possible to compare the parsimony of models with the same number of parameters and explanatory variables? | The number of parameters often turns out not to be a good measure of the complexity of a function or model. There are a number of ways of measuring complexity in different scenarios - one of the simplest is Vapnik–Chervonenkis dimension. The basic idea is to imagine a bunch of points distributed in the xy plane, some l... | Is it possible to compare the parsimony of models with the same number of parameters and explanatory | The number of parameters often turns out not to be a good measure of the complexity of a function or model. There are a number of ways of measuring complexity in different scenarios - one of the simpl | Is it possible to compare the parsimony of models with the same number of parameters and explanatory variables?
The number of parameters often turns out not to be a good measure of the complexity of a function or model. There are a number of ways of measuring complexity in different scenarios - one of the simplest is V... | Is it possible to compare the parsimony of models with the same number of parameters and explanatory
The number of parameters often turns out not to be a good measure of the complexity of a function or model. There are a number of ways of measuring complexity in different scenarios - one of the simpl |
47,327 | Is it possible to compare the parsimony of models with the same number of parameters and explanatory variables? | When statisticians say that they prefer parsimonious models they are really cautioning against over-fitting. There really is no other statistical reason to prefer a parsimonious model other than ease of interpretability and, generally speaking, that's a silly reason for a statistician. I think Gelman does a good job ar... | Is it possible to compare the parsimony of models with the same number of parameters and explanatory | When statisticians say that they prefer parsimonious models they are really cautioning against over-fitting. There really is no other statistical reason to prefer a parsimonious model other than ease | Is it possible to compare the parsimony of models with the same number of parameters and explanatory variables?
When statisticians say that they prefer parsimonious models they are really cautioning against over-fitting. There really is no other statistical reason to prefer a parsimonious model other than ease of inter... | Is it possible to compare the parsimony of models with the same number of parameters and explanatory
When statisticians say that they prefer parsimonious models they are really cautioning against over-fitting. There really is no other statistical reason to prefer a parsimonious model other than ease |
47,328 | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$ | Yes.
Let's begin by simplifying the question. The event
$$T_1\sum_{i=1}^n T_i w_i \geq 0$$
is the union of the disjoint events (determined by $T_1=\pm 1$)
$$w_1 + \sum_{i=2}^n T_i w_i \geq 0,\ -w_1 + \sum_{i=2}^n T_i w_i \geq 0.$$
After simple algebraic manipulation, and using the fact that each $T_i$ has the same dis... | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$ | Yes.
Let's begin by simplifying the question. The event
$$T_1\sum_{i=1}^n T_i w_i \geq 0$$
is the union of the disjoint events (determined by $T_1=\pm 1$)
$$w_1 + \sum_{i=2}^n T_i w_i \geq 0,\ -w_1 + | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$
Yes.
Let's begin by simplifying the question. The event
$$T_1\sum_{i=1}^n T_i w_i \geq 0$$
is the union of the disjoint events (determined by $T_1=\pm 1$)
$$w_1 + \sum_{i=2}^n T_i w_i \geq 0,\ -w_1 + \sum_{i=2}^n T_i w_i \geq 0.$$
After simpl... | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$
Yes.
Let's begin by simplifying the question. The event
$$T_1\sum_{i=1}^n T_i w_i \geq 0$$
is the union of the disjoint events (determined by $T_1=\pm 1$)
$$w_1 + \sum_{i=2}^n T_i w_i \geq 0,\ -w_1 + |
47,329 | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$ | $$T_1\sum_{i=1}^n T_i w_i = w_1 + T_1\sum_{i=2}^n T_i w_i$$
since $T_1^2 = 1$.
Write the sum as $S_{2w}$. So we are looking at the probability
$$P\left(T_1S_{2w} \geq -w_1\right) = \\P\left(T_1S_{2w} \geq -w_1 \mid T_1 =1\right)\cdot P(T_1 =1) + P\left(T_1S_{2w} \geq -w_1 \mid T_1 =-1\right)\cdot P(T_1 =-1)$$
$$\Righta... | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$ | $$T_1\sum_{i=1}^n T_i w_i = w_1 + T_1\sum_{i=2}^n T_i w_i$$
since $T_1^2 = 1$.
Write the sum as $S_{2w}$. So we are looking at the probability
$$P\left(T_1S_{2w} \geq -w_1\right) = \\P\left(T_1S_{2w} | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$
$$T_1\sum_{i=1}^n T_i w_i = w_1 + T_1\sum_{i=2}^n T_i w_i$$
since $T_1^2 = 1$.
Write the sum as $S_{2w}$. So we are looking at the probability
$$P\left(T_1S_{2w} \geq -w_1\right) = \\P\left(T_1S_{2w} \geq -w_1 \mid T_1 =1\right)\cdot P(T_1 =1)... | Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$
$$T_1\sum_{i=1}^n T_i w_i = w_1 + T_1\sum_{i=2}^n T_i w_i$$
since $T_1^2 = 1$.
Write the sum as $S_{2w}$. So we are looking at the probability
$$P\left(T_1S_{2w} \geq -w_1\right) = \\P\left(T_1S_{2w} |
47,330 | Is high AIC a bad feature of the model? | This is from the description of AIC:
The Akaike information criterion (AIC) is a measure of the relative
quality of a statistical model for a given set of data. As such, AIC
provides a means for model selection.
I don't pay attention to the absolute value of AIC. I only use it to compare in-sample fit of the can... | Is high AIC a bad feature of the model? | This is from the description of AIC:
The Akaike information criterion (AIC) is a measure of the relative
quality of a statistical model for a given set of data. As such, AIC
provides a means for | Is high AIC a bad feature of the model?
This is from the description of AIC:
The Akaike information criterion (AIC) is a measure of the relative
quality of a statistical model for a given set of data. As such, AIC
provides a means for model selection.
I don't pay attention to the absolute value of AIC. I only us... | Is high AIC a bad feature of the model?
This is from the description of AIC:
The Akaike information criterion (AIC) is a measure of the relative
quality of a statistical model for a given set of data. As such, AIC
provides a means for |
47,331 | Is high AIC a bad feature of the model? | As others said, there is not much point in evaluating a single model according to the absolute value of its AIC.
The point is to compare the AIC values of different models and the model which has lower AIC value than the other is better than the other in the sense that it is less complex but still a good fit for the da... | Is high AIC a bad feature of the model? | As others said, there is not much point in evaluating a single model according to the absolute value of its AIC.
The point is to compare the AIC values of different models and the model which has lowe | Is high AIC a bad feature of the model?
As others said, there is not much point in evaluating a single model according to the absolute value of its AIC.
The point is to compare the AIC values of different models and the model which has lower AIC value than the other is better than the other in the sense that it is less... | Is high AIC a bad feature of the model?
As others said, there is not much point in evaluating a single model according to the absolute value of its AIC.
The point is to compare the AIC values of different models and the model which has lowe |
47,332 | Why do we use the term multicollinearity, when the vectors representing two variables are never truly collinear? | I don't think anyone worries about exact collinearity. If that was the case, $X'X$ would not be invertible. That is why full column rank of $X$ in one of the first assumptions. People worry about inexact relationships, since then there are coefficients to interpret, but they are too unreliable to be useful. The world m... | Why do we use the term multicollinearity, when the vectors representing two variables are never trul | I don't think anyone worries about exact collinearity. If that was the case, $X'X$ would not be invertible. That is why full column rank of $X$ in one of the first assumptions. People worry about inex | Why do we use the term multicollinearity, when the vectors representing two variables are never truly collinear?
I don't think anyone worries about exact collinearity. If that was the case, $X'X$ would not be invertible. That is why full column rank of $X$ in one of the first assumptions. People worry about inexact rel... | Why do we use the term multicollinearity, when the vectors representing two variables are never trul
I don't think anyone worries about exact collinearity. If that was the case, $X'X$ would not be invertible. That is why full column rank of $X$ in one of the first assumptions. People worry about inex |
47,333 | How to test difference between standardized difference between means | This can be easily done with methods described in chapter 19 by Gleser and Olkin in the Handbook of Research Synthesis and Meta-Analysis (2009).
First, put the 5 d-values into a vector, $\vec{d}$.
Next, we need to construct the $5 \times 5$ variance-covariance matrix for $\vec{d}$. The diagonal elements (the variances)... | How to test difference between standardized difference between means | This can be easily done with methods described in chapter 19 by Gleser and Olkin in the Handbook of Research Synthesis and Meta-Analysis (2009).
First, put the 5 d-values into a vector, $\vec{d}$.
Nex | How to test difference between standardized difference between means
This can be easily done with methods described in chapter 19 by Gleser and Olkin in the Handbook of Research Synthesis and Meta-Analysis (2009).
First, put the 5 d-values into a vector, $\vec{d}$.
Next, we need to construct the $5 \times 5$ variance-c... | How to test difference between standardized difference between means
This can be easily done with methods described in chapter 19 by Gleser and Olkin in the Handbook of Research Synthesis and Meta-Analysis (2009).
First, put the 5 d-values into a vector, $\vec{d}$.
Nex |
47,334 | How to test difference between standardized difference between means | I don't know any statistical test to check the difference of effect sizes. But nevertheless there is a possible solution to the problem: confidence intervals.
You can calculate the confidence interval for each of your d. If the confidence intervals have some large intersection it is OK to claim that they are similar. I... | How to test difference between standardized difference between means | I don't know any statistical test to check the difference of effect sizes. But nevertheless there is a possible solution to the problem: confidence intervals.
You can calculate the confidence interval | How to test difference between standardized difference between means
I don't know any statistical test to check the difference of effect sizes. But nevertheless there is a possible solution to the problem: confidence intervals.
You can calculate the confidence interval for each of your d. If the confidence intervals ha... | How to test difference between standardized difference between means
I don't know any statistical test to check the difference of effect sizes. But nevertheless there is a possible solution to the problem: confidence intervals.
You can calculate the confidence interval |
47,335 | How to test difference between standardized difference between means | I'm a little confused at your terminology (in particular, I think you mean d is an index for the variables, but I'm not 100% sure. You also don't provide a lot of context for how the d's are related. I'm going to assume the variables are continuous because you standardized them and compare means. Without making any oth... | How to test difference between standardized difference between means | I'm a little confused at your terminology (in particular, I think you mean d is an index for the variables, but I'm not 100% sure. You also don't provide a lot of context for how the d's are related. | How to test difference between standardized difference between means
I'm a little confused at your terminology (in particular, I think you mean d is an index for the variables, but I'm not 100% sure. You also don't provide a lot of context for how the d's are related. I'm going to assume the variables are continuous be... | How to test difference between standardized difference between means
I'm a little confused at your terminology (in particular, I think you mean d is an index for the variables, but I'm not 100% sure. You also don't provide a lot of context for how the d's are related. |
47,336 | Unbiased estimator and sufficient statistic from discrete uniform distribution | To find an unbiased estimator for $N$ using $z_1$, start from here: if $z_1 \sim \textrm{Unif}(1, N)$, then we want to find some function of $z_1$ such that $E(f(z_1)) = N$ (that's just what it means to be unbiased). Since $E(z_1) = \frac1N \sum_{i=1}^N i = \frac{N(N + 1)}{2N} = (N+1)/2$, it's hopefully pretty easy to ... | Unbiased estimator and sufficient statistic from discrete uniform distribution | To find an unbiased estimator for $N$ using $z_1$, start from here: if $z_1 \sim \textrm{Unif}(1, N)$, then we want to find some function of $z_1$ such that $E(f(z_1)) = N$ (that's just what it means | Unbiased estimator and sufficient statistic from discrete uniform distribution
To find an unbiased estimator for $N$ using $z_1$, start from here: if $z_1 \sim \textrm{Unif}(1, N)$, then we want to find some function of $z_1$ such that $E(f(z_1)) = N$ (that's just what it means to be unbiased). Since $E(z_1) = \frac1N ... | Unbiased estimator and sufficient statistic from discrete uniform distribution
To find an unbiased estimator for $N$ using $z_1$, start from here: if $z_1 \sim \textrm{Unif}(1, N)$, then we want to find some function of $z_1$ such that $E(f(z_1)) = N$ (that's just what it means |
47,337 | What does muhaz return? | muhaz() doesn't return the baseline hazard rate, but the hazard function including the contribution of covariates to the final hazard. You can divide the two contribution as I do with this code. First start simulating a dataset with a fixed hazard rate $h_0$:
library(survival)
set.seed(6)
n <- 200
age <- 50 + 12... | What does muhaz return? | muhaz() doesn't return the baseline hazard rate, but the hazard function including the contribution of covariates to the final hazard. You can divide the two contribution as I do with this code. Firs | What does muhaz return?
muhaz() doesn't return the baseline hazard rate, but the hazard function including the contribution of covariates to the final hazard. You can divide the two contribution as I do with this code. First start simulating a dataset with a fixed hazard rate $h_0$:
library(survival)
set.seed(6)
n ... | What does muhaz return?
muhaz() doesn't return the baseline hazard rate, but the hazard function including the contribution of covariates to the final hazard. You can divide the two contribution as I do with this code. Firs |
47,338 | OLS versus ML estimation of VECM | You are asking a complicated questions, to which there are no clear answers.
Is (1) more efficient than (2)?
Note actually that the Johansen ML estimator has a strange finite-sample distribution with no finite moments, and hence has a large variance. So it is most likely not more efficient than the "Granger 2-SLS". O... | OLS versus ML estimation of VECM | You are asking a complicated questions, to which there are no clear answers.
Is (1) more efficient than (2)?
Note actually that the Johansen ML estimator has a strange finite-sample distribution wit | OLS versus ML estimation of VECM
You are asking a complicated questions, to which there are no clear answers.
Is (1) more efficient than (2)?
Note actually that the Johansen ML estimator has a strange finite-sample distribution with no finite moments, and hence has a large variance. So it is most likely not more effi... | OLS versus ML estimation of VECM
You are asking a complicated questions, to which there are no clear answers.
Is (1) more efficient than (2)?
Note actually that the Johansen ML estimator has a strange finite-sample distribution wit |
47,339 | OLS versus ML estimation of VECM | OLS assumptions do not cover the case when one or more predictors are equal to the lagged response. The so-called strict exogeneity assumption requires the predictor to be uncorrelated with the innovation. E.g. if in AR(1) we consider $y_{t-1}$ a predictor of $y_t$, then $y_{t-1}$ is correlated with $e_{t-1}$, $e_{t-2}... | OLS versus ML estimation of VECM | OLS assumptions do not cover the case when one or more predictors are equal to the lagged response. The so-called strict exogeneity assumption requires the predictor to be uncorrelated with the innova | OLS versus ML estimation of VECM
OLS assumptions do not cover the case when one or more predictors are equal to the lagged response. The so-called strict exogeneity assumption requires the predictor to be uncorrelated with the innovation. E.g. if in AR(1) we consider $y_{t-1}$ a predictor of $y_t$, then $y_{t-1}$ is co... | OLS versus ML estimation of VECM
OLS assumptions do not cover the case when one or more predictors are equal to the lagged response. The so-called strict exogeneity assumption requires the predictor to be uncorrelated with the innova |
47,340 | How to "regress out" some variables? [duplicate] | It seems to me that the following is the mathematically simplest way to partial-out variables from a correlated set of items.
Consider a correlation matrix R for 5 items, where we want to "partial-out" the first two variables. This is the initial correlation-matrix:
$$ \text{ R =} \small \begin{bmatrix} \begin{array... | How to "regress out" some variables? [duplicate] | It seems to me that the following is the mathematically simplest way to partial-out variables from a correlated set of items.
Consider a correlation matrix R for 5 items, where we want to "partial- | How to "regress out" some variables? [duplicate]
It seems to me that the following is the mathematically simplest way to partial-out variables from a correlated set of items.
Consider a correlation matrix R for 5 items, where we want to "partial-out" the first two variables. This is the initial correlation-matrix:
$... | How to "regress out" some variables? [duplicate]
It seems to me that the following is the mathematically simplest way to partial-out variables from a correlated set of items.
Consider a correlation matrix R for 5 items, where we want to "partial- |
47,341 | Do Bayesians believe in Fixed Effect Models? [duplicate] | An excerpt from Jospeh B. Kadane's Principles of Uncertainty (p. 336, freely available):
This idea has old historical roots. Because these roots still play out in the current literature, it is useful to retrace a bit of them. The received wisdom in the early 1960's (see for example Scheffe (1959, 1999)) was to draw a ... | Do Bayesians believe in Fixed Effect Models? [duplicate] | An excerpt from Jospeh B. Kadane's Principles of Uncertainty (p. 336, freely available):
This idea has old historical roots. Because these roots still play out in the current literature, it is useful | Do Bayesians believe in Fixed Effect Models? [duplicate]
An excerpt from Jospeh B. Kadane's Principles of Uncertainty (p. 336, freely available):
This idea has old historical roots. Because these roots still play out in the current literature, it is useful to retrace a bit of them. The received wisdom in the early 196... | Do Bayesians believe in Fixed Effect Models? [duplicate]
An excerpt from Jospeh B. Kadane's Principles of Uncertainty (p. 336, freely available):
This idea has old historical roots. Because these roots still play out in the current literature, it is useful |
47,342 | Consistency of OLS in presence of deterministic trend | Not only is the OLS estimator consistent in the presence of a deterministic trend, it is, as they say, superconsistent, because it converges to the true value of the coefficient on the linear trend faster then the usual $O(T^{-1/2})$ rate -at $O(T^{-3/2})$. The estimator for the constant term converges at the usual rat... | Consistency of OLS in presence of deterministic trend | Not only is the OLS estimator consistent in the presence of a deterministic trend, it is, as they say, superconsistent, because it converges to the true value of the coefficient on the linear trend fa | Consistency of OLS in presence of deterministic trend
Not only is the OLS estimator consistent in the presence of a deterministic trend, it is, as they say, superconsistent, because it converges to the true value of the coefficient on the linear trend faster then the usual $O(T^{-1/2})$ rate -at $O(T^{-3/2})$. The esti... | Consistency of OLS in presence of deterministic trend
Not only is the OLS estimator consistent in the presence of a deterministic trend, it is, as they say, superconsistent, because it converges to the true value of the coefficient on the linear trend fa |
47,343 | Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points (quantiles) | Solution
The transformation
$$(p, x) \to (p, (x-L)/(U-L))$$
converts these points to ones on CDFs for a Beta$(\alpha,\beta)$ distribution. Assuming this has been done (so we don't need to change the notation), the problem is to find $\alpha$ and $\beta$ for which
$$F(\alpha, \beta; x_i) = p_i, i = 1, 2$$
where the Bet... | Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points (quantiles) | Solution
The transformation
$$(p, x) \to (p, (x-L)/(U-L))$$
converts these points to ones on CDFs for a Beta$(\alpha,\beta)$ distribution. Assuming this has been done (so we don't need to change the | Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points (quantiles)
Solution
The transformation
$$(p, x) \to (p, (x-L)/(U-L))$$
converts these points to ones on CDFs for a Beta$(\alpha,\beta)$ distribution. Assuming this has been done (so we don't need to change the notation), the probl... | Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points (quantiles)
Solution
The transformation
$$(p, x) \to (p, (x-L)/(U-L))$$
converts these points to ones on CDFs for a Beta$(\alpha,\beta)$ distribution. Assuming this has been done (so we don't need to change the |
47,344 | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA? | As we have already discussed in the comments above, ANOVA controls family-wise type I error rate across the "family" of levels, not across the "family" of factors. For example, one-way ANOVA with 10 groups (levels) controls the error rate, as opposed to performing all 45 pairwise t-tests that obviously runs into the mu... | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA? | As we have already discussed in the comments above, ANOVA controls family-wise type I error rate across the "family" of levels, not across the "family" of factors. For example, one-way ANOVA with 10 g | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA?
As we have already discussed in the comments above, ANOVA controls family-wise type I error rate across the "family" of levels, not across the "family" of factors. For example, one-way ANOVA with 10 groups (levels) controls the error rate, as opposed to per... | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA?
As we have already discussed in the comments above, ANOVA controls family-wise type I error rate across the "family" of levels, not across the "family" of factors. For example, one-way ANOVA with 10 g |
47,345 | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA? | The ANOVA procedures can control the family wise error across the entire set of factors and interactions, but you need to do it correctly, not look at the minimum of multiple p-values. One way to see the overall F test is to run summary.lm on your result object rather than just summary then look at the bottom of the p... | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA? | The ANOVA procedures can control the family wise error across the entire set of factors and interactions, but you need to do it correctly, not look at the minimum of multiple p-values. One way to see | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA?
The ANOVA procedures can control the family wise error across the entire set of factors and interactions, but you need to do it correctly, not look at the minimum of multiple p-values. One way to see the overall F test is to run summary.lm on your result o... | Why am I getting a 10-15% type I error rate for a 2 x 2 ANOVA?
The ANOVA procedures can control the family wise error across the entire set of factors and interactions, but you need to do it correctly, not look at the minimum of multiple p-values. One way to see |
47,346 | How do betting sites update odds during a sporting match in real-time? | The collection of odds (which I will call 'the book') are set up so bookies will make a profit.
As the bets come in, those odds have to shift in response, to keep the book in profit, so a given bet placed at one time will get different odds than a bet placed at a different time.
A second factor: if bookies offer odds ... | How do betting sites update odds during a sporting match in real-time? | The collection of odds (which I will call 'the book') are set up so bookies will make a profit.
As the bets come in, those odds have to shift in response, to keep the book in profit, so a given bet pl | How do betting sites update odds during a sporting match in real-time?
The collection of odds (which I will call 'the book') are set up so bookies will make a profit.
As the bets come in, those odds have to shift in response, to keep the book in profit, so a given bet placed at one time will get different odds than a b... | How do betting sites update odds during a sporting match in real-time?
The collection of odds (which I will call 'the book') are set up so bookies will make a profit.
As the bets come in, those odds have to shift in response, to keep the book in profit, so a given bet pl |
47,347 | How to calculate standard error of sample quantile from normal distribution with known mean and standard deviation? | This at least gives some pointers for - and a partial answer to - this question.
In the case of sample quantiles, the standard error depends on which definition of sample quantiles you actually use. I believe R, for example, includes 9 different definitions of quantiles in its quantile function.
For cases where the sam... | How to calculate standard error of sample quantile from normal distribution with known mean and stan | This at least gives some pointers for - and a partial answer to - this question.
In the case of sample quantiles, the standard error depends on which definition of sample quantiles you actually use. I | How to calculate standard error of sample quantile from normal distribution with known mean and standard deviation?
This at least gives some pointers for - and a partial answer to - this question.
In the case of sample quantiles, the standard error depends on which definition of sample quantiles you actually use. I bel... | How to calculate standard error of sample quantile from normal distribution with known mean and stan
This at least gives some pointers for - and a partial answer to - this question.
In the case of sample quantiles, the standard error depends on which definition of sample quantiles you actually use. I |
47,348 | How to calculate standard error of sample quantile from normal distribution with known mean and standard deviation? | I encountered the problem of computing the standard error for sample quantiles of a normal distribution while attending a course of Quantitative Finance during my MSc. The main topic related to this problem regarded the analysis of Value at Risk.
This is the closed form solution:
$$
s.e.\left( \widehat{z}_{\alpha}\righ... | How to calculate standard error of sample quantile from normal distribution with known mean and stan | I encountered the problem of computing the standard error for sample quantiles of a normal distribution while attending a course of Quantitative Finance during my MSc. The main topic related to this p | How to calculate standard error of sample quantile from normal distribution with known mean and standard deviation?
I encountered the problem of computing the standard error for sample quantiles of a normal distribution while attending a course of Quantitative Finance during my MSc. The main topic related to this probl... | How to calculate standard error of sample quantile from normal distribution with known mean and stan
I encountered the problem of computing the standard error for sample quantiles of a normal distribution while attending a course of Quantitative Finance during my MSc. The main topic related to this p |
47,349 | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean? | The interpretation of the comma depends on context. In the case
$$A \perp B, C$$
which is a statement about (un-)conditional dependencies, it means "$A$ is independent of the combined set of events $B \cup C$".
In the case,
$$P(A = a, B = b)$$
which is about specific events, it means "the probability of both $a$ and $b... | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean? | The interpretation of the comma depends on context. In the case
$$A \perp B, C$$
which is a statement about (un-)conditional dependencies, it means "$A$ is independent of the combined set of events $B | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?
The interpretation of the comma depends on context. In the case
$$A \perp B, C$$
which is a statement about (un-)conditional dependencies, it means "$A$ is independent of the combined set of events $B \cup C$".
In the case,
$$P(A =... | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?
The interpretation of the comma depends on context. In the case
$$A \perp B, C$$
which is a statement about (un-)conditional dependencies, it means "$A$ is independent of the combined set of events $B |
47,350 | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean? | The puzzling equation appears to be
$$(A \perp_{\sigma} (B \cup D) \mid C) \implies (A \perp_{\sigma} B \mid C) \text{ and } (A \perp_{\sigma} D \mid C)$$
Try to write the left-hand side as an intersection (an "and")
$$(A \perp_{\sigma} (B \cap D) \mid C) \implies (A \perp_{\sigma} B \mid C) \text{ and } (A \perp_{\sig... | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean? | The puzzling equation appears to be
$$(A \perp_{\sigma} (B \cup D) \mid C) \implies (A \perp_{\sigma} B \mid C) \text{ and } (A \perp_{\sigma} D \mid C)$$
Try to write the left-hand side as an interse | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?
The puzzling equation appears to be
$$(A \perp_{\sigma} (B \cup D) \mid C) \implies (A \perp_{\sigma} B \mid C) \text{ and } (A \perp_{\sigma} D \mid C)$$
Try to write the left-hand side as an intersection (an "and")
$$(A \perp_{\s... | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?
The puzzling equation appears to be
$$(A \perp_{\sigma} (B \cup D) \mid C) \implies (A \perp_{\sigma} B \mid C) \text{ and } (A \perp_{\sigma} D \mid C)$$
Try to write the left-hand side as an interse |
47,351 | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean? | In Koller's book(2009), the two cases in your question are weak union and decomposition respectively.
The proof of the decomposition is given on the book(page 25) using the reasoning by cases, and it seems very clear that the comma represents "AND".
For the weak union property, here is my proof. Hope it may be of an... | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean? | In Koller's book(2009), the two cases in your question are weak union and decomposition respectively.
The proof of the decomposition is given on the book(page 25) using the reasoning by cases, and it | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?
In Koller's book(2009), the two cases in your question are weak union and decomposition respectively.
The proof of the decomposition is given on the book(page 25) using the reasoning by cases, and it seems very clear that the comm... | What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?
In Koller's book(2009), the two cases in your question are weak union and decomposition respectively.
The proof of the decomposition is given on the book(page 25) using the reasoning by cases, and it |
47,352 | Reference for dimension reduction techniques | Here's a good paper comparing various dimension reduction techniques to PCA:
http://www.iai.uni-bonn.de/~jz/dimensionality_reduction_a_comparative_review.pdf
In brief, the paper covers the following techniques, though there are many more:
(1) multidimensional scaling, (2) Isomap, (3) Maximum Variance Unfolding,
(4)... | Reference for dimension reduction techniques | Here's a good paper comparing various dimension reduction techniques to PCA:
http://www.iai.uni-bonn.de/~jz/dimensionality_reduction_a_comparative_review.pdf
In brief, the paper covers the following | Reference for dimension reduction techniques
Here's a good paper comparing various dimension reduction techniques to PCA:
http://www.iai.uni-bonn.de/~jz/dimensionality_reduction_a_comparative_review.pdf
In brief, the paper covers the following techniques, though there are many more:
(1) multidimensional scaling, (2) ... | Reference for dimension reduction techniques
Here's a good paper comparing various dimension reduction techniques to PCA:
http://www.iai.uni-bonn.de/~jz/dimensionality_reduction_a_comparative_review.pdf
In brief, the paper covers the following |
47,353 | How to normalize time series? | Normalization isn't always necessary. We use it with certain methods (such as Principal Component Analysis) because otherwise, the values that have a larger scale will be given an increased weight. Here's a discussion of why normalization is necessary within the PCA context -- the same basic argument applies to other t... | How to normalize time series? | Normalization isn't always necessary. We use it with certain methods (such as Principal Component Analysis) because otherwise, the values that have a larger scale will be given an increased weight. He | How to normalize time series?
Normalization isn't always necessary. We use it with certain methods (such as Principal Component Analysis) because otherwise, the values that have a larger scale will be given an increased weight. Here's a discussion of why normalization is necessary within the PCA context -- the same bas... | How to normalize time series?
Normalization isn't always necessary. We use it with certain methods (such as Principal Component Analysis) because otherwise, the values that have a larger scale will be given an increased weight. He |
47,354 | wilson's adjustment for sample proportion | To my understanding the Wilson estimate is the center of the Wilson interval, which gives
the estimate
$$\tilde{p}=\frac{\hat p + \frac{1}{2n} z^2}{1 + \frac{1}{n} z^2}=\frac{X+ \frac{1}{2} z^2}{n + z^2}\,.$$
It is also the center of the Agresti-Coull interval.
If you take $\,\alpha=0.05\ $ and round 1.96 to 2, that ... | wilson's adjustment for sample proportion | To my understanding the Wilson estimate is the center of the Wilson interval, which gives
the estimate
$$\tilde{p}=\frac{\hat p + \frac{1}{2n} z^2}{1 + \frac{1}{n} z^2}=\frac{X+ \frac{1}{2} z^2}{n + | wilson's adjustment for sample proportion
To my understanding the Wilson estimate is the center of the Wilson interval, which gives
the estimate
$$\tilde{p}=\frac{\hat p + \frac{1}{2n} z^2}{1 + \frac{1}{n} z^2}=\frac{X+ \frac{1}{2} z^2}{n + z^2}\,.$$
It is also the center of the Agresti-Coull interval.
If you take $\... | wilson's adjustment for sample proportion
To my understanding the Wilson estimate is the center of the Wilson interval, which gives
the estimate
$$\tilde{p}=\frac{\hat p + \frac{1}{2n} z^2}{1 + \frac{1}{n} z^2}=\frac{X+ \frac{1}{2} z^2}{n + |
47,355 | Comparison of two means | The problem is that the subset is correlated with the whole.
This makes them dependent. Normally the right thing to do is compare two distinct sets - the subset with what's not in the subset.
Logically, the comparison of the whole with the subset is identical to comparing the subsets --
If they behave alike, then the... | Comparison of two means | The problem is that the subset is correlated with the whole.
This makes them dependent. Normally the right thing to do is compare two distinct sets - the subset with what's not in the subset.
Logica | Comparison of two means
The problem is that the subset is correlated with the whole.
This makes them dependent. Normally the right thing to do is compare two distinct sets - the subset with what's not in the subset.
Logically, the comparison of the whole with the subset is identical to comparing the subsets --
If the... | Comparison of two means
The problem is that the subset is correlated with the whole.
This makes them dependent. Normally the right thing to do is compare two distinct sets - the subset with what's not in the subset.
Logica |
47,356 | ABC: Why not use the distance measure as a pseudo-likelihood instead? | This idea has in been implemented in several papers. Richard Wilkinson's SAGMB paper of 2013 explores the topic in some detail and makes precise the link to assuming a measurement error model.
It turns out to be useful to introduce a parameter $\epsilon$ to the weight function which corresponds to the scale of measure... | ABC: Why not use the distance measure as a pseudo-likelihood instead? | This idea has in been implemented in several papers. Richard Wilkinson's SAGMB paper of 2013 explores the topic in some detail and makes precise the link to assuming a measurement error model.
It tur | ABC: Why not use the distance measure as a pseudo-likelihood instead?
This idea has in been implemented in several papers. Richard Wilkinson's SAGMB paper of 2013 explores the topic in some detail and makes precise the link to assuming a measurement error model.
It turns out to be useful to introduce a parameter $\eps... | ABC: Why not use the distance measure as a pseudo-likelihood instead?
This idea has in been implemented in several papers. Richard Wilkinson's SAGMB paper of 2013 explores the topic in some detail and makes precise the link to assuming a measurement error model.
It tur |
47,357 | ABC: Why not use the distance measure as a pseudo-likelihood instead? | I think that modelling the distribution of the summary statistics is preferable to thresholding, as long as you are able to find a good candidate distribution. For example here the author uses a multivariate normal approximation, which is justified by the asymptotic normality of the statistics. The same method, Synthet... | ABC: Why not use the distance measure as a pseudo-likelihood instead? | I think that modelling the distribution of the summary statistics is preferable to thresholding, as long as you are able to find a good candidate distribution. For example here the author uses a multi | ABC: Why not use the distance measure as a pseudo-likelihood instead?
I think that modelling the distribution of the summary statistics is preferable to thresholding, as long as you are able to find a good candidate distribution. For example here the author uses a multivariate normal approximation, which is justified b... | ABC: Why not use the distance measure as a pseudo-likelihood instead?
I think that modelling the distribution of the summary statistics is preferable to thresholding, as long as you are able to find a good candidate distribution. For example here the author uses a multi |
47,358 | When the confidence interval of an odds ratio includes one, can the p-value be less than 0.05? | If the confidence interval and the test are not quite based on the same calculation (in at least the somewhat loose sense that they give the same partial order to the sample space), then in some cases the two won't exactly correspond.
There are a number of cases where the usual interval and test are based on different... | When the confidence interval of an odds ratio includes one, can the p-value be less than 0.05? | If the confidence interval and the test are not quite based on the same calculation (in at least the somewhat loose sense that they give the same partial order to the sample space), then in some cases | When the confidence interval of an odds ratio includes one, can the p-value be less than 0.05?
If the confidence interval and the test are not quite based on the same calculation (in at least the somewhat loose sense that they give the same partial order to the sample space), then in some cases the two won't exactly co... | When the confidence interval of an odds ratio includes one, can the p-value be less than 0.05?
If the confidence interval and the test are not quite based on the same calculation (in at least the somewhat loose sense that they give the same partial order to the sample space), then in some cases |
47,359 | Forecasting a time series with weights | This is an issue with lm.
wrapper = function(formula,...)
lm(formula=formula,...)
x=(1:27)
wrapper(ts.input~x,weights=ts.weights)
produces the exact same error. If you read the source code to tslm, you'll find that lm is called in more or less the sam way.
I found here that ..1 means the first argument included in .... | Forecasting a time series with weights | This is an issue with lm.
wrapper = function(formula,...)
lm(formula=formula,...)
x=(1:27)
wrapper(ts.input~x,weights=ts.weights)
produces the exact same error. If you read the source code to tslm, | Forecasting a time series with weights
This is an issue with lm.
wrapper = function(formula,...)
lm(formula=formula,...)
x=(1:27)
wrapper(ts.input~x,weights=ts.weights)
produces the exact same error. If you read the source code to tslm, you'll find that lm is called in more or less the sam way.
I found here that ..1... | Forecasting a time series with weights
This is an issue with lm.
wrapper = function(formula,...)
lm(formula=formula,...)
x=(1:27)
wrapper(ts.input~x,weights=ts.weights)
produces the exact same error. If you read the source code to tslm, |
47,360 | The efficiency of Decision Tree | I will share my experience on implementing those kind of decision trees. There are some ideas which I found also in R, Weka, Python implementations. In order to keep things simple, I will suppose you talk about CART-like trees, but the things I explain could be extended trivially to any kind of decision tree.
You do n... | The efficiency of Decision Tree | I will share my experience on implementing those kind of decision trees. There are some ideas which I found also in R, Weka, Python implementations. In order to keep things simple, I will suppose you | The efficiency of Decision Tree
I will share my experience on implementing those kind of decision trees. There are some ideas which I found also in R, Weka, Python implementations. In order to keep things simple, I will suppose you talk about CART-like trees, but the things I explain could be extended trivially to any ... | The efficiency of Decision Tree
I will share my experience on implementing those kind of decision trees. There are some ideas which I found also in R, Weka, Python implementations. In order to keep things simple, I will suppose you |
47,361 | Testing significance of a random effect glmmADMB model | Because glmmADMB (unlike lme4) can handle models without any random effects in the same framework, and thus get commensurate log-likelihood, you should be able to do this:
g1 <- glmmadmb(formula = Score ~ Sex * Age + Object + (1 | ID),
data = PGS, family = "nbinom1")
g2 <- glmmadmb(formula = Score ~ Sex * Age + Obje... | Testing significance of a random effect glmmADMB model | Because glmmADMB (unlike lme4) can handle models without any random effects in the same framework, and thus get commensurate log-likelihood, you should be able to do this:
g1 <- glmmadmb(formula = Sco | Testing significance of a random effect glmmADMB model
Because glmmADMB (unlike lme4) can handle models without any random effects in the same framework, and thus get commensurate log-likelihood, you should be able to do this:
g1 <- glmmadmb(formula = Score ~ Sex * Age + Object + (1 | ID),
data = PGS, family = "nbin... | Testing significance of a random effect glmmADMB model
Because glmmADMB (unlike lme4) can handle models without any random effects in the same framework, and thus get commensurate log-likelihood, you should be able to do this:
g1 <- glmmadmb(formula = Sco |
47,362 | What is the difference between (universal) kriging and spatial autoregressive models? | Short answers:
1) As you said the difference between the two is only in the spatial structure.
2) A lot of people work to find an equivalent mathematical formulation between the two, especially in the Bayesian framework. See for example the work of Rue of the paper of Lindgren http://www.math.ntnu.no/inla/r-inla.org/p... | What is the difference between (universal) kriging and spatial autoregressive models? | Short answers:
1) As you said the difference between the two is only in the spatial structure.
2) A lot of people work to find an equivalent mathematical formulation between the two, especially in th | What is the difference between (universal) kriging and spatial autoregressive models?
Short answers:
1) As you said the difference between the two is only in the spatial structure.
2) A lot of people work to find an equivalent mathematical formulation between the two, especially in the Bayesian framework. See for exam... | What is the difference between (universal) kriging and spatial autoregressive models?
Short answers:
1) As you said the difference between the two is only in the spatial structure.
2) A lot of people work to find an equivalent mathematical formulation between the two, especially in th |
47,363 | Explanation of a censored regression model | By default, the estimated standard deviation of the residuals ($\sigma$) is returned as $\ln(\sigma)$ since that is how the Tobit log likelihood maximization is performed. If you use coef(estResult,logSigma = FALSE), you will get $\sigma$ instead, which is analogous to the square root of the residual variance in OLS re... | Explanation of a censored regression model | By default, the estimated standard deviation of the residuals ($\sigma$) is returned as $\ln(\sigma)$ since that is how the Tobit log likelihood maximization is performed. If you use coef(estResult,lo | Explanation of a censored regression model
By default, the estimated standard deviation of the residuals ($\sigma$) is returned as $\ln(\sigma)$ since that is how the Tobit log likelihood maximization is performed. If you use coef(estResult,logSigma = FALSE), you will get $\sigma$ instead, which is analogous to the squ... | Explanation of a censored regression model
By default, the estimated standard deviation of the residuals ($\sigma$) is returned as $\ln(\sigma)$ since that is how the Tobit log likelihood maximization is performed. If you use coef(estResult,lo |
47,364 | Wald test and Likelihood ratio test, where do the confidence intervals on the regression coefficients come from? | When you fit a logistic regression model, there is no closed form solution for the parameter estimates unlike in linear regression. So instead, you search over the parameter space for a set of parameter estimates that maximize the log likelihood or minimize the deviance. (I usually prefer to think in terms of the dev... | Wald test and Likelihood ratio test, where do the confidence intervals on the regression coefficient | When you fit a logistic regression model, there is no closed form solution for the parameter estimates unlike in linear regression. So instead, you search over the parameter space for a set of parame | Wald test and Likelihood ratio test, where do the confidence intervals on the regression coefficients come from?
When you fit a logistic regression model, there is no closed form solution for the parameter estimates unlike in linear regression. So instead, you search over the parameter space for a set of parameter est... | Wald test and Likelihood ratio test, where do the confidence intervals on the regression coefficient
When you fit a logistic regression model, there is no closed form solution for the parameter estimates unlike in linear regression. So instead, you search over the parameter space for a set of parame |
47,365 | Loss function for linear regression with calculus of variations | I am assuming your difficulty is in the jump between Eq.2 and Eq.3. All you need is an Euler-Lagrange equation, as in their equation (3). In their notation $f(x,y,\dot y)=\int \{y(x)-t\}^2p(x,t)dx$, so that $df/d\dot{y}=0$, for instance.
UPDATE:
answering comments to make a more verbose explanation.
The Eq. (2) can be ... | Loss function for linear regression with calculus of variations | I am assuming your difficulty is in the jump between Eq.2 and Eq.3. All you need is an Euler-Lagrange equation, as in their equation (3). In their notation $f(x,y,\dot y)=\int \{y(x)-t\}^2p(x,t)dx$, s | Loss function for linear regression with calculus of variations
I am assuming your difficulty is in the jump between Eq.2 and Eq.3. All you need is an Euler-Lagrange equation, as in their equation (3). In their notation $f(x,y,\dot y)=\int \{y(x)-t\}^2p(x,t)dx$, so that $df/d\dot{y}=0$, for instance.
UPDATE:
answering ... | Loss function for linear regression with calculus of variations
I am assuming your difficulty is in the jump between Eq.2 and Eq.3. All you need is an Euler-Lagrange equation, as in their equation (3). In their notation $f(x,y,\dot y)=\int \{y(x)-t\}^2p(x,t)dx$, s |
47,366 | Loss function for linear regression with calculus of variations | I don't think you need calculus of variations. First, define the loss for every fixed $\bf x$,
$$\mathbb{E}[L | {\bf x}] = \int \{ y (\mathbf{x}) - t \}^{2} p (t | \mathbf{x}) \, dt.
\tag{2*}$$
and the minimizer of that is $y (\mathbf{x}) = \mathbb{E}_{t} [t | \mathbf{x}]$
and then just
$$\mathbb{E}[L] = \int \mathb... | Loss function for linear regression with calculus of variations | I don't think you need calculus of variations. First, define the loss for every fixed $\bf x$,
$$\mathbb{E}[L | {\bf x}] = \int \{ y (\mathbf{x}) - t \}^{2} p (t | \mathbf{x}) \, dt.
\tag{2*}$$
and | Loss function for linear regression with calculus of variations
I don't think you need calculus of variations. First, define the loss for every fixed $\bf x$,
$$\mathbb{E}[L | {\bf x}] = \int \{ y (\mathbf{x}) - t \}^{2} p (t | \mathbf{x}) \, dt.
\tag{2*}$$
and the minimizer of that is $y (\mathbf{x}) = \mathbb{E}_{t... | Loss function for linear regression with calculus of variations
I don't think you need calculus of variations. First, define the loss for every fixed $\bf x$,
$$\mathbb{E}[L | {\bf x}] = \int \{ y (\mathbf{x}) - t \}^{2} p (t | \mathbf{x}) \, dt.
\tag{2*}$$
and |
47,367 | Stepwise regression in R with both direction | The underlying procedure is beautifully documented in Chambers & Hastie (eds, 1992; Ch. 6) (contrary to what the help page says) on page 237.
stats::step() with the option direction = 'both' works by comparing the AIC improvements from
dropping each candidate variable, and adding each candidate variable between the up... | Stepwise regression in R with both direction | The underlying procedure is beautifully documented in Chambers & Hastie (eds, 1992; Ch. 6) (contrary to what the help page says) on page 237.
stats::step() with the option direction = 'both' works by | Stepwise regression in R with both direction
The underlying procedure is beautifully documented in Chambers & Hastie (eds, 1992; Ch. 6) (contrary to what the help page says) on page 237.
stats::step() with the option direction = 'both' works by comparing the AIC improvements from
dropping each candidate variable, and ... | Stepwise regression in R with both direction
The underlying procedure is beautifully documented in Chambers & Hastie (eds, 1992; Ch. 6) (contrary to what the help page says) on page 237.
stats::step() with the option direction = 'both' works by |
47,368 | When is a ARMA(p,q) process ergodic? | It is sufficient for any stationary process that the autocovariances are absolute summable, i.e. that $\sum_{j=0}^\infty |\gamma_j|<\infty$. You can find this in Hamilton's Time Series Analysis. | When is a ARMA(p,q) process ergodic? | It is sufficient for any stationary process that the autocovariances are absolute summable, i.e. that $\sum_{j=0}^\infty |\gamma_j|<\infty$. You can find this in Hamilton's Time Series Analysis. | When is a ARMA(p,q) process ergodic?
It is sufficient for any stationary process that the autocovariances are absolute summable, i.e. that $\sum_{j=0}^\infty |\gamma_j|<\infty$. You can find this in Hamilton's Time Series Analysis. | When is a ARMA(p,q) process ergodic?
It is sufficient for any stationary process that the autocovariances are absolute summable, i.e. that $\sum_{j=0}^\infty |\gamma_j|<\infty$. You can find this in Hamilton's Time Series Analysis. |
47,369 | Find the probability of an event determined by an inequality on exponential random variables | The probability density function of an Exponential($\lambda$) variate is, as shown in the question, given by
$$f_\lambda(x) = \lambda\exp(-\lambda x),\ x\ge 0.$$
($f$ is zero for $x\lt 0$.)
The independence assumption says the probability densities of $X$ and $Y$ multiply to give the joint probability density as
$$f_{X... | Find the probability of an event determined by an inequality on exponential random variables | The probability density function of an Exponential($\lambda$) variate is, as shown in the question, given by
$$f_\lambda(x) = \lambda\exp(-\lambda x),\ x\ge 0.$$
($f$ is zero for $x\lt 0$.)
The indepe | Find the probability of an event determined by an inequality on exponential random variables
The probability density function of an Exponential($\lambda$) variate is, as shown in the question, given by
$$f_\lambda(x) = \lambda\exp(-\lambda x),\ x\ge 0.$$
($f$ is zero for $x\lt 0$.)
The independence assumption says the ... | Find the probability of an event determined by an inequality on exponential random variables
The probability density function of an Exponential($\lambda$) variate is, as shown in the question, given by
$$f_\lambda(x) = \lambda\exp(-\lambda x),\ x\ge 0.$$
($f$ is zero for $x\lt 0$.)
The indepe |
47,370 | Find the probability of an event determined by an inequality on exponential random variables | Check the distribution function of the generalized integer gamma distribution.
http://en.wikipedia.org/wiki/Generalized_integer_gamma_distribution
(Edit) Also, and answering your question better, check theorem 1 from here http://ac.els-cdn.com/S0047259X97917103/1-s2.0-S0047259X97917103-main.pdf?_tid=8558a38e-cfe5-11e3-... | Find the probability of an event determined by an inequality on exponential random variables | Check the distribution function of the generalized integer gamma distribution.
http://en.wikipedia.org/wiki/Generalized_integer_gamma_distribution
(Edit) Also, and answering your question better, chec | Find the probability of an event determined by an inequality on exponential random variables
Check the distribution function of the generalized integer gamma distribution.
http://en.wikipedia.org/wiki/Generalized_integer_gamma_distribution
(Edit) Also, and answering your question better, check theorem 1 from here http:... | Find the probability of an event determined by an inequality on exponential random variables
Check the distribution function of the generalized integer gamma distribution.
http://en.wikipedia.org/wiki/Generalized_integer_gamma_distribution
(Edit) Also, and answering your question better, chec |
47,371 | Nested ANOVA: Unequal sample sizes? Variance components? | Hopefully your friend has graduated by now, but if not, the following might help.
You were on the right track in your original post Partitioning variance from logistic regression, using glmer() for mixed-effects logistic regression.
I would recommend against: the advisor's "solution", using lm() for logistic regression... | Nested ANOVA: Unequal sample sizes? Variance components? | Hopefully your friend has graduated by now, but if not, the following might help.
You were on the right track in your original post Partitioning variance from logistic regression, using glmer() for mi | Nested ANOVA: Unequal sample sizes? Variance components?
Hopefully your friend has graduated by now, but if not, the following might help.
You were on the right track in your original post Partitioning variance from logistic regression, using glmer() for mixed-effects logistic regression.
I would recommend against: the... | Nested ANOVA: Unequal sample sizes? Variance components?
Hopefully your friend has graduated by now, but if not, the following might help.
You were on the right track in your original post Partitioning variance from logistic regression, using glmer() for mi |
47,372 | Hypothesis testing on Poisson Binomial distribution | You can just use the number of successes itself as the test statistic.
If you want a one-tailed test this is simple (and I expect you will). For a two tailed test, because of the asymmetry, the usual approach would be to allocate $\alpha/2$ to each tail and compute a rejection region that way. There's some variation i... | Hypothesis testing on Poisson Binomial distribution | You can just use the number of successes itself as the test statistic.
If you want a one-tailed test this is simple (and I expect you will). For a two tailed test, because of the asymmetry, the usual | Hypothesis testing on Poisson Binomial distribution
You can just use the number of successes itself as the test statistic.
If you want a one-tailed test this is simple (and I expect you will). For a two tailed test, because of the asymmetry, the usual approach would be to allocate $\alpha/2$ to each tail and compute a... | Hypothesis testing on Poisson Binomial distribution
You can just use the number of successes itself as the test statistic.
If you want a one-tailed test this is simple (and I expect you will). For a two tailed test, because of the asymmetry, the usual |
47,373 | Is it better to use data imputation for missing data or an analysis that is not affected by missing data (e.g., HLM/mixed effects modelling)? | I would hands down use mixed-effects modeling. First, I am not aware of an easy way to pool multiple-degree-of-freedom effects (as in ANOVA with a factor with more than two levels). Also, multiple imputation and full-information maximum likelihood estimation (the latter being what mixed-effects models use) make the sam... | Is it better to use data imputation for missing data or an analysis that is not affected by missing | I would hands down use mixed-effects modeling. First, I am not aware of an easy way to pool multiple-degree-of-freedom effects (as in ANOVA with a factor with more than two levels). Also, multiple imp | Is it better to use data imputation for missing data or an analysis that is not affected by missing data (e.g., HLM/mixed effects modelling)?
I would hands down use mixed-effects modeling. First, I am not aware of an easy way to pool multiple-degree-of-freedom effects (as in ANOVA with a factor with more than two level... | Is it better to use data imputation for missing data or an analysis that is not affected by missing
I would hands down use mixed-effects modeling. First, I am not aware of an easy way to pool multiple-degree-of-freedom effects (as in ANOVA with a factor with more than two levels). Also, multiple imp |
47,374 | How important it is to have an intuition of why various statistical tests work? | Broadly speaking, the more you understand a test (or indeed any other aspect of the vrious calculations one does in statistics), the better, but it's not usually necessary to understand every specific detail of each constant in a formula to have a good understanding of what's going on.
For example, sometimes (particul... | How important it is to have an intuition of why various statistical tests work? | Broadly speaking, the more you understand a test (or indeed any other aspect of the vrious calculations one does in statistics), the better, but it's not usually necessary to understand every specifi | How important it is to have an intuition of why various statistical tests work?
Broadly speaking, the more you understand a test (or indeed any other aspect of the vrious calculations one does in statistics), the better, but it's not usually necessary to understand every specific detail of each constant in a formula t... | How important it is to have an intuition of why various statistical tests work?
Broadly speaking, the more you understand a test (or indeed any other aspect of the vrious calculations one does in statistics), the better, but it's not usually necessary to understand every specifi |
47,375 | How important it is to have an intuition of why various statistical tests work? | It's never bad to understand more details of what is going on, but I think there is an intermediate ground. E.g. take the formula for the pdf normal density
$
\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}
$
Do you need to know how this was derived and why each part of it is the way it is in order t... | How important it is to have an intuition of why various statistical tests work? | It's never bad to understand more details of what is going on, but I think there is an intermediate ground. E.g. take the formula for the pdf normal density
$
\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{ | How important it is to have an intuition of why various statistical tests work?
It's never bad to understand more details of what is going on, but I think there is an intermediate ground. E.g. take the formula for the pdf normal density
$
\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}
$
Do you need ... | How important it is to have an intuition of why various statistical tests work?
It's never bad to understand more details of what is going on, but I think there is an intermediate ground. E.g. take the formula for the pdf normal density
$
\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{ |
47,376 | F-values in ANOVA table | For age, $F=1.0812=\frac{MS_\text{age}}{MS_\text{Residuals}}$. The same is true of the other $F$ values replacing age with weight or protein. This partials out the variance in carb that is related to the other two factors not being tested directly by the $F$ test in question, whereas using $MS_\text{Residuals}$ from a ... | F-values in ANOVA table | For age, $F=1.0812=\frac{MS_\text{age}}{MS_\text{Residuals}}$. The same is true of the other $F$ values replacing age with weight or protein. This partials out the variance in carb that is related to | F-values in ANOVA table
For age, $F=1.0812=\frac{MS_\text{age}}{MS_\text{Residuals}}$. The same is true of the other $F$ values replacing age with weight or protein. This partials out the variance in carb that is related to the other two factors not being tested directly by the $F$ test in question, whereas using $MS_\... | F-values in ANOVA table
For age, $F=1.0812=\frac{MS_\text{age}}{MS_\text{Residuals}}$. The same is true of the other $F$ values replacing age with weight or protein. This partials out the variance in carb that is related to |
47,377 | F-values in ANOVA table | The anova function in R, when given only 1 model, produces the "Sequential" sums of squares. This means that each term is adjusted for those above it (to the left in the model formula) and don't include those below (to the right). So in your example you are testing weight vs. intercept only, protein + weight vs. weig... | F-values in ANOVA table | The anova function in R, when given only 1 model, produces the "Sequential" sums of squares. This means that each term is adjusted for those above it (to the left in the model formula) and don't incl | F-values in ANOVA table
The anova function in R, when given only 1 model, produces the "Sequential" sums of squares. This means that each term is adjusted for those above it (to the left in the model formula) and don't include those below (to the right). So in your example you are testing weight vs. intercept only, p... | F-values in ANOVA table
The anova function in R, when given only 1 model, produces the "Sequential" sums of squares. This means that each term is adjusted for those above it (to the left in the model formula) and don't incl |
47,378 | Prediction interval for my bus journey | You don't explicitly state in your question whether you're prepared to assume independence of the two times, but some things about the way you wrote your question do seem to suggest it. I'm not at all sure that is a reasonable assumption, since if traffic turns bad, the average wait and the average trip will be longer,... | Prediction interval for my bus journey | You don't explicitly state in your question whether you're prepared to assume independence of the two times, but some things about the way you wrote your question do seem to suggest it. I'm not at all | Prediction interval for my bus journey
You don't explicitly state in your question whether you're prepared to assume independence of the two times, but some things about the way you wrote your question do seem to suggest it. I'm not at all sure that is a reasonable assumption, since if traffic turns bad, the average wa... | Prediction interval for my bus journey
You don't explicitly state in your question whether you're prepared to assume independence of the two times, but some things about the way you wrote your question do seem to suggest it. I'm not at all |
47,379 | Prediction interval for my bus journey | As indicated above by Glen_b, 99.34 minutes is the 99th percentile.
Below are the density(PDF) and cumulative distribution (CDF) plots and a table of CDF values for the combined distribution. | Prediction interval for my bus journey | As indicated above by Glen_b, 99.34 minutes is the 99th percentile.
Below are the density(PDF) and cumulative distribution (CDF) plots and a table of CDF values for the combined distribution. | Prediction interval for my bus journey
As indicated above by Glen_b, 99.34 minutes is the 99th percentile.
Below are the density(PDF) and cumulative distribution (CDF) plots and a table of CDF values for the combined distribution. | Prediction interval for my bus journey
As indicated above by Glen_b, 99.34 minutes is the 99th percentile.
Below are the density(PDF) and cumulative distribution (CDF) plots and a table of CDF values for the combined distribution. |
47,380 | ABC. How can it avoid the likelihood function? | Approximate Bayesian Computation (ABC) is useful when you can simulate data, but cannot evaluate the likelihood function analytically. You seem to assume that it is necessary to know the likelihood function $l(\theta) = P[D|\theta]$ to simulate data. I'm not sure how you came to that conclusion, but there are ways to ... | ABC. How can it avoid the likelihood function? | Approximate Bayesian Computation (ABC) is useful when you can simulate data, but cannot evaluate the likelihood function analytically. You seem to assume that it is necessary to know the likelihood fu | ABC. How can it avoid the likelihood function?
Approximate Bayesian Computation (ABC) is useful when you can simulate data, but cannot evaluate the likelihood function analytically. You seem to assume that it is necessary to know the likelihood function $l(\theta) = P[D|\theta]$ to simulate data. I'm not sure how you ... | ABC. How can it avoid the likelihood function?
Approximate Bayesian Computation (ABC) is useful when you can simulate data, but cannot evaluate the likelihood function analytically. You seem to assume that it is necessary to know the likelihood fu |
47,381 | Are there any probabilistic models for graph-based recommender systems? | There is the very-well known approach based on restricted BOltzmann machines (RBM), which won the Netflix competition. For more details you may have a look at the Wikipedia site, and the references therein.
Restricted Boltzmann machines are a particular instance of Markov Random Fields, with some properties that makes ... | Are there any probabilistic models for graph-based recommender systems? | There is the very-well known approach based on restricted BOltzmann machines (RBM), which won the Netflix competition. For more details you may have a look at the Wikipedia site, and the references th | Are there any probabilistic models for graph-based recommender systems?
There is the very-well known approach based on restricted BOltzmann machines (RBM), which won the Netflix competition. For more details you may have a look at the Wikipedia site, and the references therein.
Restricted Boltzmann machines are a parti... | Are there any probabilistic models for graph-based recommender systems?
There is the very-well known approach based on restricted BOltzmann machines (RBM), which won the Netflix competition. For more details you may have a look at the Wikipedia site, and the references th |
47,382 | Are there any probabilistic models for graph-based recommender systems? | There is another good paper on this for unrestricted Boltzmann machines. You might also look at sum/max product networks.
It may be that what you really want to do is compute marginal distributions rather than a real recommendation systems. In that case consider Markov Random Fields or perhaps log-linear models. | Are there any probabilistic models for graph-based recommender systems? | There is another good paper on this for unrestricted Boltzmann machines. You might also look at sum/max product networks.
It may be that what you really want to do is compute marginal distributions r | Are there any probabilistic models for graph-based recommender systems?
There is another good paper on this for unrestricted Boltzmann machines. You might also look at sum/max product networks.
It may be that what you really want to do is compute marginal distributions rather than a real recommendation systems. In tha... | Are there any probabilistic models for graph-based recommender systems?
There is another good paper on this for unrestricted Boltzmann machines. You might also look at sum/max product networks.
It may be that what you really want to do is compute marginal distributions r |
47,383 | Does Principle of Marginality apply to interactions of categorical variables? | In the full model there are $n-1$ coefficients for the main effect of $X$, $p-1$ for the main effect of $M$, & $np -n - p +1$ for the interaction; giving a total, as you say of $np-1$. In the model with interaction only, there are just $np -n - p +1$ coefficients; so some combinations of levels of $X$ & $M$ share the s... | Does Principle of Marginality apply to interactions of categorical variables? | In the full model there are $n-1$ coefficients for the main effect of $X$, $p-1$ for the main effect of $M$, & $np -n - p +1$ for the interaction; giving a total, as you say of $np-1$. In the model wi | Does Principle of Marginality apply to interactions of categorical variables?
In the full model there are $n-1$ coefficients for the main effect of $X$, $p-1$ for the main effect of $M$, & $np -n - p +1$ for the interaction; giving a total, as you say of $np-1$. In the model with interaction only, there are just $np -n... | Does Principle of Marginality apply to interactions of categorical variables?
In the full model there are $n-1$ coefficients for the main effect of $X$, $p-1$ for the main effect of $M$, & $np -n - p +1$ for the interaction; giving a total, as you say of $np-1$. In the model wi |
47,384 | Does Principle of Marginality apply to interactions of categorical variables? | @scortchi gave you a good answer, but I thought a specific example might be useful, if not for you then for others who will see this.
Suppose your dependent variable is log(income) and your two categorical independent variables are sex (male, female, other) and race (White, Black, Asian, Native American, Hawaiian/Pacif... | Does Principle of Marginality apply to interactions of categorical variables? | @scortchi gave you a good answer, but I thought a specific example might be useful, if not for you then for others who will see this.
Suppose your dependent variable is log(income) and your two catego | Does Principle of Marginality apply to interactions of categorical variables?
@scortchi gave you a good answer, but I thought a specific example might be useful, if not for you then for others who will see this.
Suppose your dependent variable is log(income) and your two categorical independent variables are sex (male,... | Does Principle of Marginality apply to interactions of categorical variables?
@scortchi gave you a good answer, but I thought a specific example might be useful, if not for you then for others who will see this.
Suppose your dependent variable is log(income) and your two catego |
47,385 | Chi-squared test when two vectors have different lengths | I think (as mentioned in comments) that a hypothesis test doesn't really answer the question you say you're interested in. (It also lacks power if any of the factors are ordered).
The thing is, 'not so much different' relates to a question about effect size (how different are they?) not a hypothesis test ("is our sampl... | Chi-squared test when two vectors have different lengths | I think (as mentioned in comments) that a hypothesis test doesn't really answer the question you say you're interested in. (It also lacks power if any of the factors are ordered).
The thing is, 'not s | Chi-squared test when two vectors have different lengths
I think (as mentioned in comments) that a hypothesis test doesn't really answer the question you say you're interested in. (It also lacks power if any of the factors are ordered).
The thing is, 'not so much different' relates to a question about effect size (how ... | Chi-squared test when two vectors have different lengths
I think (as mentioned in comments) that a hypothesis test doesn't really answer the question you say you're interested in. (It also lacks power if any of the factors are ordered).
The thing is, 'not s |
47,386 | Why the sample mean is not a good (sufficient) statistic? | Sufficiency pertains to data reduction, not estimation per se. This is an important distinction to understand. Yes, a "good" estimator is usually a function of a sufficient statistic, but that doesn't mean that all sufficient statistics are estimators.
As for your specific example, a simple way to understand why $\ba... | Why the sample mean is not a good (sufficient) statistic? | Sufficiency pertains to data reduction, not estimation per se. This is an important distinction to understand. Yes, a "good" estimator is usually a function of a sufficient statistic, but that doesn | Why the sample mean is not a good (sufficient) statistic?
Sufficiency pertains to data reduction, not estimation per se. This is an important distinction to understand. Yes, a "good" estimator is usually a function of a sufficient statistic, but that doesn't mean that all sufficient statistics are estimators.
As for ... | Why the sample mean is not a good (sufficient) statistic?
Sufficiency pertains to data reduction, not estimation per se. This is an important distinction to understand. Yes, a "good" estimator is usually a function of a sufficient statistic, but that doesn |
47,387 | How to deal with graphing overlapping error bars without color? | You've received some good comments so far. Offsetting as Glen_b mentions is what is used in clustered bar charts, and in the grammer of graphics is referred to as dodging. Below is an example of similar data (using SPSS). Also note that I took away the handle bars at the ends, they are typically distracting and wasted ... | How to deal with graphing overlapping error bars without color? | You've received some good comments so far. Offsetting as Glen_b mentions is what is used in clustered bar charts, and in the grammer of graphics is referred to as dodging. Below is an example of simil | How to deal with graphing overlapping error bars without color?
You've received some good comments so far. Offsetting as Glen_b mentions is what is used in clustered bar charts, and in the grammer of graphics is referred to as dodging. Below is an example of similar data (using SPSS). Also note that I took away the han... | How to deal with graphing overlapping error bars without color?
You've received some good comments so far. Offsetting as Glen_b mentions is what is used in clustered bar charts, and in the grammer of graphics is referred to as dodging. Below is an example of simil |
47,388 | Definition of likelihood ratio test | You're right in the context of "submodel" testing, the likelihood ratio statistic is the ratio of the maximum likelihoods (not the maximum likelihood estimates: the maximal values of the likelihoods).
Consider a statistical model with likelihood $l(\theta \mid y)$ where $y$ is the vector of observations generated from... | Definition of likelihood ratio test | You're right in the context of "submodel" testing, the likelihood ratio statistic is the ratio of the maximum likelihoods (not the maximum likelihood estimates: the maximal values of the likelihoods). | Definition of likelihood ratio test
You're right in the context of "submodel" testing, the likelihood ratio statistic is the ratio of the maximum likelihoods (not the maximum likelihood estimates: the maximal values of the likelihoods).
Consider a statistical model with likelihood $l(\theta \mid y)$ where $y$ is the v... | Definition of likelihood ratio test
You're right in the context of "submodel" testing, the likelihood ratio statistic is the ratio of the maximum likelihoods (not the maximum likelihood estimates: the maximal values of the likelihoods). |
47,389 | Definition of likelihood ratio test | The distinction between the likelihood ratio for completely specified probability mass or density functions (simple hypotheses) & the likelihood ratio for incompletely specified ones (composite hypotheses) is sometimes expressed by calling the latter a generalized likelihood ratio. So your quote could be giving a preci... | Definition of likelihood ratio test | The distinction between the likelihood ratio for completely specified probability mass or density functions (simple hypotheses) & the likelihood ratio for incompletely specified ones (composite hypoth | Definition of likelihood ratio test
The distinction between the likelihood ratio for completely specified probability mass or density functions (simple hypotheses) & the likelihood ratio for incompletely specified ones (composite hypotheses) is sometimes expressed by calling the latter a generalized likelihood ratio. S... | Definition of likelihood ratio test
The distinction between the likelihood ratio for completely specified probability mass or density functions (simple hypotheses) & the likelihood ratio for incompletely specified ones (composite hypoth |
47,390 | Is there a branch of statistics that tries to explain "why" the dataset has certain statistical properties? | I am not sure if there is a pithy title for this entire topic but it is certainly an important issue. Maybe "robust statistics" would be a good place to start?
The aptly-named empirical influence function describes how an estimator (e.g., the mean or median) depends on the value of one of the points in its sample. It c... | Is there a branch of statistics that tries to explain "why" the dataset has certain statistical prop | I am not sure if there is a pithy title for this entire topic but it is certainly an important issue. Maybe "robust statistics" would be a good place to start?
The aptly-named empirical influence func | Is there a branch of statistics that tries to explain "why" the dataset has certain statistical properties?
I am not sure if there is a pithy title for this entire topic but it is certainly an important issue. Maybe "robust statistics" would be a good place to start?
The aptly-named empirical influence function describ... | Is there a branch of statistics that tries to explain "why" the dataset has certain statistical prop
I am not sure if there is a pithy title for this entire topic but it is certainly an important issue. Maybe "robust statistics" would be a good place to start?
The aptly-named empirical influence func |
47,391 | Reformulation of OLS estimators in a simple Regression with a dummy variable | The theoretical model is
$$E(Y\mid X)=\alpha +\beta X$$
Assuming that $X$ is a $0/1$ binary variable we notice that
$$E(Y\mid X=1) - E(Y\mid X=0)=\alpha +\beta -\alpha = \beta $$
I think that the OP asks "does the OLS estimator "mimics" this relationship, being perhaps its sample analogue?"
Let's see: we have that
$$... | Reformulation of OLS estimators in a simple Regression with a dummy variable | The theoretical model is
$$E(Y\mid X)=\alpha +\beta X$$
Assuming that $X$ is a $0/1$ binary variable we notice that
$$E(Y\mid X=1) - E(Y\mid X=0)=\alpha +\beta -\alpha = \beta $$
I think that the OP | Reformulation of OLS estimators in a simple Regression with a dummy variable
The theoretical model is
$$E(Y\mid X)=\alpha +\beta X$$
Assuming that $X$ is a $0/1$ binary variable we notice that
$$E(Y\mid X=1) - E(Y\mid X=0)=\alpha +\beta -\alpha = \beta $$
I think that the OP asks "does the OLS estimator "mimics" this ... | Reformulation of OLS estimators in a simple Regression with a dummy variable
The theoretical model is
$$E(Y\mid X)=\alpha +\beta X$$
Assuming that $X$ is a $0/1$ binary variable we notice that
$$E(Y\mid X=1) - E(Y\mid X=0)=\alpha +\beta -\alpha = \beta $$
I think that the OP |
47,392 | What is an F test? | What is an F test is and what does it show?
The term "F test" may mean any test whose sampling distribution under the null hypothesis has an F-distribution. There are several quite distinct tests.
Here are a couple of the more common ones:
(i) an F-test for equality of means of multiple groups (also called ANOVA, sho... | What is an F test? | What is an F test is and what does it show?
The term "F test" may mean any test whose sampling distribution under the null hypothesis has an F-distribution. There are several quite distinct tests.
H | What is an F test?
What is an F test is and what does it show?
The term "F test" may mean any test whose sampling distribution under the null hypothesis has an F-distribution. There are several quite distinct tests.
Here are a couple of the more common ones:
(i) an F-test for equality of means of multiple groups (als... | What is an F test?
What is an F test is and what does it show?
The term "F test" may mean any test whose sampling distribution under the null hypothesis has an F-distribution. There are several quite distinct tests.
H |
47,393 | Inverse function for a non-decreasing CDF | Let $U$ be a $\mathrm{U}[0,1]$ r.v. Let $F$ be a distribution function. Remember that every distribution function is non decreasing and right continuous . Define the quantile function
$$
F^{-1}(u) = \inf\,\{x:u \leq F(x)\}.
$$
Drawing a picture
we see that $F^{-1}(u)\leq x$ if and only if $u\leq F(x)$. Please, make ... | Inverse function for a non-decreasing CDF | Let $U$ be a $\mathrm{U}[0,1]$ r.v. Let $F$ be a distribution function. Remember that every distribution function is non decreasing and right continuous . Define the quantile function
$$
F^{-1}(u) = | Inverse function for a non-decreasing CDF
Let $U$ be a $\mathrm{U}[0,1]$ r.v. Let $F$ be a distribution function. Remember that every distribution function is non decreasing and right continuous . Define the quantile function
$$
F^{-1}(u) = \inf\,\{x:u \leq F(x)\}.
$$
Drawing a picture
we see that $F^{-1}(u)\leq x$ ... | Inverse function for a non-decreasing CDF
Let $U$ be a $\mathrm{U}[0,1]$ r.v. Let $F$ be a distribution function. Remember that every distribution function is non decreasing and right continuous . Define the quantile function
$$
F^{-1}(u) = |
47,394 | Generalized linear models with continuous proportions | Generalized linear models for responses that are continuous proportions are well known in at least some literatures and well supported in at least some software. I will leave to others with R expertise to comment on how far and/or how well they are supported by R.
A friendly miniature review is offered by Baum in http... | Generalized linear models with continuous proportions | Generalized linear models for responses that are continuous proportions are well known in at least some literatures and well supported in at least some software. I will leave to others with R expertis | Generalized linear models with continuous proportions
Generalized linear models for responses that are continuous proportions are well known in at least some literatures and well supported in at least some software. I will leave to others with R expertise to comment on how far and/or how well they are supported by R.
... | Generalized linear models with continuous proportions
Generalized linear models for responses that are continuous proportions are well known in at least some literatures and well supported in at least some software. I will leave to others with R expertis |
47,395 | Difference of 'centers' of 2 non-normal samples with Mann-Whitney test | Yes, if your alternative is a shift alternative, the corresponding estimate is the Hodges-Lehmann.
The estimate is easy enough.
The Hodges Lehmann estimate is the sample median of the cross-sample pairwise differences.
For really large samples, there are efficient methods (for example, ones that sort the two samples a... | Difference of 'centers' of 2 non-normal samples with Mann-Whitney test | Yes, if your alternative is a shift alternative, the corresponding estimate is the Hodges-Lehmann.
The estimate is easy enough.
The Hodges Lehmann estimate is the sample median of the cross-sample pai | Difference of 'centers' of 2 non-normal samples with Mann-Whitney test
Yes, if your alternative is a shift alternative, the corresponding estimate is the Hodges-Lehmann.
The estimate is easy enough.
The Hodges Lehmann estimate is the sample median of the cross-sample pairwise differences.
For really large samples, the... | Difference of 'centers' of 2 non-normal samples with Mann-Whitney test
Yes, if your alternative is a shift alternative, the corresponding estimate is the Hodges-Lehmann.
The estimate is easy enough.
The Hodges Lehmann estimate is the sample median of the cross-sample pai |
47,396 | When finding outliers from the Interquartile range why I have to multiply by 1.5? | Certainly you can change the criterion.
The 1.5 multiplier is so that a certain proportion of the sample in a normal population will be outside it. But there is nothing sacred about it.
However, I would caution against any automatic method of selecting outliers. | When finding outliers from the Interquartile range why I have to multiply by 1.5? | Certainly you can change the criterion.
The 1.5 multiplier is so that a certain proportion of the sample in a normal population will be outside it. But there is nothing sacred about it.
However, I wou | When finding outliers from the Interquartile range why I have to multiply by 1.5?
Certainly you can change the criterion.
The 1.5 multiplier is so that a certain proportion of the sample in a normal population will be outside it. But there is nothing sacred about it.
However, I would caution against any automatic metho... | When finding outliers from the Interquartile range why I have to multiply by 1.5?
Certainly you can change the criterion.
The 1.5 multiplier is so that a certain proportion of the sample in a normal population will be outside it. But there is nothing sacred about it.
However, I wou |
47,397 | Where does the term "covariate" come from in statistics? | (Making comment into an answer.)
A good starting point is the list of earliest known uses of mathematical terms: jeff560.tripod.com/c.html which gives a reference to 1949 (but with covariate meaning specifically the "x" variable in a regression.) The same source says that the word variate goes back to Pearson in 1909, ... | Where does the term "covariate" come from in statistics? | (Making comment into an answer.)
A good starting point is the list of earliest known uses of mathematical terms: jeff560.tripod.com/c.html which gives a reference to 1949 (but with covariate meaning s | Where does the term "covariate" come from in statistics?
(Making comment into an answer.)
A good starting point is the list of earliest known uses of mathematical terms: jeff560.tripod.com/c.html which gives a reference to 1949 (but with covariate meaning specifically the "x" variable in a regression.) The same source ... | Where does the term "covariate" come from in statistics?
(Making comment into an answer.)
A good starting point is the list of earliest known uses of mathematical terms: jeff560.tripod.com/c.html which gives a reference to 1949 (but with covariate meaning s |
47,398 | Selecting the best subset of variables for parsimonious binary logistic regression models | Variable selection without penalization is invalid. | Selecting the best subset of variables for parsimonious binary logistic regression models | Variable selection without penalization is invalid. | Selecting the best subset of variables for parsimonious binary logistic regression models
Variable selection without penalization is invalid. | Selecting the best subset of variables for parsimonious binary logistic regression models
Variable selection without penalization is invalid. |
47,399 | Selecting the best subset of variables for parsimonious binary logistic regression models | Rarely does a question appear that I believe I can answer.
This isn't in R (at least I don't believe there is a addin for it). It doesn't answer your exact questions either, although I believe may be of help.
I am seeking other methods of variable selection in lieu of using
stepwise methods for building more parsim... | Selecting the best subset of variables for parsimonious binary logistic regression models | Rarely does a question appear that I believe I can answer.
This isn't in R (at least I don't believe there is a addin for it). It doesn't answer your exact questions either, although I believe may be | Selecting the best subset of variables for parsimonious binary logistic regression models
Rarely does a question appear that I believe I can answer.
This isn't in R (at least I don't believe there is a addin for it). It doesn't answer your exact questions either, although I believe may be of help.
I am seeking other ... | Selecting the best subset of variables for parsimonious binary logistic regression models
Rarely does a question appear that I believe I can answer.
This isn't in R (at least I don't believe there is a addin for it). It doesn't answer your exact questions either, although I believe may be |
47,400 | Selecting the best subset of variables for parsimonious binary logistic regression models | To answer the above two questions:
1) In layman terms, Kullback-Leibler divergence, as displayed in R when using the FSelector package, is the relative amount of information that can be gained by using a given potential predictor variable.
2) It is NOT a valid approach to select a desired number of variables for a bina... | Selecting the best subset of variables for parsimonious binary logistic regression models | To answer the above two questions:
1) In layman terms, Kullback-Leibler divergence, as displayed in R when using the FSelector package, is the relative amount of information that can be gained by usin | Selecting the best subset of variables for parsimonious binary logistic regression models
To answer the above two questions:
1) In layman terms, Kullback-Leibler divergence, as displayed in R when using the FSelector package, is the relative amount of information that can be gained by using a given potential predictor ... | Selecting the best subset of variables for parsimonious binary logistic regression models
To answer the above two questions:
1) In layman terms, Kullback-Leibler divergence, as displayed in R when using the FSelector package, is the relative amount of information that can be gained by usin |
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