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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9,001 | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value? | Steepest descent can be inefficient even if the objective function is strongly convex.
Ordinary gradient descent
I mean "inefficient" in the sense that steepest descent can take steps that oscillate wildly away from the optimum, even if the function is strongly convex or even quadratic.
Consider $f(x)=x_1^2 + 25x_2^2$.... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e | Steepest descent can be inefficient even if the objective function is strongly convex.
Ordinary gradient descent
I mean "inefficient" in the sense that steepest descent can take steps that oscillate w | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?
Steepest descent can be inefficient even if the objective function is strongly convex.
Ordinary gradient descent
I mean "inefficient" in the sense that steepest descent can take steps that oscillate wildly ... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e
Steepest descent can be inefficient even if the objective function is strongly convex.
Ordinary gradient descent
I mean "inefficient" in the sense that steepest descent can take steps that oscillate w |
9,002 | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value? | Local steepest direction is not the same with the global optimum direction. If it were, then your gradient direction wouldn't change; because if you go towards your optimum always, your direction vector would point optimum always. But, that's not the case. If it were the case, why bother calculating your gradient every... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e | Local steepest direction is not the same with the global optimum direction. If it were, then your gradient direction wouldn't change; because if you go towards your optimum always, your direction vect | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?
Local steepest direction is not the same with the global optimum direction. If it were, then your gradient direction wouldn't change; because if you go towards your optimum always, your direction vector wou... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e
Local steepest direction is not the same with the global optimum direction. If it were, then your gradient direction wouldn't change; because if you go towards your optimum always, your direction vect |
9,003 | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value? | The other answers highlight some annoying rate-of-convergence issues for GD/SGD, but your comment "SGD can eventually converge..." isn't always correct (ignoring pedantic usage remarks about the word "can" since it seems you meant "will").
One nice trick for finding counter-examples with SGD is to notice that if every ... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e | The other answers highlight some annoying rate-of-convergence issues for GD/SGD, but your comment "SGD can eventually converge..." isn't always correct (ignoring pedantic usage remarks about the word | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?
The other answers highlight some annoying rate-of-convergence issues for GD/SGD, but your comment "SGD can eventually converge..." isn't always correct (ignoring pedantic usage remarks about the word "can" ... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e
The other answers highlight some annoying rate-of-convergence issues for GD/SGD, but your comment "SGD can eventually converge..." isn't always correct (ignoring pedantic usage remarks about the word |
9,004 | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value? | Maybe the answers to this question need a quick update. It seems like SGD yields a global minimum also in the non-convex case (convex is just a special case of that):
SGD Converges To Global Minimum In Deep Learning via Star-Convex Path, Anonymous authors, Paper under double-blind review at ICLR 2019
https://openrevie... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e | Maybe the answers to this question need a quick update. It seems like SGD yields a global minimum also in the non-convex case (convex is just a special case of that):
SGD Converges To Global Minimum | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?
Maybe the answers to this question need a quick update. It seems like SGD yields a global minimum also in the non-convex case (convex is just a special case of that):
SGD Converges To Global Minimum In Dee... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e
Maybe the answers to this question need a quick update. It seems like SGD yields a global minimum also in the non-convex case (convex is just a special case of that):
SGD Converges To Global Minimum |
9,005 | Sample two numbers from 1 to 10; maximize the expected product | Hint: Note the relationship between $E[XY]$ and the covariance. Now think about the sign of the covariance - or if you prefer it in those terms, the sign of the correlation will work - under the two sampling schemes (it's zero under one but clearly not under the other, noting that we're here taking $X$ and $Y$ as the v... | Sample two numbers from 1 to 10; maximize the expected product | Hint: Note the relationship between $E[XY]$ and the covariance. Now think about the sign of the covariance - or if you prefer it in those terms, the sign of the correlation will work - under the two s | Sample two numbers from 1 to 10; maximize the expected product
Hint: Note the relationship between $E[XY]$ and the covariance. Now think about the sign of the covariance - or if you prefer it in those terms, the sign of the correlation will work - under the two sampling schemes (it's zero under one but clearly not unde... | Sample two numbers from 1 to 10; maximize the expected product
Hint: Note the relationship between $E[XY]$ and the covariance. Now think about the sign of the covariance - or if you prefer it in those terms, the sign of the correlation will work - under the two s |
9,006 | Sample two numbers from 1 to 10; maximize the expected product | If you don't get to the smart covariance trick by Glen B, then you could also consider the following approach which is one level of abstraction lower
Step 1: consider computing the hard way by adding all 10 by 10 terms from a table $$\frac{1}{100}\sum_{x_1=1}^{10}\sum_{x_2=1}^{10} x_1 \cdot x_2 = E[X]^2 = 5.5^2$$
$$\b... | Sample two numbers from 1 to 10; maximize the expected product | If you don't get to the smart covariance trick by Glen B, then you could also consider the following approach which is one level of abstraction lower
Step 1: consider computing the hard way by adding | Sample two numbers from 1 to 10; maximize the expected product
If you don't get to the smart covariance trick by Glen B, then you could also consider the following approach which is one level of abstraction lower
Step 1: consider computing the hard way by adding all 10 by 10 terms from a table $$\frac{1}{100}\sum_{x_1... | Sample two numbers from 1 to 10; maximize the expected product
If you don't get to the smart covariance trick by Glen B, then you could also consider the following approach which is one level of abstraction lower
Step 1: consider computing the hard way by adding |
9,007 | Sample two numbers from 1 to 10; maximize the expected product | Here is an intuitive approach to the problem. Suppose the first number we pick is a 1 - we'd obviously be better off picking the second number without replacement, in order to eliminate the chance of getting another 1. Suppose the first number we pick is a 10 - we'd obviously be better off picking the second number wit... | Sample two numbers from 1 to 10; maximize the expected product | Here is an intuitive approach to the problem. Suppose the first number we pick is a 1 - we'd obviously be better off picking the second number without replacement, in order to eliminate the chance of | Sample two numbers from 1 to 10; maximize the expected product
Here is an intuitive approach to the problem. Suppose the first number we pick is a 1 - we'd obviously be better off picking the second number without replacement, in order to eliminate the chance of getting another 1. Suppose the first number we pick is a ... | Sample two numbers from 1 to 10; maximize the expected product
Here is an intuitive approach to the problem. Suppose the first number we pick is a 1 - we'd obviously be better off picking the second number without replacement, in order to eliminate the chance of |
9,008 | Sample two numbers from 1 to 10; maximize the expected product | If you're better at programming than maths, I believe there's a reasonably simple way to get this by brute force as well.
It provides a slightly different intuition: $E[XY]$ is higher without replacement when $X < \text{mean}(X)$, because removing a low value of $X$ increases $E[Y]$, it is lower, and by a greater amoun... | Sample two numbers from 1 to 10; maximize the expected product | If you're better at programming than maths, I believe there's a reasonably simple way to get this by brute force as well.
It provides a slightly different intuition: $E[XY]$ is higher without replacem | Sample two numbers from 1 to 10; maximize the expected product
If you're better at programming than maths, I believe there's a reasonably simple way to get this by brute force as well.
It provides a slightly different intuition: $E[XY]$ is higher without replacement when $X < \text{mean}(X)$, because removing a low val... | Sample two numbers from 1 to 10; maximize the expected product
If you're better at programming than maths, I believe there's a reasonably simple way to get this by brute force as well.
It provides a slightly different intuition: $E[XY]$ is higher without replacem |
9,009 | Sample two numbers from 1 to 10; maximize the expected product | There are three facts that led me to the conclusion that replacement gives a higher expected value:
1. Products result in right-skewed distributions. When you multiply numbers together, you tend to get results clustered mostly in small numbers, with a few large results.
2. Among right-skewed distribution, increasing th... | Sample two numbers from 1 to 10; maximize the expected product | There are three facts that led me to the conclusion that replacement gives a higher expected value:
1. Products result in right-skewed distributions. When you multiply numbers together, you tend to ge | Sample two numbers from 1 to 10; maximize the expected product
There are three facts that led me to the conclusion that replacement gives a higher expected value:
1. Products result in right-skewed distributions. When you multiply numbers together, you tend to get results clustered mostly in small numbers, with a few l... | Sample two numbers from 1 to 10; maximize the expected product
There are three facts that led me to the conclusion that replacement gives a higher expected value:
1. Products result in right-skewed distributions. When you multiply numbers together, you tend to ge |
9,010 | Sample two numbers from 1 to 10; maximize the expected product | This is a different shortcut than Glen_B's -- but of course they must be related at some level. It all comes down to the fact that squares of numbers are non-negative.
Let there be $n$ ($10$ in this instance) objects $i_1, i_2, \ldots, i_n$ in the box bearing the numbers $x_1, x_2, \ldots, x_n,$ respectively. Write $... | Sample two numbers from 1 to 10; maximize the expected product | This is a different shortcut than Glen_B's -- but of course they must be related at some level. It all comes down to the fact that squares of numbers are non-negative.
Let there be $n$ ($10$ in this | Sample two numbers from 1 to 10; maximize the expected product
This is a different shortcut than Glen_B's -- but of course they must be related at some level. It all comes down to the fact that squares of numbers are non-negative.
Let there be $n$ ($10$ in this instance) objects $i_1, i_2, \ldots, i_n$ in the box bear... | Sample two numbers from 1 to 10; maximize the expected product
This is a different shortcut than Glen_B's -- but of course they must be related at some level. It all comes down to the fact that squares of numbers are non-negative.
Let there be $n$ ($10$ in this |
9,011 | Sample two numbers from 1 to 10; maximize the expected product | I think Glen_b's answer is wonderful intuition that you need to only consider the the covariance, as the unconditional expectations are the same. Below I prove the unconditional expectations are the same (ie $EX = EY$)
$$
\begin{align*}
EX &= \dfrac{1}{n}\sum_{i=1}^n i = \dfrac{n(n+1)}{2n} = \dfrac{(n+1)}{2}\\
E[Y|X=j]... | Sample two numbers from 1 to 10; maximize the expected product | I think Glen_b's answer is wonderful intuition that you need to only consider the the covariance, as the unconditional expectations are the same. Below I prove the unconditional expectations are the s | Sample two numbers from 1 to 10; maximize the expected product
I think Glen_b's answer is wonderful intuition that you need to only consider the the covariance, as the unconditional expectations are the same. Below I prove the unconditional expectations are the same (ie $EX = EY$)
$$
\begin{align*}
EX &= \dfrac{1}{n}\s... | Sample two numbers from 1 to 10; maximize the expected product
I think Glen_b's answer is wonderful intuition that you need to only consider the the covariance, as the unconditional expectations are the same. Below I prove the unconditional expectations are the s |
9,012 | Sample two numbers from 1 to 10; maximize the expected product | Don't know if this counts as simpler than doing direct computation (you have to know Gauss's formula for the sum of the first $n$ numbers), but you can prove your guess by induction on the number of randomly drawn numbers $n$ (and then, your case follows from the special case $n=10$).
So, we have to prove that for each... | Sample two numbers from 1 to 10; maximize the expected product | Don't know if this counts as simpler than doing direct computation (you have to know Gauss's formula for the sum of the first $n$ numbers), but you can prove your guess by induction on the number of r | Sample two numbers from 1 to 10; maximize the expected product
Don't know if this counts as simpler than doing direct computation (you have to know Gauss's formula for the sum of the first $n$ numbers), but you can prove your guess by induction on the number of randomly drawn numbers $n$ (and then, your case follows fr... | Sample two numbers from 1 to 10; maximize the expected product
Don't know if this counts as simpler than doing direct computation (you have to know Gauss's formula for the sum of the first $n$ numbers), but you can prove your guess by induction on the number of r |
9,013 | Sample two numbers from 1 to 10; maximize the expected product | I would pick 10 twice, this results in 100 which is the largest possible product of two numbers between 1 and 10. | Sample two numbers from 1 to 10; maximize the expected product | I would pick 10 twice, this results in 100 which is the largest possible product of two numbers between 1 and 10. | Sample two numbers from 1 to 10; maximize the expected product
I would pick 10 twice, this results in 100 which is the largest possible product of two numbers between 1 and 10. | Sample two numbers from 1 to 10; maximize the expected product
I would pick 10 twice, this results in 100 which is the largest possible product of two numbers between 1 and 10. |
9,014 | Sample two numbers from 1 to 10; maximize the expected product | There are two states: pick new number or not. In replacement there are four
choices and without replacement there are three:$(0, 0), (0, 1), (1, 0)$.
The probability of the last two is $\frac{1\cdot(n-1)}{n(n-1)}$ and the
expected value is $n\frac{n-1+1}{2}$. Multiplying and simplifying gives $n/2$.
Let $e_n$ be the re... | Sample two numbers from 1 to 10; maximize the expected product | There are two states: pick new number or not. In replacement there are four
choices and without replacement there are three:$(0, 0), (0, 1), (1, 0)$.
The probability of the last two is $\frac{1\cdot(n | Sample two numbers from 1 to 10; maximize the expected product
There are two states: pick new number or not. In replacement there are four
choices and without replacement there are three:$(0, 0), (0, 1), (1, 0)$.
The probability of the last two is $\frac{1\cdot(n-1)}{n(n-1)}$ and the
expected value is $n\frac{n-1+1}{2}... | Sample two numbers from 1 to 10; maximize the expected product
There are two states: pick new number or not. In replacement there are four
choices and without replacement there are three:$(0, 0), (0, 1), (1, 0)$.
The probability of the last two is $\frac{1\cdot(n |
9,015 | What's a good way to use R to make a scatterplot that separates the data by treatment? | large clusters: if overprinting is a problem, you could either use a lower alpha, so single points are dim, but overprining makes more intense colour. Or you switch to 2d histograms or density estimates.
require ("ggplot2")
ggplot (iris, aes (x = Sepal.Length, y = Sepal.Width, colour = Species)) + stat_density2d ()... | What's a good way to use R to make a scatterplot that separates the data by treatment? | large clusters: if overprinting is a problem, you could either use a lower alpha, so single points are dim, but overprining makes more intense colour. Or you switch to 2d histograms or density estima | What's a good way to use R to make a scatterplot that separates the data by treatment?
large clusters: if overprinting is a problem, you could either use a lower alpha, so single points are dim, but overprining makes more intense colour. Or you switch to 2d histograms or density estimates.
require ("ggplot2")
ggplo... | What's a good way to use R to make a scatterplot that separates the data by treatment?
large clusters: if overprinting is a problem, you could either use a lower alpha, so single points are dim, but overprining makes more intense colour. Or you switch to 2d histograms or density estima |
9,016 | What's a good way to use R to make a scatterplot that separates the data by treatment? | This is one of the classic problems for the 'Iris' data set. This is a link to a whole set of plotting projects based on that data set with R code, which you may be able to adapt to your problem.
Here is an approach that uses with base R rather than an add-on package.
plot(iris$Petal.Length, iris$Petal.Width, pch=21,
... | What's a good way to use R to make a scatterplot that separates the data by treatment? | This is one of the classic problems for the 'Iris' data set. This is a link to a whole set of plotting projects based on that data set with R code, which you may be able to adapt to your problem.
Here | What's a good way to use R to make a scatterplot that separates the data by treatment?
This is one of the classic problems for the 'Iris' data set. This is a link to a whole set of plotting projects based on that data set with R code, which you may be able to adapt to your problem.
Here is an approach that uses with ba... | What's a good way to use R to make a scatterplot that separates the data by treatment?
This is one of the classic problems for the 'Iris' data set. This is a link to a whole set of plotting projects based on that data set with R code, which you may be able to adapt to your problem.
Here |
9,017 | What's a good way to use R to make a scatterplot that separates the data by treatment? | Or with ggplot2:
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, colour = Species)) + geom_point()
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + facet_grid(~Species)
Which produces | What's a good way to use R to make a scatterplot that separates the data by treatment? | Or with ggplot2:
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, colour = Species)) + geom_point()
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + facet_grid(~Species)
Which | What's a good way to use R to make a scatterplot that separates the data by treatment?
Or with ggplot2:
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, colour = Species)) + geom_point()
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + facet_grid(~Species)
Which produces | What's a good way to use R to make a scatterplot that separates the data by treatment?
Or with ggplot2:
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, colour = Species)) + geom_point()
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + facet_grid(~Species)
Which |
9,018 | What theories should every statistician know? | Frankly, I don't think the law of large numbers has a huge role in industry. It is helpful to understand the asymptotic justifications of the common procedures, such as maximum likelihood estimates and tests (including the omniimportant GLMs and logistic regression, in particular), the bootstrap, but these are distribu... | What theories should every statistician know? | Frankly, I don't think the law of large numbers has a huge role in industry. It is helpful to understand the asymptotic justifications of the common procedures, such as maximum likelihood estimates an | What theories should every statistician know?
Frankly, I don't think the law of large numbers has a huge role in industry. It is helpful to understand the asymptotic justifications of the common procedures, such as maximum likelihood estimates and tests (including the omniimportant GLMs and logistic regression, in part... | What theories should every statistician know?
Frankly, I don't think the law of large numbers has a huge role in industry. It is helpful to understand the asymptotic justifications of the common procedures, such as maximum likelihood estimates an |
9,019 | What theories should every statistician know? | I think a good understanding of the issues relating to the bias-variance tradeoff. Most statisticians will end up, at some point, analysing a dataset that is small enough for the variance of an estimator or the parameters of the model to be sufficiently high that bias is a secondary consideration. | What theories should every statistician know? | I think a good understanding of the issues relating to the bias-variance tradeoff. Most statisticians will end up, at some point, analysing a dataset that is small enough for the variance of an estim | What theories should every statistician know?
I think a good understanding of the issues relating to the bias-variance tradeoff. Most statisticians will end up, at some point, analysing a dataset that is small enough for the variance of an estimator or the parameters of the model to be sufficiently high that bias is a... | What theories should every statistician know?
I think a good understanding of the issues relating to the bias-variance tradeoff. Most statisticians will end up, at some point, analysing a dataset that is small enough for the variance of an estim |
9,020 | What theories should every statistician know? | To point out the super obvious one:
Central Limit Theorem
since it allows practitioners to approximate $p$-values in many situations where getting exact $p$-values is intractable. Along those same lines, any successful practitioner would be well served to be familiar, in general, with
Bootstrapping | What theories should every statistician know? | To point out the super obvious one:
Central Limit Theorem
since it allows practitioners to approximate $p$-values in many situations where getting exact $p$-values is intractable. Along those same lin | What theories should every statistician know?
To point out the super obvious one:
Central Limit Theorem
since it allows practitioners to approximate $p$-values in many situations where getting exact $p$-values is intractable. Along those same lines, any successful practitioner would be well served to be familiar, in ge... | What theories should every statistician know?
To point out the super obvious one:
Central Limit Theorem
since it allows practitioners to approximate $p$-values in many situations where getting exact $p$-values is intractable. Along those same lin |
9,021 | What theories should every statistician know? | I wouldn't say this is very similar to something like the law of large numbers or the central limit theorem, but because making inferences about causality is often central, understanding Judea Pearl's work on using structured graphs to model causality is something people should be familiar with. It provides a way to u... | What theories should every statistician know? | I wouldn't say this is very similar to something like the law of large numbers or the central limit theorem, but because making inferences about causality is often central, understanding Judea Pearl's | What theories should every statistician know?
I wouldn't say this is very similar to something like the law of large numbers or the central limit theorem, but because making inferences about causality is often central, understanding Judea Pearl's work on using structured graphs to model causality is something people sh... | What theories should every statistician know?
I wouldn't say this is very similar to something like the law of large numbers or the central limit theorem, but because making inferences about causality is often central, understanding Judea Pearl's |
9,022 | What theories should every statistician know? | A solid understanding of the substantive problem to be addressed is as important as any particular statistical approach. A good scientist in the industry is more likely than a statistician without such knowledge to come to a reasonable solution to their problem. A statistician with substantive knowledge can help. | What theories should every statistician know? | A solid understanding of the substantive problem to be addressed is as important as any particular statistical approach. A good scientist in the industry is more likely than a statistician without su | What theories should every statistician know?
A solid understanding of the substantive problem to be addressed is as important as any particular statistical approach. A good scientist in the industry is more likely than a statistician without such knowledge to come to a reasonable solution to their problem. A statist... | What theories should every statistician know?
A solid understanding of the substantive problem to be addressed is as important as any particular statistical approach. A good scientist in the industry is more likely than a statistician without su |
9,023 | What theories should every statistician know? | The Delta-Method, how to calculate the variance of bizarre statistics and find their asymptotic relative efficiency, to recommend changes of variable and explain efficiency boosts by "estimating the right thing". In conjunction with that, Jensen's Inequality for understanding GLMs and strange kinds of bias which arise ... | What theories should every statistician know? | The Delta-Method, how to calculate the variance of bizarre statistics and find their asymptotic relative efficiency, to recommend changes of variable and explain efficiency boosts by "estimating the r | What theories should every statistician know?
The Delta-Method, how to calculate the variance of bizarre statistics and find their asymptotic relative efficiency, to recommend changes of variable and explain efficiency boosts by "estimating the right thing". In conjunction with that, Jensen's Inequality for understandi... | What theories should every statistician know?
The Delta-Method, how to calculate the variance of bizarre statistics and find their asymptotic relative efficiency, to recommend changes of variable and explain efficiency boosts by "estimating the r |
9,024 | What theories should every statistician know? | In my view, statistical inference is most important for a practitioner. Inference has two parts: 1) Estimation & 2) Hypothesis testing. Hypothesis testing is important one. Since in estimation mostly a unique procedure, maximum likelihood estimation, followed and it is available most statistical package(so there is no ... | What theories should every statistician know? | In my view, statistical inference is most important for a practitioner. Inference has two parts: 1) Estimation & 2) Hypothesis testing. Hypothesis testing is important one. Since in estimation mostly | What theories should every statistician know?
In my view, statistical inference is most important for a practitioner. Inference has two parts: 1) Estimation & 2) Hypothesis testing. Hypothesis testing is important one. Since in estimation mostly a unique procedure, maximum likelihood estimation, followed and it is avai... | What theories should every statistician know?
In my view, statistical inference is most important for a practitioner. Inference has two parts: 1) Estimation & 2) Hypothesis testing. Hypothesis testing is important one. Since in estimation mostly |
9,025 | What theories should every statistician know? | Casual inference is must. And how to address it's fundamental problem, you can't go back in time and not give someone a treatment. Read articles about rubin, fisher the founder of modern statistics student.)....
What to learn to address this problem, proper randomisation and how Law of large numbers says things are pr... | What theories should every statistician know? | Casual inference is must. And how to address it's fundamental problem, you can't go back in time and not give someone a treatment. Read articles about rubin, fisher the founder of modern statistics st | What theories should every statistician know?
Casual inference is must. And how to address it's fundamental problem, you can't go back in time and not give someone a treatment. Read articles about rubin, fisher the founder of modern statistics student.)....
What to learn to address this problem, proper randomisation a... | What theories should every statistician know?
Casual inference is must. And how to address it's fundamental problem, you can't go back in time and not give someone a treatment. Read articles about rubin, fisher the founder of modern statistics st |
9,026 | If X and Y are uncorrelated, are X^2 and Y also uncorrelated? | No. A counterexample:
Let $X$ be uniformly distributed on $[-1, 1]$, $Y = X^2$.
Then $E[X]=0$ and also $E[XY]=E[X^3]=0$ ($X^3$ is odd function), so $X,Y$ are uncorrelated.
But $E[X^2Y] = E[X^4] = E[{X^2}^2] > E[X^2]^2 = E[X^2]E[Y]$
The last inequality follows from Jensen's inequality. It also follows from the fact tha... | If X and Y are uncorrelated, are X^2 and Y also uncorrelated? | No. A counterexample:
Let $X$ be uniformly distributed on $[-1, 1]$, $Y = X^2$.
Then $E[X]=0$ and also $E[XY]=E[X^3]=0$ ($X^3$ is odd function), so $X,Y$ are uncorrelated.
But $E[X^2Y] = E[X^4] = E[{X | If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
No. A counterexample:
Let $X$ be uniformly distributed on $[-1, 1]$, $Y = X^2$.
Then $E[X]=0$ and also $E[XY]=E[X^3]=0$ ($X^3$ is odd function), so $X,Y$ are uncorrelated.
But $E[X^2Y] = E[X^4] = E[{X^2}^2] > E[X^2]^2 = E[X^2]E[Y]$
The last inequality follo... | If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
No. A counterexample:
Let $X$ be uniformly distributed on $[-1, 1]$, $Y = X^2$.
Then $E[X]=0$ and also $E[XY]=E[X^3]=0$ ($X^3$ is odd function), so $X,Y$ are uncorrelated.
But $E[X^2Y] = E[X^4] = E[{X |
9,027 | If X and Y are uncorrelated, are X^2 and Y also uncorrelated? | Even if $\operatorname{Corr}(X,Y)=0$, not only is it possible that $X^2$ and $Y$ are correlated, but they may even be perfectly correlated, with $\operatorname{Corr}(X^2,Y)=1$:
> x <- c(-1,0,1); y <- c(1,0,1)
> cor(x,y)
[1] 0
> cor(x^2,y)
[1] 1
Or $\operatorname{Corr}(X^2,Y)=-1$:
> x <- c(-1,0,1); y <- c(-1,0,-1)
> co... | If X and Y are uncorrelated, are X^2 and Y also uncorrelated? | Even if $\operatorname{Corr}(X,Y)=0$, not only is it possible that $X^2$ and $Y$ are correlated, but they may even be perfectly correlated, with $\operatorname{Corr}(X^2,Y)=1$:
> x <- c(-1,0,1); y <- | If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
Even if $\operatorname{Corr}(X,Y)=0$, not only is it possible that $X^2$ and $Y$ are correlated, but they may even be perfectly correlated, with $\operatorname{Corr}(X^2,Y)=1$:
> x <- c(-1,0,1); y <- c(1,0,1)
> cor(x,y)
[1] 0
> cor(x^2,y)
[1] 1
Or $\operato... | If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
Even if $\operatorname{Corr}(X,Y)=0$, not only is it possible that $X^2$ and $Y$ are correlated, but they may even be perfectly correlated, with $\operatorname{Corr}(X^2,Y)=1$:
> x <- c(-1,0,1); y <- |
9,028 | If X and Y are uncorrelated, are X^2 and Y also uncorrelated? | The error in your reasoning is that you write the following about $E[h(X,Y)]$:
$$E[h(X,Y)]=\int h(x,y) f_X(x)f_Y(y)dxdy$$
while in general
$$E[h(X,Y)]=\int h(x,y) f_{XY}(x,y)dxdy.$$
The two coincide if $f_{XY}(x,y)=f_X(x)f_Y(y)$, i.e. if $X$ and $Y$ are independent. Being uncorrelated is a necessary but not sufficient ... | If X and Y are uncorrelated, are X^2 and Y also uncorrelated? | The error in your reasoning is that you write the following about $E[h(X,Y)]$:
$$E[h(X,Y)]=\int h(x,y) f_X(x)f_Y(y)dxdy$$
while in general
$$E[h(X,Y)]=\int h(x,y) f_{XY}(x,y)dxdy.$$
The two coincide i | If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
The error in your reasoning is that you write the following about $E[h(X,Y)]$:
$$E[h(X,Y)]=\int h(x,y) f_X(x)f_Y(y)dxdy$$
while in general
$$E[h(X,Y)]=\int h(x,y) f_{XY}(x,y)dxdy.$$
The two coincide if $f_{XY}(x,y)=f_X(x)f_Y(y)$, i.e. if $X$ and $Y$ are inde... | If X and Y are uncorrelated, are X^2 and Y also uncorrelated?
The error in your reasoning is that you write the following about $E[h(X,Y)]$:
$$E[h(X,Y)]=\int h(x,y) f_X(x)f_Y(y)dxdy$$
while in general
$$E[h(X,Y)]=\int h(x,y) f_{XY}(x,y)dxdy.$$
The two coincide i |
9,029 | Bayes' Theorem Intuition | Although there are four components listed in Bayes' law, I prefer to think in terms of three conceptual components:
$$
\underbrace{P(B|A)}_2 = \underbrace{\frac{P(A|B)}{P(A)}}_3 \underbrace{P(B)}_1
$$
The prior is what you believed about $B$ before having encountered a new and relevant piece of information (i.e., $A... | Bayes' Theorem Intuition | Although there are four components listed in Bayes' law, I prefer to think in terms of three conceptual components:
$$
\underbrace{P(B|A)}_2 = \underbrace{\frac{P(A|B)}{P(A)}}_3 \underbrace{P(B)}_1
$$ | Bayes' Theorem Intuition
Although there are four components listed in Bayes' law, I prefer to think in terms of three conceptual components:
$$
\underbrace{P(B|A)}_2 = \underbrace{\frac{P(A|B)}{P(A)}}_3 \underbrace{P(B)}_1
$$
The prior is what you believed about $B$ before having encountered a new and relevant piece... | Bayes' Theorem Intuition
Although there are four components listed in Bayes' law, I prefer to think in terms of three conceptual components:
$$
\underbrace{P(B|A)}_2 = \underbrace{\frac{P(A|B)}{P(A)}}_3 \underbrace{P(B)}_1
$$ |
9,030 | Bayes' Theorem Intuition | There are several good answers already, but perhaps this can add something new ...
I always think of Bayes rule in terms of the component probabilities, which can be understood geometrically in terms of the events $A$ and $B$ as pictured below.
The marginal probabilities $P(A)$ and $P(B)$ are given by the areas of the... | Bayes' Theorem Intuition | There are several good answers already, but perhaps this can add something new ...
I always think of Bayes rule in terms of the component probabilities, which can be understood geometrically in terms | Bayes' Theorem Intuition
There are several good answers already, but perhaps this can add something new ...
I always think of Bayes rule in terms of the component probabilities, which can be understood geometrically in terms of the events $A$ and $B$ as pictured below.
The marginal probabilities $P(A)$ and $P(B)$ are ... | Bayes' Theorem Intuition
There are several good answers already, but perhaps this can add something new ...
I always think of Bayes rule in terms of the component probabilities, which can be understood geometrically in terms |
9,031 | Bayes' Theorem Intuition | @gung has a great answer. I would add one example to explain the "initiation" in a real world example.
For better connection with real world examples, I would like to change the notation, where use $H$ to represent the hypothesis (the $A$ in your equation), and use $E$ to represent evidence. (the $B$ in your equation.)... | Bayes' Theorem Intuition | @gung has a great answer. I would add one example to explain the "initiation" in a real world example.
For better connection with real world examples, I would like to change the notation, where use $H | Bayes' Theorem Intuition
@gung has a great answer. I would add one example to explain the "initiation" in a real world example.
For better connection with real world examples, I would like to change the notation, where use $H$ to represent the hypothesis (the $A$ in your equation), and use $E$ to represent evidence. (t... | Bayes' Theorem Intuition
@gung has a great answer. I would add one example to explain the "initiation" in a real world example.
For better connection with real world examples, I would like to change the notation, where use $H |
9,032 | Bayes' Theorem Intuition | Aug 7 2015 Medium article explains with many pictures! 1 in 10 people are sick.
To simplify the example, we assume we know which ones are sick and which ones are healthy, but in a real test you don’t know that information. Now we test everybody for the disease:
The true positives = number of positive results among ... | Bayes' Theorem Intuition | Aug 7 2015 Medium article explains with many pictures! 1 in 10 people are sick.
To simplify the example, we assume we know which ones are sick and which ones are healthy, but in a real test you don | Bayes' Theorem Intuition
Aug 7 2015 Medium article explains with many pictures! 1 in 10 people are sick.
To simplify the example, we assume we know which ones are sick and which ones are healthy, but in a real test you don’t know that information. Now we test everybody for the disease:
The true positives = number o... | Bayes' Theorem Intuition
Aug 7 2015 Medium article explains with many pictures! 1 in 10 people are sick.
To simplify the example, we assume we know which ones are sick and which ones are healthy, but in a real test you don |
9,033 | Bayes' Theorem Intuition | Here's a super straightforward and intuitive explanation.
https://metagrokker.medium.com/an-intuitive-interpretation-of-bayes-theorem-d3e43b05bb2a
Here's a summary; think of Bayes in the following form:
P(A|B) = P(A) * (P(B|A) / P(B))
P(A) is our confidence about hypothesis A being true, before accounting for the new e... | Bayes' Theorem Intuition | Here's a super straightforward and intuitive explanation.
https://metagrokker.medium.com/an-intuitive-interpretation-of-bayes-theorem-d3e43b05bb2a
Here's a summary; think of Bayes in the following for | Bayes' Theorem Intuition
Here's a super straightforward and intuitive explanation.
https://metagrokker.medium.com/an-intuitive-interpretation-of-bayes-theorem-d3e43b05bb2a
Here's a summary; think of Bayes in the following form:
P(A|B) = P(A) * (P(B|A) / P(B))
P(A) is our confidence about hypothesis A being true, before... | Bayes' Theorem Intuition
Here's a super straightforward and intuitive explanation.
https://metagrokker.medium.com/an-intuitive-interpretation-of-bayes-theorem-d3e43b05bb2a
Here's a summary; think of Bayes in the following for |
9,034 | Bayes' Theorem Intuition | Note that Bayes' rule is
$P(a|b)=\frac{P(b,a)}{P(b)}=\frac{P(b,a)}{P(b)P(a)}P(a)$.
Note the ratio
$$\frac{P(b,a)}{P(b)P(a)}.$$
If $B \perp A$, then $P(b,a)=P(b)P(a)$. So it’s almost like telling us how far the joint deviates from full independence, or how much information the variables have in common.
Of course this i... | Bayes' Theorem Intuition | Note that Bayes' rule is
$P(a|b)=\frac{P(b,a)}{P(b)}=\frac{P(b,a)}{P(b)P(a)}P(a)$.
Note the ratio
$$\frac{P(b,a)}{P(b)P(a)}.$$
If $B \perp A$, then $P(b,a)=P(b)P(a)$. So it’s almost like telling us h | Bayes' Theorem Intuition
Note that Bayes' rule is
$P(a|b)=\frac{P(b,a)}{P(b)}=\frac{P(b,a)}{P(b)P(a)}P(a)$.
Note the ratio
$$\frac{P(b,a)}{P(b)P(a)}.$$
If $B \perp A$, then $P(b,a)=P(b)P(a)$. So it’s almost like telling us how far the joint deviates from full independence, or how much information the variables have in... | Bayes' Theorem Intuition
Note that Bayes' rule is
$P(a|b)=\frac{P(b,a)}{P(b)}=\frac{P(b,a)}{P(b)P(a)}P(a)$.
Note the ratio
$$\frac{P(b,a)}{P(b)P(a)}.$$
If $B \perp A$, then $P(b,a)=P(b)P(a)$. So it’s almost like telling us h |
9,035 | Bayes' Theorem Intuition | I often find viewing the theorem as a table, with the possible outcomes for "B" as the rows, and the possible outcomes for "A" as the columns. The joint probabilities $P(A,B)$ are the values for each cell. In this table we have
likelihood = row proportions
posterior = column proportions
The prior and marginal are analo... | Bayes' Theorem Intuition | I often find viewing the theorem as a table, with the possible outcomes for "B" as the rows, and the possible outcomes for "A" as the columns. The joint probabilities $P(A,B)$ are the values for each | Bayes' Theorem Intuition
I often find viewing the theorem as a table, with the possible outcomes for "B" as the rows, and the possible outcomes for "A" as the columns. The joint probabilities $P(A,B)$ are the values for each cell. In this table we have
likelihood = row proportions
posterior = column proportions
The pri... | Bayes' Theorem Intuition
I often find viewing the theorem as a table, with the possible outcomes for "B" as the rows, and the possible outcomes for "A" as the columns. The joint probabilities $P(A,B)$ are the values for each |
9,036 | Bayes' Theorem Intuition | Here is an additional graphic to the intuition of Bayes rule in terms $A$ and $B$ following some joint distribution.
$$P(B|A)\cdot P(A) = P(A,B) = P(A|B) \cdot P(B)$$
or
$$P(B|A) = \frac{P(A,B)}{P(A)} = \frac{P(A|B) \cdot P(B)}{P(A) }$$
The prior (independent of the observation of A), is the marginal distribution in th... | Bayes' Theorem Intuition | Here is an additional graphic to the intuition of Bayes rule in terms $A$ and $B$ following some joint distribution.
$$P(B|A)\cdot P(A) = P(A,B) = P(A|B) \cdot P(B)$$
or
$$P(B|A) = \frac{P(A,B)}{P(A)} | Bayes' Theorem Intuition
Here is an additional graphic to the intuition of Bayes rule in terms $A$ and $B$ following some joint distribution.
$$P(B|A)\cdot P(A) = P(A,B) = P(A|B) \cdot P(B)$$
or
$$P(B|A) = \frac{P(A,B)}{P(A)} = \frac{P(A|B) \cdot P(B)}{P(A) }$$
The prior (independent of the observation of A), is the ma... | Bayes' Theorem Intuition
Here is an additional graphic to the intuition of Bayes rule in terms $A$ and $B$ following some joint distribution.
$$P(B|A)\cdot P(A) = P(A,B) = P(A|B) \cdot P(B)$$
or
$$P(B|A) = \frac{P(A,B)}{P(A)} |
9,037 | When can correlation be useful without causation? | Correlation (or any other measure of association) is useful for prediction regardless of causation. Suppose that you measure a clear, stable association between two variables. What this means is that knowing the level of one variable also provides you with some information about another variable of interest, which you ... | When can correlation be useful without causation? | Correlation (or any other measure of association) is useful for prediction regardless of causation. Suppose that you measure a clear, stable association between two variables. What this means is that | When can correlation be useful without causation?
Correlation (or any other measure of association) is useful for prediction regardless of causation. Suppose that you measure a clear, stable association between two variables. What this means is that knowing the level of one variable also provides you with some informat... | When can correlation be useful without causation?
Correlation (or any other measure of association) is useful for prediction regardless of causation. Suppose that you measure a clear, stable association between two variables. What this means is that |
9,038 | When can correlation be useful without causation? | There are a lot of good points here already. Let me unpack your claim that "it seems that if X is a predictor of Y, it would be useful in predicting future values of Y based on X, regardless of causality" a little bit. You are correct: If all you want is to be able to predict an unknown Y value from a known X value a... | When can correlation be useful without causation? | There are a lot of good points here already. Let me unpack your claim that "it seems that if X is a predictor of Y, it would be useful in predicting future values of Y based on X, regardless of causa | When can correlation be useful without causation?
There are a lot of good points here already. Let me unpack your claim that "it seems that if X is a predictor of Y, it would be useful in predicting future values of Y based on X, regardless of causality" a little bit. You are correct: If all you want is to be able to... | When can correlation be useful without causation?
There are a lot of good points here already. Let me unpack your claim that "it seems that if X is a predictor of Y, it would be useful in predicting future values of Y based on X, regardless of causa |
9,039 | When can correlation be useful without causation? | They aren't poopooing the importance of correlation. It's just that the tendency is to interpret correlation as causation.
Take breastfeeding as the perfect example. Mothers almost always interpret the (observational studies') findings about breastfeeding as a suggestion as to whether or not they should actually breast... | When can correlation be useful without causation? | They aren't poopooing the importance of correlation. It's just that the tendency is to interpret correlation as causation.
Take breastfeeding as the perfect example. Mothers almost always interpret th | When can correlation be useful without causation?
They aren't poopooing the importance of correlation. It's just that the tendency is to interpret correlation as causation.
Take breastfeeding as the perfect example. Mothers almost always interpret the (observational studies') findings about breastfeeding as a suggestio... | When can correlation be useful without causation?
They aren't poopooing the importance of correlation. It's just that the tendency is to interpret correlation as causation.
Take breastfeeding as the perfect example. Mothers almost always interpret th |
9,040 | When can correlation be useful without causation? | You're right that correlation is useful. The reason that causal models are better than associational models is that — as Pearl says — they are oracles for interventions. In other words, they allow you to reason hypothetically. A causal model answers the question "if I were to make X happen, what would happen to Y?"
... | When can correlation be useful without causation? | You're right that correlation is useful. The reason that causal models are better than associational models is that — as Pearl says — they are oracles for interventions. In other words, they allow y | When can correlation be useful without causation?
You're right that correlation is useful. The reason that causal models are better than associational models is that — as Pearl says — they are oracles for interventions. In other words, they allow you to reason hypothetically. A causal model answers the question "if ... | When can correlation be useful without causation?
You're right that correlation is useful. The reason that causal models are better than associational models is that — as Pearl says — they are oracles for interventions. In other words, they allow y |
9,041 | When can correlation be useful without causation? | You are correct that correlation is useful for prediction. It is also useful for getting a better understanding of the system under study.
One case where knowledge about the causal mechanism is necessary is if the target distribution has been manipulated (e.g. some variables have been "forced" to take certain values). ... | When can correlation be useful without causation? | You are correct that correlation is useful for prediction. It is also useful for getting a better understanding of the system under study.
One case where knowledge about the causal mechanism is necess | When can correlation be useful without causation?
You are correct that correlation is useful for prediction. It is also useful for getting a better understanding of the system under study.
One case where knowledge about the causal mechanism is necessary is if the target distribution has been manipulated (e.g. some vari... | When can correlation be useful without causation?
You are correct that correlation is useful for prediction. It is also useful for getting a better understanding of the system under study.
One case where knowledge about the causal mechanism is necess |
9,042 | When can correlation be useful without causation? | As you stated, correlation alone has plenty of utility, mainly prediction.
The reason this phrase is used (or misused, see my comment up top to the post) so often is that causation is often a much more interesting question. That is to say, if we've spent a lot of effort to examine the relation between $A$ and $B$, it... | When can correlation be useful without causation? | As you stated, correlation alone has plenty of utility, mainly prediction.
The reason this phrase is used (or misused, see my comment up top to the post) so often is that causation is often a much m | When can correlation be useful without causation?
As you stated, correlation alone has plenty of utility, mainly prediction.
The reason this phrase is used (or misused, see my comment up top to the post) so often is that causation is often a much more interesting question. That is to say, if we've spent a lot of effo... | When can correlation be useful without causation?
As you stated, correlation alone has plenty of utility, mainly prediction.
The reason this phrase is used (or misused, see my comment up top to the post) so often is that causation is often a much m |
9,043 | When can correlation be useful without causation? | Correlation is an useful tool if you have an underlying model that explains causality.
For example if you know that applying a force to an object influences its movement, you can measure the correlation between the force and velocity and force and acceleration. The stronger correlation (with the acceleration) will be e... | When can correlation be useful without causation? | Correlation is an useful tool if you have an underlying model that explains causality.
For example if you know that applying a force to an object influences its movement, you can measure the correlati | When can correlation be useful without causation?
Correlation is an useful tool if you have an underlying model that explains causality.
For example if you know that applying a force to an object influences its movement, you can measure the correlation between the force and velocity and force and acceleration. The stro... | When can correlation be useful without causation?
Correlation is an useful tool if you have an underlying model that explains causality.
For example if you know that applying a force to an object influences its movement, you can measure the correlati |
9,044 | When can correlation be useful without causation? | Correlation is an observable phenomenon. You can measure it. You can act on those measurements. On its own, it can be useful.
However, if all you have is a correlation, you do not have any guarantee that a change you make will actually have an effect (see the famous graphs tying the rise of iPhones to overseas slave... | When can correlation be useful without causation? | Correlation is an observable phenomenon. You can measure it. You can act on those measurements. On its own, it can be useful.
However, if all you have is a correlation, you do not have any guarante | When can correlation be useful without causation?
Correlation is an observable phenomenon. You can measure it. You can act on those measurements. On its own, it can be useful.
However, if all you have is a correlation, you do not have any guarantee that a change you make will actually have an effect (see the famous ... | When can correlation be useful without causation?
Correlation is an observable phenomenon. You can measure it. You can act on those measurements. On its own, it can be useful.
However, if all you have is a correlation, you do not have any guarante |
9,045 | When can correlation be useful without causation? | There's value in correlation, but one should look at more evidence to conclude causation.
Years ago, there was a study resulting in "coffee causes cancer." As soon as I heard this on the news I told my wife "false correlation." It turned out I was correct. The 2-3 cup per day coffee population had a higher rate of smo... | When can correlation be useful without causation? | There's value in correlation, but one should look at more evidence to conclude causation.
Years ago, there was a study resulting in "coffee causes cancer." As soon as I heard this on the news I told | When can correlation be useful without causation?
There's value in correlation, but one should look at more evidence to conclude causation.
Years ago, there was a study resulting in "coffee causes cancer." As soon as I heard this on the news I told my wife "false correlation." It turned out I was correct. The 2-3 cup ... | When can correlation be useful without causation?
There's value in correlation, but one should look at more evidence to conclude causation.
Years ago, there was a study resulting in "coffee causes cancer." As soon as I heard this on the news I told |
9,046 | Probability of being born on a leap day? | To accurately predict that probability using statistics, it would be helpful to know where the birth took place.
This page http://chmullig.com/2012/06/births-by-day-of-year/ has a graph showing a subset of the number of births per day (multiplying the 29th by 4, which is incorrect, and undesirable for this question, bu... | Probability of being born on a leap day? | To accurately predict that probability using statistics, it would be helpful to know where the birth took place.
This page http://chmullig.com/2012/06/births-by-day-of-year/ has a graph showing a subs | Probability of being born on a leap day?
To accurately predict that probability using statistics, it would be helpful to know where the birth took place.
This page http://chmullig.com/2012/06/births-by-day-of-year/ has a graph showing a subset of the number of births per day (multiplying the 29th by 4, which is incorre... | Probability of being born on a leap day?
To accurately predict that probability using statistics, it would be helpful to know where the birth took place.
This page http://chmullig.com/2012/06/births-by-day-of-year/ has a graph showing a subs |
9,047 | Probability of being born on a leap day? | Sure. See here for a more detailed explanation: http://www.public.iastate.edu/~mlamias/LeapYear.pdf.
But essentially the author concludes, "There are 485 leap years in 2 millennia. So, in 2 millennia, there are $485(366) + (2000-485)(365)= 730485$ total days. Of those days, February 29 occurs in 485 of them (the lea... | Probability of being born on a leap day? | Sure. See here for a more detailed explanation: http://www.public.iastate.edu/~mlamias/LeapYear.pdf.
But essentially the author concludes, "There are 485 leap years in 2 millennia. So, in 2 millenni | Probability of being born on a leap day?
Sure. See here for a more detailed explanation: http://www.public.iastate.edu/~mlamias/LeapYear.pdf.
But essentially the author concludes, "There are 485 leap years in 2 millennia. So, in 2 millennia, there are $485(366) + (2000-485)(365)= 730485$ total days. Of those days, F... | Probability of being born on a leap day?
Sure. See here for a more detailed explanation: http://www.public.iastate.edu/~mlamias/LeapYear.pdf.
But essentially the author concludes, "There are 485 leap years in 2 millennia. So, in 2 millenni |
9,048 | Probability of being born on a leap day? | I think the answer to this question can only be empirical. Any theoretical answer would be flawed without accounting birthday selection phenomena, seasonality etc. These things are impossible to deal with theoretically.
The birthday data is hard to find in US for privacy reasons. There's one anonymous data set here. It... | Probability of being born on a leap day? | I think the answer to this question can only be empirical. Any theoretical answer would be flawed without accounting birthday selection phenomena, seasonality etc. These things are impossible to deal | Probability of being born on a leap day?
I think the answer to this question can only be empirical. Any theoretical answer would be flawed without accounting birthday selection phenomena, seasonality etc. These things are impossible to deal with theoretically.
The birthday data is hard to find in US for privacy reasons... | Probability of being born on a leap day?
I think the answer to this question can only be empirical. Any theoretical answer would be flawed without accounting birthday selection phenomena, seasonality etc. These things are impossible to deal |
9,049 | Probability of being born on a leap day? | My all-time favorite cover to a book provides some highly relevant evidence against the assumption of a uniform allocation of births to dates. Specifically that births in the US since 1970 exhibit several trends superimposed on each other: a long, multi-decade trend, a non-periodic trend, day-of-week trends, day-of-yea... | Probability of being born on a leap day? | My all-time favorite cover to a book provides some highly relevant evidence against the assumption of a uniform allocation of births to dates. Specifically that births in the US since 1970 exhibit sev | Probability of being born on a leap day?
My all-time favorite cover to a book provides some highly relevant evidence against the assumption of a uniform allocation of births to dates. Specifically that births in the US since 1970 exhibit several trends superimposed on each other: a long, multi-decade trend, a non-perio... | Probability of being born on a leap day?
My all-time favorite cover to a book provides some highly relevant evidence against the assumption of a uniform allocation of births to dates. Specifically that births in the US since 1970 exhibit sev |
9,050 | Probability of being born on a leap day? | February 29th is a date that occurs each year that is a multiple of 4.
However years that are a multiple of 100 but aren't one of 400, are not considered as leap years (E.g: 1900 is not a leap year while 2000 or 1600 are). Therefore, nowadays, it is the same pattern every 400 years.
So let's do the maths on a [0;400[ i... | Probability of being born on a leap day? | February 29th is a date that occurs each year that is a multiple of 4.
However years that are a multiple of 100 but aren't one of 400, are not considered as leap years (E.g: 1900 is not a leap year wh | Probability of being born on a leap day?
February 29th is a date that occurs each year that is a multiple of 4.
However years that are a multiple of 100 but aren't one of 400, are not considered as leap years (E.g: 1900 is not a leap year while 2000 or 1600 are). Therefore, nowadays, it is the same pattern every 400 ye... | Probability of being born on a leap day?
February 29th is a date that occurs each year that is a multiple of 4.
However years that are a multiple of 100 but aren't one of 400, are not considered as leap years (E.g: 1900 is not a leap year wh |
9,051 | Probability of being born on a leap day? | I believe there are two questions being mixed up here. The one is "What is the probability of any given day being a Feb. 29th?". The second one is (and the one actually asked) "What is the probability of being born on a leap day?"
The approach of simply counting days seems to be misleading as Aksakal is pointing it. Co... | Probability of being born on a leap day? | I believe there are two questions being mixed up here. The one is "What is the probability of any given day being a Feb. 29th?". The second one is (and the one actually asked) "What is the probability | Probability of being born on a leap day?
I believe there are two questions being mixed up here. The one is "What is the probability of any given day being a Feb. 29th?". The second one is (and the one actually asked) "What is the probability of being born on a leap day?"
The approach of simply counting days seems to be... | Probability of being born on a leap day?
I believe there are two questions being mixed up here. The one is "What is the probability of any given day being a Feb. 29th?". The second one is (and the one actually asked) "What is the probability |
9,052 | Probability of being born on a leap day? | I've noticed that most of the answers above work this out by calculating the number of leap days in a particular period. There is a simpler way to get the answer, 100% accurately, by definition:
We use leap years to adjust the regular (365 day) calendar to the mean tropical year (aka mean solar year). The mean tropical... | Probability of being born on a leap day? | I've noticed that most of the answers above work this out by calculating the number of leap days in a particular period. There is a simpler way to get the answer, 100% accurately, by definition:
We us | Probability of being born on a leap day?
I've noticed that most of the answers above work this out by calculating the number of leap days in a particular period. There is a simpler way to get the answer, 100% accurately, by definition:
We use leap years to adjust the regular (365 day) calendar to the mean tropical year... | Probability of being born on a leap day?
I've noticed that most of the answers above work this out by calculating the number of leap days in a particular period. There is a simpler way to get the answer, 100% accurately, by definition:
We us |
9,053 | Probability of being born on a leap day? | I asked my sister, whose bithday is February 29, and she said, "The result of my own empirical study was that it is 1.00, obviously." | Probability of being born on a leap day? | I asked my sister, whose bithday is February 29, and she said, "The result of my own empirical study was that it is 1.00, obviously." | Probability of being born on a leap day?
I asked my sister, whose bithday is February 29, and she said, "The result of my own empirical study was that it is 1.00, obviously." | Probability of being born on a leap day?
I asked my sister, whose bithday is February 29, and she said, "The result of my own empirical study was that it is 1.00, obviously." |
9,054 | Why not use the third derivative for numerical optimization? | I am interpreting the question as being "Why does Newton's method only use first and second derivatives, not third or higher derivatives?"
Actually, in many cases, going to the third derivative does help; I've done it with custom stuff before. However, in general, going to higher derivatives adds computational complex... | Why not use the third derivative for numerical optimization? | I am interpreting the question as being "Why does Newton's method only use first and second derivatives, not third or higher derivatives?"
Actually, in many cases, going to the third derivative does h | Why not use the third derivative for numerical optimization?
I am interpreting the question as being "Why does Newton's method only use first and second derivatives, not third or higher derivatives?"
Actually, in many cases, going to the third derivative does help; I've done it with custom stuff before. However, in ge... | Why not use the third derivative for numerical optimization?
I am interpreting the question as being "Why does Newton's method only use first and second derivatives, not third or higher derivatives?"
Actually, in many cases, going to the third derivative does h |
9,055 | Why not use the third derivative for numerical optimization? | I don't really see what the statistical aspect of this question is, so I'll answer the optimization part.
There are 2 parts to convergence: iteration cost & iteration count
Pretty much every answer here is focusing on just the iteration cost and ignoring the iteration count. But both of them matter. An method that iter... | Why not use the third derivative for numerical optimization? | I don't really see what the statistical aspect of this question is, so I'll answer the optimization part.
There are 2 parts to convergence: iteration cost & iteration count
Pretty much every answer he | Why not use the third derivative for numerical optimization?
I don't really see what the statistical aspect of this question is, so I'll answer the optimization part.
There are 2 parts to convergence: iteration cost & iteration count
Pretty much every answer here is focusing on just the iteration cost and ignoring the ... | Why not use the third derivative for numerical optimization?
I don't really see what the statistical aspect of this question is, so I'll answer the optimization part.
There are 2 parts to convergence: iteration cost & iteration count
Pretty much every answer he |
9,056 | Why not use the third derivative for numerical optimization? | Even calculating Hessians is quite a bit of work:
$$H = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2... | Why not use the third derivative for numerical optimization? | Even calculating Hessians is quite a bit of work:
$$H = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\parti | Why not use the third derivative for numerical optimization?
Even calculating Hessians is quite a bit of work:
$$H = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
\dfrac{\partial^2 f}{\par... | Why not use the third derivative for numerical optimization?
Even calculating Hessians is quite a bit of work:
$$H = \begin{bmatrix}
\dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\parti |
9,057 | Why not use the third derivative for numerical optimization? | Typically, when you analyze the effectiveness of such algorithms, you'll find results such as one step of a fourth order algorithm having roughly the same effectiveness as two steps of a second order algorithm.
So the choice of which algorithm to use is relatively simple: if one step of the fourth order algorithm takes... | Why not use the third derivative for numerical optimization? | Typically, when you analyze the effectiveness of such algorithms, you'll find results such as one step of a fourth order algorithm having roughly the same effectiveness as two steps of a second order | Why not use the third derivative for numerical optimization?
Typically, when you analyze the effectiveness of such algorithms, you'll find results such as one step of a fourth order algorithm having roughly the same effectiveness as two steps of a second order algorithm.
So the choice of which algorithm to use is relat... | Why not use the third derivative for numerical optimization?
Typically, when you analyze the effectiveness of such algorithms, you'll find results such as one step of a fourth order algorithm having roughly the same effectiveness as two steps of a second order |
9,058 | Why not use the third derivative for numerical optimization? | You can think of the order of derivatives as the order of a polynomial approximation to the function. Most optimization routines rely on convexity. A quadratic polynomial will be convex/concave everywhere whereas a 3rd order or higher polynomial will not be convex everywhere. Most optimization routines rely on successi... | Why not use the third derivative for numerical optimization? | You can think of the order of derivatives as the order of a polynomial approximation to the function. Most optimization routines rely on convexity. A quadratic polynomial will be convex/concave everyw | Why not use the third derivative for numerical optimization?
You can think of the order of derivatives as the order of a polynomial approximation to the function. Most optimization routines rely on convexity. A quadratic polynomial will be convex/concave everywhere whereas a 3rd order or higher polynomial will not be c... | Why not use the third derivative for numerical optimization?
You can think of the order of derivatives as the order of a polynomial approximation to the function. Most optimization routines rely on convexity. A quadratic polynomial will be convex/concave everyw |
9,059 | Why not use the third derivative for numerical optimization? | Let me be the only one here defending 3rd order methods for SGD convergence, but definitely not in the entire space what would need $\approx dim^3/6$ coefficients, but e.g. in just a single direction, which needs only a single additional coefficient if already having 2nd order model in this direction.
Why single direct... | Why not use the third derivative for numerical optimization? | Let me be the only one here defending 3rd order methods for SGD convergence, but definitely not in the entire space what would need $\approx dim^3/6$ coefficients, but e.g. in just a single direction, | Why not use the third derivative for numerical optimization?
Let me be the only one here defending 3rd order methods for SGD convergence, but definitely not in the entire space what would need $\approx dim^3/6$ coefficients, but e.g. in just a single direction, which needs only a single additional coefficient if alread... | Why not use the third derivative for numerical optimization?
Let me be the only one here defending 3rd order methods for SGD convergence, but definitely not in the entire space what would need $\approx dim^3/6$ coefficients, but e.g. in just a single direction, |
9,060 | Where does the offset go in Poisson/negative binomial regression? [duplicate] | Recall that an offset is just a predictor variable whose coefficient is fixed at 1. So, using the standard setup for a Poisson regression with a log link, we have:
$$\log \mathrm{E}(Y) = \beta' \mathrm{X} + \log \mathcal{E}$$
where $\mathcal{E}$ is the offset/exposure variable. This can be rewritten as
$$\log \mathrm{E... | Where does the offset go in Poisson/negative binomial regression? [duplicate] | Recall that an offset is just a predictor variable whose coefficient is fixed at 1. So, using the standard setup for a Poisson regression with a log link, we have:
$$\log \mathrm{E}(Y) = \beta' \mathr | Where does the offset go in Poisson/negative binomial regression? [duplicate]
Recall that an offset is just a predictor variable whose coefficient is fixed at 1. So, using the standard setup for a Poisson regression with a log link, we have:
$$\log \mathrm{E}(Y) = \beta' \mathrm{X} + \log \mathcal{E}$$
where $\mathcal{... | Where does the offset go in Poisson/negative binomial regression? [duplicate]
Recall that an offset is just a predictor variable whose coefficient is fixed at 1. So, using the standard setup for a Poisson regression with a log link, we have:
$$\log \mathrm{E}(Y) = \beta' \mathr |
9,061 | Where does the offset go in Poisson/negative binomial regression? [duplicate] | The offset does act similarly for both Poisson and NB. The offset has two functions. For Poisson models, the actual number of events defines the variance, so that's needed. It also provides the denominator, so you can compare rates. It's unite-less.
Just using a ratio will mess up the standard errors. Having a m... | Where does the offset go in Poisson/negative binomial regression? [duplicate] | The offset does act similarly for both Poisson and NB. The offset has two functions. For Poisson models, the actual number of events defines the variance, so that's needed. It also provides the den | Where does the offset go in Poisson/negative binomial regression? [duplicate]
The offset does act similarly for both Poisson and NB. The offset has two functions. For Poisson models, the actual number of events defines the variance, so that's needed. It also provides the denominator, so you can compare rates. It's ... | Where does the offset go in Poisson/negative binomial regression? [duplicate]
The offset does act similarly for both Poisson and NB. The offset has two functions. For Poisson models, the actual number of events defines the variance, so that's needed. It also provides the den |
9,062 | Sufficient statistics for layman | A sufficient statistic summarizes all the information contained in a sample so that you would make the same parameter estimate whether we gave you the sample or just the statistic itself. It's reduction of the data without information loss.
Here's one example. Suppose $X$ has a symmetric distribution about zero. Instea... | Sufficient statistics for layman | A sufficient statistic summarizes all the information contained in a sample so that you would make the same parameter estimate whether we gave you the sample or just the statistic itself. It's reducti | Sufficient statistics for layman
A sufficient statistic summarizes all the information contained in a sample so that you would make the same parameter estimate whether we gave you the sample or just the statistic itself. It's reduction of the data without information loss.
Here's one example. Suppose $X$ has a symmetri... | Sufficient statistics for layman
A sufficient statistic summarizes all the information contained in a sample so that you would make the same parameter estimate whether we gave you the sample or just the statistic itself. It's reducti |
9,063 | Sufficient statistics for layman | In Bayesian terms, you have some observable property $X$ and a parameter $\Theta$. The joint distribution for $X,\Theta$ is specified, but factored as the conditional distribution of $X\mid \Theta$ and the prior distribution of $\Theta$. A statistic $T$ is sufficient for this model if and only if the posterior distribu... | Sufficient statistics for layman | In Bayesian terms, you have some observable property $X$ and a parameter $\Theta$. The joint distribution for $X,\Theta$ is specified, but factored as the conditional distribution of $X\mid \Theta$ an | Sufficient statistics for layman
In Bayesian terms, you have some observable property $X$ and a parameter $\Theta$. The joint distribution for $X,\Theta$ is specified, but factored as the conditional distribution of $X\mid \Theta$ and the prior distribution of $\Theta$. A statistic $T$ is sufficient for this model if a... | Sufficient statistics for layman
In Bayesian terms, you have some observable property $X$ and a parameter $\Theta$. The joint distribution for $X,\Theta$ is specified, but factored as the conditional distribution of $X\mid \Theta$ an |
9,064 | Sufficient statistics for layman | Say you have a coin, and you don't know whether it's fair or not. In other words, it has probability $p$ of coming up heads ($H$) and $1 - p$ of coming up tails ($T$), and you don't know the value of $p$.
You try to get an idea of the value of $p$ by tossing the coin several times, say $n$ times.
Let's say $n = 5$ and ... | Sufficient statistics for layman | Say you have a coin, and you don't know whether it's fair or not. In other words, it has probability $p$ of coming up heads ($H$) and $1 - p$ of coming up tails ($T$), and you don't know the value of | Sufficient statistics for layman
Say you have a coin, and you don't know whether it's fair or not. In other words, it has probability $p$ of coming up heads ($H$) and $1 - p$ of coming up tails ($T$), and you don't know the value of $p$.
You try to get an idea of the value of $p$ by tossing the coin several times, say ... | Sufficient statistics for layman
Say you have a coin, and you don't know whether it's fair or not. In other words, it has probability $p$ of coming up heads ($H$) and $1 - p$ of coming up tails ($T$), and you don't know the value of |
9,065 | What is the definition of Top-n accuracy? | In top-5 accuracy you give yourself credit for having the right answer if the right answer appears in your top five guesses. | What is the definition of Top-n accuracy? | In top-5 accuracy you give yourself credit for having the right answer if the right answer appears in your top five guesses. | What is the definition of Top-n accuracy?
In top-5 accuracy you give yourself credit for having the right answer if the right answer appears in your top five guesses. | What is the definition of Top-n accuracy?
In top-5 accuracy you give yourself credit for having the right answer if the right answer appears in your top five guesses. |
9,066 | What is the definition of Top-n accuracy? | I found this explanation by one Nathan Yan on Quora
Top-N accuracy means that the correct class gets to be in the Top-N probabilities for it to count as “correct”. As an example, suppose I have a data set of images and the images are a:
Dog
Cat
Dog
Bird
Cat
Cat
Mouse
Penguin
For each of these input images, the model ... | What is the definition of Top-n accuracy? | I found this explanation by one Nathan Yan on Quora
Top-N accuracy means that the correct class gets to be in the Top-N probabilities for it to count as “correct”. As an example, suppose I have a data | What is the definition of Top-n accuracy?
I found this explanation by one Nathan Yan on Quora
Top-N accuracy means that the correct class gets to be in the Top-N probabilities for it to count as “correct”. As an example, suppose I have a data set of images and the images are a:
Dog
Cat
Dog
Bird
Cat
Cat
Mouse
Penguin
... | What is the definition of Top-n accuracy?
I found this explanation by one Nathan Yan on Quora
Top-N accuracy means that the correct class gets to be in the Top-N probabilities for it to count as “correct”. As an example, suppose I have a data |
9,067 | Time taken to hit a pattern of heads and tails in a series of coin-tosses | Think about what happens the first time you get an H followed by a T.
Case 1: you're looking for H-T-H, and you've seen H-T for the first time. If the next toss is H, you're done. If it's T, you're back to square one: since the last two tosses were T-T you now need the full H-T-H.
Case 2: you're looking for H-T-T, and ... | Time taken to hit a pattern of heads and tails in a series of coin-tosses | Think about what happens the first time you get an H followed by a T.
Case 1: you're looking for H-T-H, and you've seen H-T for the first time. If the next toss is H, you're done. If it's T, you're ba | Time taken to hit a pattern of heads and tails in a series of coin-tosses
Think about what happens the first time you get an H followed by a T.
Case 1: you're looking for H-T-H, and you've seen H-T for the first time. If the next toss is H, you're done. If it's T, you're back to square one: since the last two tosses we... | Time taken to hit a pattern of heads and tails in a series of coin-tosses
Think about what happens the first time you get an H followed by a T.
Case 1: you're looking for H-T-H, and you've seen H-T for the first time. If the next toss is H, you're done. If it's T, you're ba |
9,068 | Time taken to hit a pattern of heads and tails in a series of coin-tosses | I like to draw pictures.
These diagrams are finite state automata (FSAs). They are tiny children's games (like Chutes and Ladders) that "recognize" or "accept" the HTT and HTH sequences, respectively, by moving a token from one node to another in response to the coin flips. The token begins at the top node, pointed ... | Time taken to hit a pattern of heads and tails in a series of coin-tosses | I like to draw pictures.
These diagrams are finite state automata (FSAs). They are tiny children's games (like Chutes and Ladders) that "recognize" or "accept" the HTT and HTH sequences, respectivel | Time taken to hit a pattern of heads and tails in a series of coin-tosses
I like to draw pictures.
These diagrams are finite state automata (FSAs). They are tiny children's games (like Chutes and Ladders) that "recognize" or "accept" the HTT and HTH sequences, respectively, by moving a token from one node to another ... | Time taken to hit a pattern of heads and tails in a series of coin-tosses
I like to draw pictures.
These diagrams are finite state automata (FSAs). They are tiny children's games (like Chutes and Ladders) that "recognize" or "accept" the HTT and HTH sequences, respectivel |
9,069 | Time taken to hit a pattern of heads and tails in a series of coin-tosses | Suppose you toss the coin $8n+2$ times and count the number of times you see a "HTH" pattern (including overlaps). The expected number is $n$. But it is also $n$ for "HTT". Since $HTH$ can overlap itself and "HTT" cannot, you would expect more clumping with "HTH", which increases the expected time for the first app... | Time taken to hit a pattern of heads and tails in a series of coin-tosses | Suppose you toss the coin $8n+2$ times and count the number of times you see a "HTH" pattern (including overlaps). The expected number is $n$. But it is also $n$ for "HTT". Since $HTH$ can overlap | Time taken to hit a pattern of heads and tails in a series of coin-tosses
Suppose you toss the coin $8n+2$ times and count the number of times you see a "HTH" pattern (including overlaps). The expected number is $n$. But it is also $n$ for "HTT". Since $HTH$ can overlap itself and "HTT" cannot, you would expect mor... | Time taken to hit a pattern of heads and tails in a series of coin-tosses
Suppose you toss the coin $8n+2$ times and count the number of times you see a "HTH" pattern (including overlaps). The expected number is $n$. But it is also $n$ for "HTT". Since $HTH$ can overlap |
9,070 | Time taken to hit a pattern of heads and tails in a series of coin-tosses | Some great answers. I'd like to take a slightly different tack, and address the question of counter-intuitivity. (I quite agree, BTW)
Here's how I make sense of it. Imagine a column of random sequential coin-toss results printed on a paper tape, consisting of the letters "H" and "T".
Arbitrarily tear off a section of t... | Time taken to hit a pattern of heads and tails in a series of coin-tosses | Some great answers. I'd like to take a slightly different tack, and address the question of counter-intuitivity. (I quite agree, BTW)
Here's how I make sense of it. Imagine a column of random sequenti | Time taken to hit a pattern of heads and tails in a series of coin-tosses
Some great answers. I'd like to take a slightly different tack, and address the question of counter-intuitivity. (I quite agree, BTW)
Here's how I make sense of it. Imagine a column of random sequential coin-toss results printed on a paper tape, ... | Time taken to hit a pattern of heads and tails in a series of coin-tosses
Some great answers. I'd like to take a slightly different tack, and address the question of counter-intuitivity. (I quite agree, BTW)
Here's how I make sense of it. Imagine a column of random sequenti |
9,071 | Time taken to hit a pattern of heads and tails in a series of coin-tosses | I was looking for the intuition to this in the integer case (as I'm slogging through Ross' Intro. to Probability Models). So I was thinking about integer cases. I found this helped:
Let $A$ be the symbol needed to begin the pattern I'm waiting for.
Let $B$ be the symbol needed to complete the pattern I'm waiting for.
I... | Time taken to hit a pattern of heads and tails in a series of coin-tosses | I was looking for the intuition to this in the integer case (as I'm slogging through Ross' Intro. to Probability Models). So I was thinking about integer cases. I found this helped:
Let $A$ be the sym | Time taken to hit a pattern of heads and tails in a series of coin-tosses
I was looking for the intuition to this in the integer case (as I'm slogging through Ross' Intro. to Probability Models). So I was thinking about integer cases. I found this helped:
Let $A$ be the symbol needed to begin the pattern I'm waiting fo... | Time taken to hit a pattern of heads and tails in a series of coin-tosses
I was looking for the intuition to this in the integer case (as I'm slogging through Ross' Intro. to Probability Models). So I was thinking about integer cases. I found this helped:
Let $A$ be the sym |
9,072 | Who is Gail Gasram? | It looks like "Gail Gasram" is "Marsaglia G" (George Marsaglia's surname and first initial) spelled backwards. | Who is Gail Gasram? | It looks like "Gail Gasram" is "Marsaglia G" (George Marsaglia's surname and first initial) spelled backwards. | Who is Gail Gasram?
It looks like "Gail Gasram" is "Marsaglia G" (George Marsaglia's surname and first initial) spelled backwards. | Who is Gail Gasram?
It looks like "Gail Gasram" is "Marsaglia G" (George Marsaglia's surname and first initial) spelled backwards. |
9,073 | Who is Gail Gasram? | Diehard Code
After some extensive digging, it appears that Gail Gasram participated in developing Diehard code, which represented a suite of programs for testing random number generators. Furthermore, the project was developed at Florida State University, being supported by a grant from the U.S. National Science Founda... | Who is Gail Gasram? | Diehard Code
After some extensive digging, it appears that Gail Gasram participated in developing Diehard code, which represented a suite of programs for testing random number generators. Furthermore, | Who is Gail Gasram?
Diehard Code
After some extensive digging, it appears that Gail Gasram participated in developing Diehard code, which represented a suite of programs for testing random number generators. Furthermore, the project was developed at Florida State University, being supported by a grant from the U.S. Nat... | Who is Gail Gasram?
Diehard Code
After some extensive digging, it appears that Gail Gasram participated in developing Diehard code, which represented a suite of programs for testing random number generators. Furthermore, |
9,074 | Estimating a distribution based on three percentiles | Using a purely statistical method to do this work will provide absolutely no additional information about the distribution of school spending: the result will merely reflect an arbitrary choice of algorithm.
You need more data.
This is easy to come by: use data from previous years, from comparable districts, whatever. ... | Estimating a distribution based on three percentiles | Using a purely statistical method to do this work will provide absolutely no additional information about the distribution of school spending: the result will merely reflect an arbitrary choice of alg | Estimating a distribution based on three percentiles
Using a purely statistical method to do this work will provide absolutely no additional information about the distribution of school spending: the result will merely reflect an arbitrary choice of algorithm.
You need more data.
This is easy to come by: use data from ... | Estimating a distribution based on three percentiles
Using a purely statistical method to do this work will provide absolutely no additional information about the distribution of school spending: the result will merely reflect an arbitrary choice of alg |
9,075 | Estimating a distribution based on three percentiles | As @whuber pointed out, statistical methods do not exactly work here. You need to infer the distribution from other sources. When you know the distribution you have a non-linear equation solving exercise. Denote by $f$ the quantile function of your chosen probability distribution with parameter vector $\theta$. What yo... | Estimating a distribution based on three percentiles | As @whuber pointed out, statistical methods do not exactly work here. You need to infer the distribution from other sources. When you know the distribution you have a non-linear equation solving exerc | Estimating a distribution based on three percentiles
As @whuber pointed out, statistical methods do not exactly work here. You need to infer the distribution from other sources. When you know the distribution you have a non-linear equation solving exercise. Denote by $f$ the quantile function of your chosen probability... | Estimating a distribution based on three percentiles
As @whuber pointed out, statistical methods do not exactly work here. You need to infer the distribution from other sources. When you know the distribution you have a non-linear equation solving exerc |
9,076 | Estimating a distribution based on three percentiles | Try the rriskDistributions package, and -- if you are sure about the lognormal distribution family -- use the command
get.lnorm.par(p=c(0.05,0.5,0.95),q=c(8.135,11.259,23.611))
which should solve your problem. Use fit.perc instead if you do not want to restrict to one known pdf. | Estimating a distribution based on three percentiles | Try the rriskDistributions package, and -- if you are sure about the lognormal distribution family -- use the command
get.lnorm.par(p=c(0.05,0.5,0.95),q=c(8.135,11.259,23.611))
which should solve you | Estimating a distribution based on three percentiles
Try the rriskDistributions package, and -- if you are sure about the lognormal distribution family -- use the command
get.lnorm.par(p=c(0.05,0.5,0.95),q=c(8.135,11.259,23.611))
which should solve your problem. Use fit.perc instead if you do not want to restrict to o... | Estimating a distribution based on three percentiles
Try the rriskDistributions package, and -- if you are sure about the lognormal distribution family -- use the command
get.lnorm.par(p=c(0.05,0.5,0.95),q=c(8.135,11.259,23.611))
which should solve you |
9,077 | Estimating a distribution based on three percentiles | For a lognormal the ratio of the 95th percentile to the median is the same as the ratio of the median to the 5th percentile. That's not even nearly true here so lognormal wouldn't be a good fit.
You have enough information to fit a distribution with three parameters, and you clearly need a skew distribution. For analyt... | Estimating a distribution based on three percentiles | For a lognormal the ratio of the 95th percentile to the median is the same as the ratio of the median to the 5th percentile. That's not even nearly true here so lognormal wouldn't be a good fit.
You h | Estimating a distribution based on three percentiles
For a lognormal the ratio of the 95th percentile to the median is the same as the ratio of the median to the 5th percentile. That's not even nearly true here so lognormal wouldn't be a good fit.
You have enough information to fit a distribution with three parameters,... | Estimating a distribution based on three percentiles
For a lognormal the ratio of the 95th percentile to the median is the same as the ratio of the median to the 5th percentile. That's not even nearly true here so lognormal wouldn't be a good fit.
You h |
9,078 | Estimating a distribution based on three percentiles | About the only things you can infer from the data is that the distribution is nonsymmetric. You can't even tell whether those quantiles came from a fitted distribution or just the ecdf.
If they came from a fitted distribution, you could try all the distributions you can think of and see if any match. If not, there's no... | Estimating a distribution based on three percentiles | About the only things you can infer from the data is that the distribution is nonsymmetric. You can't even tell whether those quantiles came from a fitted distribution or just the ecdf.
If they came f | Estimating a distribution based on three percentiles
About the only things you can infer from the data is that the distribution is nonsymmetric. You can't even tell whether those quantiles came from a fitted distribution or just the ecdf.
If they came from a fitted distribution, you could try all the distributions you ... | Estimating a distribution based on three percentiles
About the only things you can infer from the data is that the distribution is nonsymmetric. You can't even tell whether those quantiles came from a fitted distribution or just the ecdf.
If they came f |
9,079 | Estimating a distribution based on three percentiles | The use of quantiles to estimate parameters of a priori distributions is discussed in the literature on human response time measurement as "quantile maximum probability estimation" (QMPE, though originally erroneously dubbed "quantile maximum likelihood estimation", QMLE), discussed at length by Heathcote and colleague... | Estimating a distribution based on three percentiles | The use of quantiles to estimate parameters of a priori distributions is discussed in the literature on human response time measurement as "quantile maximum probability estimation" (QMPE, though origi | Estimating a distribution based on three percentiles
The use of quantiles to estimate parameters of a priori distributions is discussed in the literature on human response time measurement as "quantile maximum probability estimation" (QMPE, though originally erroneously dubbed "quantile maximum likelihood estimation", ... | Estimating a distribution based on three percentiles
The use of quantiles to estimate parameters of a priori distributions is discussed in the literature on human response time measurement as "quantile maximum probability estimation" (QMPE, though origi |
9,080 | Estimating a distribution based on three percentiles | You can use your percentile information to simulate the data in some way and use the R package "logspline" to estimate the distribution nonparametrically. Below is my function that employs a method like this.
calc.dist.from.median.and.range <- function(m, r)
{
## PURPOSE: Return a Log-Logspline Distribution giv... | Estimating a distribution based on three percentiles | You can use your percentile information to simulate the data in some way and use the R package "logspline" to estimate the distribution nonparametrically. Below is my function that employs a method | Estimating a distribution based on three percentiles
You can use your percentile information to simulate the data in some way and use the R package "logspline" to estimate the distribution nonparametrically. Below is my function that employs a method like this.
calc.dist.from.median.and.range <- function(m, r)
{
... | Estimating a distribution based on three percentiles
You can use your percentile information to simulate the data in some way and use the R package "logspline" to estimate the distribution nonparametrically. Below is my function that employs a method |
9,081 | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [closed] | There must be some features in your training set with class 'char' .
Please check this
> a <- c("1", "2",letters[1:5], "3")
> as.numeric(a)
[1] 1 2 NA NA NA NA NA 3
Warning message:
NAs introduced by coercion | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [clos | There must be some features in your training set with class 'char' .
Please check this
> a <- c("1", "2",letters[1:5], "3")
> as.numeric(a)
[1] 1 2 NA NA NA NA NA 3
Warning message:
NAs introduced | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [closed]
There must be some features in your training set with class 'char' .
Please check this
> a <- c("1", "2",letters[1:5], "3")
> as.numeric(a)
[1] 1 2 NA NA NA NA NA 3
Warning message:
NAs introduced by coercion | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [clos
There must be some features in your training set with class 'char' .
Please check this
> a <- c("1", "2",letters[1:5], "3")
> as.numeric(a)
[1] 1 2 NA NA NA NA NA 3
Warning message:
NAs introduced |
9,082 | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [closed] | Probably the cause is you have some character variables in your data frame.
Convert all character variable into factor in one line:
library(dplyr)
data_fac=data_char %>% mutate_if(is.character, as.factor) | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [clos | Probably the cause is you have some character variables in your data frame.
Convert all character variable into factor in one line:
library(dplyr)
data_fac=data_char %>% mutate_if(is.character, as.fa | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [closed]
Probably the cause is you have some character variables in your data frame.
Convert all character variable into factor in one line:
library(dplyr)
data_fac=data_char %>% mutate_if(is.character, as.factor) | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [clos
Probably the cause is you have some character variables in your data frame.
Convert all character variable into factor in one line:
library(dplyr)
data_fac=data_char %>% mutate_if(is.character, as.fa |
9,083 | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [closed] | As shown in the warning there were 28 errors which happened to be the number of columns with character datatypes ("chr"). Forcing these columns to factors allowed for the run to commence. | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [clos | As shown in the warning there were 28 errors which happened to be the number of columns with character datatypes ("chr"). Forcing these columns to factors allowed for the run to commence. | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [closed]
As shown in the warning there were 28 errors which happened to be the number of columns with character datatypes ("chr"). Forcing these columns to factors allowed for the run to commence. | R: Random Forest throwing NaN/Inf in "foreign function call" error despite no NaN's in dataset [clos
As shown in the warning there were 28 errors which happened to be the number of columns with character datatypes ("chr"). Forcing these columns to factors allowed for the run to commence. |
9,084 | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in achievement by teaching better? | You are right in suspecting that your professor misunderstood.
The correct answer is that we cannot say anything whatsoever about the percentage improvement in student achievement driven by teacher expertise. Nothing at all.
Why is this so? The quote is in terms of variance explained. Variance explained has nothing to ... | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in a | You are right in suspecting that your professor misunderstood.
The correct answer is that we cannot say anything whatsoever about the percentage improvement in student achievement driven by teacher ex | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in achievement by teaching better?
You are right in suspecting that your professor misunderstood.
The correct answer is that we cannot say anything whatsoever about the percentage improvement in student achievement driven by... | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in a
You are right in suspecting that your professor misunderstood.
The correct answer is that we cannot say anything whatsoever about the percentage improvement in student achievement driven by teacher ex |
9,085 | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in achievement by teaching better? | The Hattie 2003 paper mentions a simple form of hierarchical linear modelling ignoring interactions. The paper’s description of the 30% isn’t particularly thorough, with broken links in the references making it difficult to see where the number even came from. I assume his approach relied on partial R-squared.
The answ... | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in a | The Hattie 2003 paper mentions a simple form of hierarchical linear modelling ignoring interactions. The paper’s description of the 30% isn’t particularly thorough, with broken links in the references | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in achievement by teaching better?
The Hattie 2003 paper mentions a simple form of hierarchical linear modelling ignoring interactions. The paper’s description of the 30% isn’t particularly thorough, with broken links in the... | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in a
The Hattie 2003 paper mentions a simple form of hierarchical linear modelling ignoring interactions. The paper’s description of the 30% isn’t particularly thorough, with broken links in the references |
9,086 | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in achievement by teaching better? | You write '"Teaching expertise accounts for about 30 percent of the variance in student achievement" means that a teacher is responsible for 30% of what a student achieves.'
A better formulation would be "A teacher is responsible for 30% of the difference in performance between students".
In other words, if the average... | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in a | You write '"Teaching expertise accounts for about 30 percent of the variance in student achievement" means that a teacher is responsible for 30% of what a student achieves.'
A better formulation would | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in achievement by teaching better?
You write '"Teaching expertise accounts for about 30 percent of the variance in student achievement" means that a teacher is responsible for 30% of what a student achieves.'
A better formul... | If teachers account for 30% of variance of student achievement, can a teacher have 30% increase in a
You write '"Teaching expertise accounts for about 30 percent of the variance in student achievement" means that a teacher is responsible for 30% of what a student achieves.'
A better formulation would |
9,087 | Why do researchers use 10-fold cross validation instead of testing on a validation set? | This is not a problem if the CV is nested, i.e. all optimisations, feature selections and model selections, whether they themselves use CV or not, are wrapped in one big CV.
How does this compare to having an extra validation set? While the validation set is usually just a more or less randomly selected part of the who... | Why do researchers use 10-fold cross validation instead of testing on a validation set? | This is not a problem if the CV is nested, i.e. all optimisations, feature selections and model selections, whether they themselves use CV or not, are wrapped in one big CV.
How does this compare to h | Why do researchers use 10-fold cross validation instead of testing on a validation set?
This is not a problem if the CV is nested, i.e. all optimisations, feature selections and model selections, whether they themselves use CV or not, are wrapped in one big CV.
How does this compare to having an extra validation set? W... | Why do researchers use 10-fold cross validation instead of testing on a validation set?
This is not a problem if the CV is nested, i.e. all optimisations, feature selections and model selections, whether they themselves use CV or not, are wrapped in one big CV.
How does this compare to h |
9,088 | Why do researchers use 10-fold cross validation instead of testing on a validation set? | The main reason is that the k-fold cross-validation estimator has a lower variance than a single hold-out set estimator, which can be very important if the amount of data available is limited. If you have a single hold out set, where 90% of data are used for training and 10% used for testing, the test set is very smal... | Why do researchers use 10-fold cross validation instead of testing on a validation set? | The main reason is that the k-fold cross-validation estimator has a lower variance than a single hold-out set estimator, which can be very important if the amount of data available is limited. If you | Why do researchers use 10-fold cross validation instead of testing on a validation set?
The main reason is that the k-fold cross-validation estimator has a lower variance than a single hold-out set estimator, which can be very important if the amount of data available is limited. If you have a single hold out set, whe... | Why do researchers use 10-fold cross validation instead of testing on a validation set?
The main reason is that the k-fold cross-validation estimator has a lower variance than a single hold-out set estimator, which can be very important if the amount of data available is limited. If you |
9,089 | Why do researchers use 10-fold cross validation instead of testing on a validation set? | [EDITED in light of the comment]
I think there is a problem if you use CV results to select among multiple models.
CV allows you to use the entire dataset to train and test one model/method, while being able to have a reasonable idea of how well it will generalize. But if you're comparing multiple models, my instinct ... | Why do researchers use 10-fold cross validation instead of testing on a validation set? | [EDITED in light of the comment]
I think there is a problem if you use CV results to select among multiple models.
CV allows you to use the entire dataset to train and test one model/method, while be | Why do researchers use 10-fold cross validation instead of testing on a validation set?
[EDITED in light of the comment]
I think there is a problem if you use CV results to select among multiple models.
CV allows you to use the entire dataset to train and test one model/method, while being able to have a reasonable id... | Why do researchers use 10-fold cross validation instead of testing on a validation set?
[EDITED in light of the comment]
I think there is a problem if you use CV results to select among multiple models.
CV allows you to use the entire dataset to train and test one model/method, while be |
9,090 | Why do researchers use 10-fold cross validation instead of testing on a validation set? | In my experience, the main reason is usually that you don't have enough samples.
In my field (classification of biological/medical samples), sometimes a test set is kept separate, but often it comprises only few cases. In that case confidence intervals are usually too wide to be of any use.
Another advantage of repeate... | Why do researchers use 10-fold cross validation instead of testing on a validation set? | In my experience, the main reason is usually that you don't have enough samples.
In my field (classification of biological/medical samples), sometimes a test set is kept separate, but often it compris | Why do researchers use 10-fold cross validation instead of testing on a validation set?
In my experience, the main reason is usually that you don't have enough samples.
In my field (classification of biological/medical samples), sometimes a test set is kept separate, but often it comprises only few cases. In that case ... | Why do researchers use 10-fold cross validation instead of testing on a validation set?
In my experience, the main reason is usually that you don't have enough samples.
In my field (classification of biological/medical samples), sometimes a test set is kept separate, but often it compris |
9,091 | Why do researchers use 10-fold cross validation instead of testing on a validation set? | Why we should do cross-validation instead of using separate validation set?
Aurélien Géron talks about this in his book
To avoid “wasting” too much training data in validation sets, a common
technique isto use cross-validation.
Instead of other k values, why we may prefer to use k=10 in cross-validation?
To answer ... | Why do researchers use 10-fold cross validation instead of testing on a validation set? | Why we should do cross-validation instead of using separate validation set?
Aurélien Géron talks about this in his book
To avoid “wasting” too much training data in validation sets, a common
techni | Why do researchers use 10-fold cross validation instead of testing on a validation set?
Why we should do cross-validation instead of using separate validation set?
Aurélien Géron talks about this in his book
To avoid “wasting” too much training data in validation sets, a common
technique isto use cross-validation.
... | Why do researchers use 10-fold cross validation instead of testing on a validation set?
Why we should do cross-validation instead of using separate validation set?
Aurélien Géron talks about this in his book
To avoid “wasting” too much training data in validation sets, a common
techni |
9,092 | Is PCA always recommended? | Blindly using PCA is a recipe for disaster. (As an aside, automatically applying any method is not a good idea, because what works in one context is not guaranteed to work in another. We can formalize this intuitive idea with the No Free Lunch theorem.)
It's easy enough to construct an example where the eigenvectors to... | Is PCA always recommended? | Blindly using PCA is a recipe for disaster. (As an aside, automatically applying any method is not a good idea, because what works in one context is not guaranteed to work in another. We can formalize | Is PCA always recommended?
Blindly using PCA is a recipe for disaster. (As an aside, automatically applying any method is not a good idea, because what works in one context is not guaranteed to work in another. We can formalize this intuitive idea with the No Free Lunch theorem.)
It's easy enough to construct an exampl... | Is PCA always recommended?
Blindly using PCA is a recipe for disaster. (As an aside, automatically applying any method is not a good idea, because what works in one context is not guaranteed to work in another. We can formalize |
9,093 | Is PCA always recommended? | First of all, blindly throwing a model on some data cannot be possibly recommended (you may be able to relax that no-no if you have an infinite amount of independent cases at hand...).
There is a formulation of the no-free lunch theorem that is related to the question: it states that over all possible data sets, no mo... | Is PCA always recommended? | First of all, blindly throwing a model on some data cannot be possibly recommended (you may be able to relax that no-no if you have an infinite amount of independent cases at hand...).
There is a for | Is PCA always recommended?
First of all, blindly throwing a model on some data cannot be possibly recommended (you may be able to relax that no-no if you have an infinite amount of independent cases at hand...).
There is a formulation of the no-free lunch theorem that is related to the question: it states that over al... | Is PCA always recommended?
First of all, blindly throwing a model on some data cannot be possibly recommended (you may be able to relax that no-no if you have an infinite amount of independent cases at hand...).
There is a for |
9,094 | Is PCA always recommended? | Of course not, I don't recall reading/hearing any scientific method's name with the word always, let alone PCA. And, there are many other methods that can be used for dimensionality reduction, e.g. ICA, LDA, variuous feature selection methods, matrix/tensor factorization techniques, autoencoders ... | Is PCA always recommended? | Of course not, I don't recall reading/hearing any scientific method's name with the word always, let alone PCA. And, there are many other methods that can be used for dimensionality reduction, e.g. IC | Is PCA always recommended?
Of course not, I don't recall reading/hearing any scientific method's name with the word always, let alone PCA. And, there are many other methods that can be used for dimensionality reduction, e.g. ICA, LDA, variuous feature selection methods, matrix/tensor factorization techniques, autoencod... | Is PCA always recommended?
Of course not, I don't recall reading/hearing any scientific method's name with the word always, let alone PCA. And, there are many other methods that can be used for dimensionality reduction, e.g. IC |
9,095 | Is PCA always recommended? | The two major limitations of PCA:
1) It assumes linear relationship between variables.
2) The components are much harder to interpret than the original data.
If the limitations outweigh the benefit, one should not use it; hence, pca should not always be used. IMO, it is better to not use PCA, unless there is a good r... | Is PCA always recommended? | The two major limitations of PCA:
1) It assumes linear relationship between variables.
2) The components are much harder to interpret than the original data.
If the limitations outweigh the benefit, | Is PCA always recommended?
The two major limitations of PCA:
1) It assumes linear relationship between variables.
2) The components are much harder to interpret than the original data.
If the limitations outweigh the benefit, one should not use it; hence, pca should not always be used. IMO, it is better to not use PC... | Is PCA always recommended?
The two major limitations of PCA:
1) It assumes linear relationship between variables.
2) The components are much harder to interpret than the original data.
If the limitations outweigh the benefit, |
9,096 | Introduction to structural equation modeling | I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially
Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent indicators. Psychometrika, 49, 115–132.
Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference usi... | Introduction to structural equation modeling | I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially
Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continu | Introduction to structural equation modeling
I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially
Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent indicators. Psychometrika, 49, 115–132.
Muthén, B., du Toit, S.H... | Introduction to structural equation modeling
I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially
Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continu |
9,097 | Introduction to structural equation modeling | While only tangent to your goals at this point, if you continue on projects using latent variables I would highly suggest you read Denny Boorsboom's Measuring the Mind. Don't be fooled by the title, it is mainly a detailed essay on the logic of latent variables, and a large critique of classical test theory. I would sa... | Introduction to structural equation modeling | While only tangent to your goals at this point, if you continue on projects using latent variables I would highly suggest you read Denny Boorsboom's Measuring the Mind. Don't be fooled by the title, i | Introduction to structural equation modeling
While only tangent to your goals at this point, if you continue on projects using latent variables I would highly suggest you read Denny Boorsboom's Measuring the Mind. Don't be fooled by the title, it is mainly a detailed essay on the logic of latent variables, and a large ... | Introduction to structural equation modeling
While only tangent to your goals at this point, if you continue on projects using latent variables I would highly suggest you read Denny Boorsboom's Measuring the Mind. Don't be fooled by the title, i |
9,098 | Introduction to structural equation modeling | This was the recommended text on the course I took:
P.B.Kline, Principles and Practice of Structural Equation Modeling, The Guilford Press.
It is an introductory text, and not heavily mathematical.
For a more mathematical, Bayesian, treatment, you could try:
S-Y. Lee, Structural Equation Modeling: A Bayesian Approach,... | Introduction to structural equation modeling | This was the recommended text on the course I took:
P.B.Kline, Principles and Practice of Structural Equation Modeling, The Guilford Press.
It is an introductory text, and not heavily mathematical.
F | Introduction to structural equation modeling
This was the recommended text on the course I took:
P.B.Kline, Principles and Practice of Structural Equation Modeling, The Guilford Press.
It is an introductory text, and not heavily mathematical.
For a more mathematical, Bayesian, treatment, you could try:
S-Y. Lee, Struc... | Introduction to structural equation modeling
This was the recommended text on the course I took:
P.B.Kline, Principles and Practice of Structural Equation Modeling, The Guilford Press.
It is an introductory text, and not heavily mathematical.
F |
9,099 | Introduction to structural equation modeling | Kline's book is excellent. For a quick intro as a paper see
Gefen, D. 2000. Structural equation modeling and regression: Guidelines for research practice. CAIS. Volume 4. http://aisel.aisnet.org/cais/vol4/iss1/7/
Hox, J.J. and Bechger, T.M. An introduction to structural equation modeling. Family Science Review. 11:... | Introduction to structural equation modeling | Kline's book is excellent. For a quick intro as a paper see
Gefen, D. 2000. Structural equation modeling and regression: Guidelines for research practice. CAIS. Volume 4. http://aisel.aisnet.org/ca | Introduction to structural equation modeling
Kline's book is excellent. For a quick intro as a paper see
Gefen, D. 2000. Structural equation modeling and regression: Guidelines for research practice. CAIS. Volume 4. http://aisel.aisnet.org/cais/vol4/iss1/7/
Hox, J.J. and Bechger, T.M. An introduction to structural e... | Introduction to structural equation modeling
Kline's book is excellent. For a quick intro as a paper see
Gefen, D. 2000. Structural equation modeling and regression: Guidelines for research practice. CAIS. Volume 4. http://aisel.aisnet.org/ca |
9,100 | Introduction to structural equation modeling | I'm studying SEM at the moment, using LISREL. We're using these two books:
A Beginner's Guide to Structural Equation Modelling
New Developments and Techniques in Structural Equation Modelling
Dr Schumaker is the instructor on my course. The first book is really good at introducing SEM, as it takes you through the pro... | Introduction to structural equation modeling | I'm studying SEM at the moment, using LISREL. We're using these two books:
A Beginner's Guide to Structural Equation Modelling
New Developments and Techniques in Structural Equation Modelling
Dr Sch | Introduction to structural equation modeling
I'm studying SEM at the moment, using LISREL. We're using these two books:
A Beginner's Guide to Structural Equation Modelling
New Developments and Techniques in Structural Equation Modelling
Dr Schumaker is the instructor on my course. The first book is really good at int... | Introduction to structural equation modeling
I'm studying SEM at the moment, using LISREL. We're using these two books:
A Beginner's Guide to Structural Equation Modelling
New Developments and Techniques in Structural Equation Modelling
Dr Sch |
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