idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
6,701 | What is the relationship between $Y$ and $X$ in this plot? | Let me describe what I see as soon as I look at it:
If we're interested in the conditional distribution of $y$ (which if often where interest focuses if we see $x$ as IV and $y$ as DV),
then for $x\leq 0.5$ the conditional distribution of $Y|x$ appears bimodal with an upper group (between about 70 and 125, with mean a... | What is the relationship between $Y$ and $X$ in this plot? | Let me describe what I see as soon as I look at it:
If we're interested in the conditional distribution of $y$ (which if often where interest focuses if we see $x$ as IV and $y$ as DV),
then for $x\l | What is the relationship between $Y$ and $X$ in this plot?
Let me describe what I see as soon as I look at it:
If we're interested in the conditional distribution of $y$ (which if often where interest focuses if we see $x$ as IV and $y$ as DV),
then for $x\leq 0.5$ the conditional distribution of $Y|x$ appears bimodal... | What is the relationship between $Y$ and $X$ in this plot?
Let me describe what I see as soon as I look at it:
If we're interested in the conditional distribution of $y$ (which if often where interest focuses if we see $x$ as IV and $y$ as DV),
then for $x\l |
6,702 | What is the relationship between $Y$ and $X$ in this plot? | OK folks, I followed Alexis's lead and captured the data. Here is a plot of $\log y$ versus $x$.
And the correlations:
> cor.test(~ x + y, data = data)
Pearson's product-moment correlation
data: x and y
t = -2.6311, df = 169, p-value = 0.009298
alternative hypothesis: true correlation is not equal to 0
95 perce... | What is the relationship between $Y$ and $X$ in this plot? | OK folks, I followed Alexis's lead and captured the data. Here is a plot of $\log y$ versus $x$.
And the correlations:
> cor.test(~ x + y, data = data)
Pearson's product-moment correlation
data | What is the relationship between $Y$ and $X$ in this plot?
OK folks, I followed Alexis's lead and captured the data. Here is a plot of $\log y$ versus $x$.
And the correlations:
> cor.test(~ x + y, data = data)
Pearson's product-moment correlation
data: x and y
t = -2.6311, df = 169, p-value = 0.009298
alternat... | What is the relationship between $Y$ and $X$ in this plot?
OK folks, I followed Alexis's lead and captured the data. Here is a plot of $\log y$ versus $x$.
And the correlations:
> cor.test(~ x + y, data = data)
Pearson's product-moment correlation
data |
6,703 | What is the relationship between $Y$ and $X$ in this plot? | Russ Lenth wondered how the graph would look if the Y axis were logarithmic. Alexis scraped the data, so it is easy to plot on with a log axis:
On a log scale, there is no hint of bimodality or trend. Whether a log scale makes sense or not depends, of course, on the details of what the data represent. Similarly, wheth... | What is the relationship between $Y$ and $X$ in this plot? | Russ Lenth wondered how the graph would look if the Y axis were logarithmic. Alexis scraped the data, so it is easy to plot on with a log axis:
On a log scale, there is no hint of bimodality or trend | What is the relationship between $Y$ and $X$ in this plot?
Russ Lenth wondered how the graph would look if the Y axis were logarithmic. Alexis scraped the data, so it is easy to plot on with a log axis:
On a log scale, there is no hint of bimodality or trend. Whether a log scale makes sense or not depends, of course, ... | What is the relationship between $Y$ and $X$ in this plot?
Russ Lenth wondered how the graph would look if the Y axis were logarithmic. Alexis scraped the data, so it is easy to plot on with a log axis:
On a log scale, there is no hint of bimodality or trend |
6,704 | What is the relationship between $Y$ and $X$ in this plot? | Well, you are right, the relationship is weak, but not zero. I would guess positive. However, don't guess, just run a simple linear regression (OLS regression) and find out! There you will get a slope of xxx which tells you what the relationship is. And yes, you do have outliers that might bias the results. That can be... | What is the relationship between $Y$ and $X$ in this plot? | Well, you are right, the relationship is weak, but not zero. I would guess positive. However, don't guess, just run a simple linear regression (OLS regression) and find out! There you will get a slope | What is the relationship between $Y$ and $X$ in this plot?
Well, you are right, the relationship is weak, but not zero. I would guess positive. However, don't guess, just run a simple linear regression (OLS regression) and find out! There you will get a slope of xxx which tells you what the relationship is. And yes, yo... | What is the relationship between $Y$ and $X$ in this plot?
Well, you are right, the relationship is weak, but not zero. I would guess positive. However, don't guess, just run a simple linear regression (OLS regression) and find out! There you will get a slope |
6,705 | What is the relationship between $Y$ and $X$ in this plot? | You already provided some intuition to your question by looking at the orientation of the X/Y data points and their dispersion. In short you're correct.
In formal terms orientation can be referred to as correlation sign and dispersion as variance. These two links will give you more information on how to interpret the l... | What is the relationship between $Y$ and $X$ in this plot? | You already provided some intuition to your question by looking at the orientation of the X/Y data points and their dispersion. In short you're correct.
In formal terms orientation can be referred to | What is the relationship between $Y$ and $X$ in this plot?
You already provided some intuition to your question by looking at the orientation of the X/Y data points and their dispersion. In short you're correct.
In formal terms orientation can be referred to as correlation sign and dispersion as variance. These two lin... | What is the relationship between $Y$ and $X$ in this plot?
You already provided some intuition to your question by looking at the orientation of the X/Y data points and their dispersion. In short you're correct.
In formal terms orientation can be referred to |
6,706 | What is the relationship between $Y$ and $X$ in this plot? | This is a home work. So, the answer to your question is simple. Run a linear regression of Y on X, you'll get something like this:
Coefficient Standard Er t Stat
C 53.14404163 6.522516463 8.147781908
X -44.8798926 16.80565866 -2.670522684
So, the t-statistics is significant on X variable at 99% confidence. Hen... | What is the relationship between $Y$ and $X$ in this plot? | This is a home work. So, the answer to your question is simple. Run a linear regression of Y on X, you'll get something like this:
Coefficient Standard Er t Stat
C 53.14404163 6.522516463 8.1477 | What is the relationship between $Y$ and $X$ in this plot?
This is a home work. So, the answer to your question is simple. Run a linear regression of Y on X, you'll get something like this:
Coefficient Standard Er t Stat
C 53.14404163 6.522516463 8.147781908
X -44.8798926 16.80565866 -2.670522684
So, the t-sta... | What is the relationship between $Y$ and $X$ in this plot?
This is a home work. So, the answer to your question is simple. Run a linear regression of Y on X, you'll get something like this:
Coefficient Standard Er t Stat
C 53.14404163 6.522516463 8.1477 |
6,707 | Variance of a bounded random variable | You can prove Popoviciu's inequality as follows. Use the notation $m=\inf X$ and $M=\sup X$. Define a function $g$ by
$$
g(t)=\mathbb{E}\!\left[\left(X-t\right)^2\right] \, .
$$
Computing the derivative $g'$, and solving
$$
g'(t) = -2\mathbb{E}[X] +2t=0 \, ,
$$
we find that $g$ achieves its minimum at $t=\mathbb{E}... | Variance of a bounded random variable | You can prove Popoviciu's inequality as follows. Use the notation $m=\inf X$ and $M=\sup X$. Define a function $g$ by
$$
g(t)=\mathbb{E}\!\left[\left(X-t\right)^2\right] \, .
$$
Computing the deriva | Variance of a bounded random variable
You can prove Popoviciu's inequality as follows. Use the notation $m=\inf X$ and $M=\sup X$. Define a function $g$ by
$$
g(t)=\mathbb{E}\!\left[\left(X-t\right)^2\right] \, .
$$
Computing the derivative $g'$, and solving
$$
g'(t) = -2\mathbb{E}[X] +2t=0 \, ,
$$
we find that $g$... | Variance of a bounded random variable
You can prove Popoviciu's inequality as follows. Use the notation $m=\inf X$ and $M=\sup X$. Define a function $g$ by
$$
g(t)=\mathbb{E}\!\left[\left(X-t\right)^2\right] \, .
$$
Computing the deriva |
6,708 | Variance of a bounded random variable | If the random variable is restricted to $[a,b]$ and we know the mean $\mu=E[X]$, the variance is bounded by $(b-\mu)(\mu-a)$.
Let us first consider the case $a=0, b=1$. Note that for all $x\in [0,1]$, $x^2\leq x$, wherefore also $E[X^2]\leq E[X]$. Using this result,
\begin{equation}
\sigma^2 = E[X^2] - (E[X]^2) = E... | Variance of a bounded random variable | If the random variable is restricted to $[a,b]$ and we know the mean $\mu=E[X]$, the variance is bounded by $(b-\mu)(\mu-a)$.
Let us first consider the case $a=0, b=1$. Note that for all $x\in [0,1]$, | Variance of a bounded random variable
If the random variable is restricted to $[a,b]$ and we know the mean $\mu=E[X]$, the variance is bounded by $(b-\mu)(\mu-a)$.
Let us first consider the case $a=0, b=1$. Note that for all $x\in [0,1]$, $x^2\leq x$, wherefore also $E[X^2]\leq E[X]$. Using this result,
\begin{equatio... | Variance of a bounded random variable
If the random variable is restricted to $[a,b]$ and we know the mean $\mu=E[X]$, the variance is bounded by $(b-\mu)(\mu-a)$.
Let us first consider the case $a=0, b=1$. Note that for all $x\in [0,1]$, |
6,709 | Variance of a bounded random variable | Let $F$ be a distribution on $[0,1]$. We will show that if the variance of $F$ is maximal, then $F$ can have no support in the interior, from which it follows that $F$ is Bernoulli and the rest is trivial.
As a matter of notation, let $\mu_k = \int_0^1 x^k dF(x)$ be the $k$th raw moment of $F$ (and, as usual, we write... | Variance of a bounded random variable | Let $F$ be a distribution on $[0,1]$. We will show that if the variance of $F$ is maximal, then $F$ can have no support in the interior, from which it follows that $F$ is Bernoulli and the rest is tr | Variance of a bounded random variable
Let $F$ be a distribution on $[0,1]$. We will show that if the variance of $F$ is maximal, then $F$ can have no support in the interior, from which it follows that $F$ is Bernoulli and the rest is trivial.
As a matter of notation, let $\mu_k = \int_0^1 x^k dF(x)$ be the $k$th raw ... | Variance of a bounded random variable
Let $F$ be a distribution on $[0,1]$. We will show that if the variance of $F$ is maximal, then $F$ can have no support in the interior, from which it follows that $F$ is Bernoulli and the rest is tr |
6,710 | Variance of a bounded random variable | At @user603's request....
A useful upper bound on the variance $\sigma^2$ of a random variable that takes on values in $[a,b]$ with probability $1$ is $\sigma^2 \leq \frac{(b−a)^2}{4}$. A proof for the
special case $a=0, b=1$ (which is what the OP asked about) can be found
here on math.SE, and
it is easily adapted to
... | Variance of a bounded random variable | At @user603's request....
A useful upper bound on the variance $\sigma^2$ of a random variable that takes on values in $[a,b]$ with probability $1$ is $\sigma^2 \leq \frac{(b−a)^2}{4}$. A proof for th | Variance of a bounded random variable
At @user603's request....
A useful upper bound on the variance $\sigma^2$ of a random variable that takes on values in $[a,b]$ with probability $1$ is $\sigma^2 \leq \frac{(b−a)^2}{4}$. A proof for the
special case $a=0, b=1$ (which is what the OP asked about) can be found
here on ... | Variance of a bounded random variable
At @user603's request....
A useful upper bound on the variance $\sigma^2$ of a random variable that takes on values in $[a,b]$ with probability $1$ is $\sigma^2 \leq \frac{(b−a)^2}{4}$. A proof for th |
6,711 | Variance of a bounded random variable | Here's a really simple proof I found in Sheldon Ross's A first course in probability 10th ed., "theory problem 5.8".
Suppose we have a random variable $X$ between $0$ and $c$. Then $X \leq c$ and thus $E(X^2) \leq c E(X)$. We thus have
$$\mathrm{Var}(X) \leq c E(X) - E(X)^2 = c^2 \alpha (1 - \alpha) \leq c^2 / 4$$
wher... | Variance of a bounded random variable | Here's a really simple proof I found in Sheldon Ross's A first course in probability 10th ed., "theory problem 5.8".
Suppose we have a random variable $X$ between $0$ and $c$. Then $X \leq c$ and thus | Variance of a bounded random variable
Here's a really simple proof I found in Sheldon Ross's A first course in probability 10th ed., "theory problem 5.8".
Suppose we have a random variable $X$ between $0$ and $c$. Then $X \leq c$ and thus $E(X^2) \leq c E(X)$. We thus have
$$\mathrm{Var}(X) \leq c E(X) - E(X)^2 = c^2 \... | Variance of a bounded random variable
Here's a really simple proof I found in Sheldon Ross's A first course in probability 10th ed., "theory problem 5.8".
Suppose we have a random variable $X$ between $0$ and $c$. Then $X \leq c$ and thus |
6,712 | Variance of a bounded random variable | Given random variable $D$ with mean $E D=\mu$, when $a\le D\le b$, we have
\begin{eqnarray*}
E (D-\mu)^2&\le& E[(D-\mu)^2-(D-a)(D-b)]\\
&=& E[\mu^2-2\mu D+(a+b)D-ab]\\
&=& (a+b)\mu-\mu^2-ab\\
&=&(\mu-a)(b-\mu),
\end{eqnarray*}
where the equation holds if and only if $D\in\{a,b\}$ with probability $1$.
Moreover, if $\mu... | Variance of a bounded random variable | Given random variable $D$ with mean $E D=\mu$, when $a\le D\le b$, we have
\begin{eqnarray*}
E (D-\mu)^2&\le& E[(D-\mu)^2-(D-a)(D-b)]\\
&=& E[\mu^2-2\mu D+(a+b)D-ab]\\
&=& (a+b)\mu-\mu^2-ab\\
&=&(\mu- | Variance of a bounded random variable
Given random variable $D$ with mean $E D=\mu$, when $a\le D\le b$, we have
\begin{eqnarray*}
E (D-\mu)^2&\le& E[(D-\mu)^2-(D-a)(D-b)]\\
&=& E[\mu^2-2\mu D+(a+b)D-ab]\\
&=& (a+b)\mu-\mu^2-ab\\
&=&(\mu-a)(b-\mu),
\end{eqnarray*}
where the equation holds if and only if $D\in\{a,b\}$ w... | Variance of a bounded random variable
Given random variable $D$ with mean $E D=\mu$, when $a\le D\le b$, we have
\begin{eqnarray*}
E (D-\mu)^2&\le& E[(D-\mu)^2-(D-a)(D-b)]\\
&=& E[\mu^2-2\mu D+(a+b)D-ab]\\
&=& (a+b)\mu-\mu^2-ab\\
&=&(\mu- |
6,713 | Variance of a bounded random variable | are you sure that this is true in general - for continuous as well as discrete distributions? Can you provide a link to the other pages?
For a general distibution on $[a,b]$ it is trivial to show that
$$
Var(X) = E[(X-E[X])^2] \le E[(b-a)^2] = (b-a)^2.
$$
I can imagine that sharper inequalities exist ...
Do you need t... | Variance of a bounded random variable | are you sure that this is true in general - for continuous as well as discrete distributions? Can you provide a link to the other pages?
For a general distibution on $[a,b]$ it is trivial to show that | Variance of a bounded random variable
are you sure that this is true in general - for continuous as well as discrete distributions? Can you provide a link to the other pages?
For a general distibution on $[a,b]$ it is trivial to show that
$$
Var(X) = E[(X-E[X])^2] \le E[(b-a)^2] = (b-a)^2.
$$
I can imagine that sharper... | Variance of a bounded random variable
are you sure that this is true in general - for continuous as well as discrete distributions? Can you provide a link to the other pages?
For a general distibution on $[a,b]$ it is trivial to show that |
6,714 | Variance of a bounded random variable | The key elements here are that $f(x) = x^2$ is convex, $EX$ minimises $E(X-t)^2$ and $X(\omega) \in [a,b]$.
Let $x \in [a,b]$, then
$f(x-{1 \over 2}(a+b)) \le {1 \over 2} (f({x-a \over 2}) + f({x-b \over 2}))$, or
$(x-{1 \over 2}(a+b))^2 \le {1 \over 2} (({x-a \over 2})^2 + ({x-b \over 2})^2 ) \le ({b-a \over 2})^2$.
S... | Variance of a bounded random variable | The key elements here are that $f(x) = x^2$ is convex, $EX$ minimises $E(X-t)^2$ and $X(\omega) \in [a,b]$.
Let $x \in [a,b]$, then
$f(x-{1 \over 2}(a+b)) \le {1 \over 2} (f({x-a \over 2}) + f({x-b \o | Variance of a bounded random variable
The key elements here are that $f(x) = x^2$ is convex, $EX$ minimises $E(X-t)^2$ and $X(\omega) \in [a,b]$.
Let $x \in [a,b]$, then
$f(x-{1 \over 2}(a+b)) \le {1 \over 2} (f({x-a \over 2}) + f({x-b \over 2}))$, or
$(x-{1 \over 2}(a+b))^2 \le {1 \over 2} (({x-a \over 2})^2 + ({x-b \... | Variance of a bounded random variable
The key elements here are that $f(x) = x^2$ is convex, $EX$ minimises $E(X-t)^2$ and $X(\omega) \in [a,b]$.
Let $x \in [a,b]$, then
$f(x-{1 \over 2}(a+b)) \le {1 \over 2} (f({x-a \over 2}) + f({x-b \o |
6,715 | Variance of a bounded random variable | A simple proof of Popoviciu's inequality is the following, where $X\in [m, M]$:
\begin{equation}
\color{blue}{\operatorname{Var}[X] \le \operatorname{Var}[X] + \mathbb{E}[(M-X)(X-m)] = \frac{(M-m)^2}{4} - \left(\mathbb{E}[X] - \frac{M+m}{2}\right)^2 \le \frac{(M-m)^2}{4}.}
\end{equation}
Source: https://math.stackexcha... | Variance of a bounded random variable | A simple proof of Popoviciu's inequality is the following, where $X\in [m, M]$:
\begin{equation}
\color{blue}{\operatorname{Var}[X] \le \operatorname{Var}[X] + \mathbb{E}[(M-X)(X-m)] = \frac{(M-m)^2}{ | Variance of a bounded random variable
A simple proof of Popoviciu's inequality is the following, where $X\in [m, M]$:
\begin{equation}
\color{blue}{\operatorname{Var}[X] \le \operatorname{Var}[X] + \mathbb{E}[(M-X)(X-m)] = \frac{(M-m)^2}{4} - \left(\mathbb{E}[X] - \frac{M+m}{2}\right)^2 \le \frac{(M-m)^2}{4}.}
\end{equ... | Variance of a bounded random variable
A simple proof of Popoviciu's inequality is the following, where $X\in [m, M]$:
\begin{equation}
\color{blue}{\operatorname{Var}[X] \le \operatorname{Var}[X] + \mathbb{E}[(M-X)(X-m)] = \frac{(M-m)^2}{ |
6,716 | Why are survival times assumed to be exponentially distributed? | Exponential distributions are often used to model survival times because they are the simplest distributions that can be used to characterize survival / reliability data. This is because they are memoryless, and thus the hazard function is constant w/r/t time, which makes analysis very simple. This kind of assumption m... | Why are survival times assumed to be exponentially distributed? | Exponential distributions are often used to model survival times because they are the simplest distributions that can be used to characterize survival / reliability data. This is because they are memo | Why are survival times assumed to be exponentially distributed?
Exponential distributions are often used to model survival times because they are the simplest distributions that can be used to characterize survival / reliability data. This is because they are memoryless, and thus the hazard function is constant w/r/t t... | Why are survival times assumed to be exponentially distributed?
Exponential distributions are often used to model survival times because they are the simplest distributions that can be used to characterize survival / reliability data. This is because they are memo |
6,717 | Why are survival times assumed to be exponentially distributed? | To add a bit of mathematical intuition behind how exponents pop up in survival distributions:
The probability density of a survival variable is $f(t) = h(t)S(t)$, where $h(t)$ is the current hazard (risk for a person to "die" this day) and $S(t)$ is the probability that a person survived until $t$. $S(t)$ can be expa... | Why are survival times assumed to be exponentially distributed? | To add a bit of mathematical intuition behind how exponents pop up in survival distributions:
The probability density of a survival variable is $f(t) = h(t)S(t)$, where $h(t)$ is the current hazard | Why are survival times assumed to be exponentially distributed?
To add a bit of mathematical intuition behind how exponents pop up in survival distributions:
The probability density of a survival variable is $f(t) = h(t)S(t)$, where $h(t)$ is the current hazard (risk for a person to "die" this day) and $S(t)$ is the ... | Why are survival times assumed to be exponentially distributed?
To add a bit of mathematical intuition behind how exponents pop up in survival distributions:
The probability density of a survival variable is $f(t) = h(t)S(t)$, where $h(t)$ is the current hazard |
6,718 | Why are survival times assumed to be exponentially distributed? | You'll almost certainly want to look at reliability engineering and predictions for thorough analyses of survival times. Within that, there are a few distributions which get used often:
The Weibull (or "bathtub") distribution is the most complex. It accounts for three types of failure modes, which dominate at differen... | Why are survival times assumed to be exponentially distributed? | You'll almost certainly want to look at reliability engineering and predictions for thorough analyses of survival times. Within that, there are a few distributions which get used often:
The Weibull ( | Why are survival times assumed to be exponentially distributed?
You'll almost certainly want to look at reliability engineering and predictions for thorough analyses of survival times. Within that, there are a few distributions which get used often:
The Weibull (or "bathtub") distribution is the most complex. It accou... | Why are survival times assumed to be exponentially distributed?
You'll almost certainly want to look at reliability engineering and predictions for thorough analyses of survival times. Within that, there are a few distributions which get used often:
The Weibull ( |
6,719 | Why are survival times assumed to be exponentially distributed? | Some ecology might help answer the "Why" behind this question.
The reason why exponential distribution is used for modeling survival is due to the life strategies involved in organisms living in nature. There's essentially two extremes with regard to survival strategy with some room for the middle ground.
Here's an ima... | Why are survival times assumed to be exponentially distributed? | Some ecology might help answer the "Why" behind this question.
The reason why exponential distribution is used for modeling survival is due to the life strategies involved in organisms living in natur | Why are survival times assumed to be exponentially distributed?
Some ecology might help answer the "Why" behind this question.
The reason why exponential distribution is used for modeling survival is due to the life strategies involved in organisms living in nature. There's essentially two extremes with regard to survi... | Why are survival times assumed to be exponentially distributed?
Some ecology might help answer the "Why" behind this question.
The reason why exponential distribution is used for modeling survival is due to the life strategies involved in organisms living in natur |
6,720 | Why are survival times assumed to be exponentially distributed? | To answer your explicit question, you cannot use the normal distribution for survival because the normal distribution goes to negative infinity, and survival is strictly non-negative. Moreover, I don't think it's true that "survival times are assumed to be exponentially distributed" by anyone in reality.
When surviv... | Why are survival times assumed to be exponentially distributed? | To answer your explicit question, you cannot use the normal distribution for survival because the normal distribution goes to negative infinity, and survival is strictly non-negative. Moreover, I don | Why are survival times assumed to be exponentially distributed?
To answer your explicit question, you cannot use the normal distribution for survival because the normal distribution goes to negative infinity, and survival is strictly non-negative. Moreover, I don't think it's true that "survival times are assumed to b... | Why are survival times assumed to be exponentially distributed?
To answer your explicit question, you cannot use the normal distribution for survival because the normal distribution goes to negative infinity, and survival is strictly non-negative. Moreover, I don |
6,721 | Why are survival times assumed to be exponentially distributed? | This doesn't directly answer the question, but I think it's very important to note, and does not fit nicely into a single comment.
While the exponential distribution has a very nice theoretical derivation, and thus assuming the data produced follows the mechanisms assumed in the exponential distribution, it should the... | Why are survival times assumed to be exponentially distributed? | This doesn't directly answer the question, but I think it's very important to note, and does not fit nicely into a single comment.
While the exponential distribution has a very nice theoretical deriv | Why are survival times assumed to be exponentially distributed?
This doesn't directly answer the question, but I think it's very important to note, and does not fit nicely into a single comment.
While the exponential distribution has a very nice theoretical derivation, and thus assuming the data produced follows the m... | Why are survival times assumed to be exponentially distributed?
This doesn't directly answer the question, but I think it's very important to note, and does not fit nicely into a single comment.
While the exponential distribution has a very nice theoretical deriv |
6,722 | Why are survival times assumed to be exponentially distributed? | Another reason why the exponential distribution crops up often to model interval between events is the following.
It is well known that, under some assumptions, the sum of a large number of independent random variables will be close to a Gaussian distribution. A similar theorem holds for renewal processes, i.e. stochas... | Why are survival times assumed to be exponentially distributed? | Another reason why the exponential distribution crops up often to model interval between events is the following.
It is well known that, under some assumptions, the sum of a large number of independen | Why are survival times assumed to be exponentially distributed?
Another reason why the exponential distribution crops up often to model interval between events is the following.
It is well known that, under some assumptions, the sum of a large number of independent random variables will be close to a Gaussian distribut... | Why are survival times assumed to be exponentially distributed?
Another reason why the exponential distribution crops up often to model interval between events is the following.
It is well known that, under some assumptions, the sum of a large number of independen |
6,723 | Why are survival times assumed to be exponentially distributed? | tl;dr- An expontential distribution is equivalent to assuming that individuals are as likely to die at any given moment as any other.
Derivation
Assume that a living individual is as likely to die at any given moment as at any other.
So, the death rate $-\frac{\text{d}P}{\text{d}t}$ is proportional to the population... | Why are survival times assumed to be exponentially distributed? | tl;dr- An expontential distribution is equivalent to assuming that individuals are as likely to die at any given moment as any other.
Derivation
Assume that a living individual is as likely to die a | Why are survival times assumed to be exponentially distributed?
tl;dr- An expontential distribution is equivalent to assuming that individuals are as likely to die at any given moment as any other.
Derivation
Assume that a living individual is as likely to die at any given moment as at any other.
So, the death rate ... | Why are survival times assumed to be exponentially distributed?
tl;dr- An expontential distribution is equivalent to assuming that individuals are as likely to die at any given moment as any other.
Derivation
Assume that a living individual is as likely to die a |
6,724 | Why are survival times assumed to be exponentially distributed? | (Note that in the part you quoted, the statement was conditional; the sentence itself didn't assume exponential survival, it explained a consequence of doing so. Nevertheless assumption of exponential survival are common, so it's worth dealing with the question of "why exponential" and "why not normal" -- since the fir... | Why are survival times assumed to be exponentially distributed? | (Note that in the part you quoted, the statement was conditional; the sentence itself didn't assume exponential survival, it explained a consequence of doing so. Nevertheless assumption of exponential | Why are survival times assumed to be exponentially distributed?
(Note that in the part you quoted, the statement was conditional; the sentence itself didn't assume exponential survival, it explained a consequence of doing so. Nevertheless assumption of exponential survival are common, so it's worth dealing with the que... | Why are survival times assumed to be exponentially distributed?
(Note that in the part you quoted, the statement was conditional; the sentence itself didn't assume exponential survival, it explained a consequence of doing so. Nevertheless assumption of exponential |
6,725 | Why are survival times assumed to be exponentially distributed? | If we want time to be strictly positive, why not make normal distribution with higher mean and very small variance (will have almost no chance to get negative number.)?
Because
that still has a nonzero probability of being negative, so it's not strictly positive;
the mean and variance are something that you can meas... | Why are survival times assumed to be exponentially distributed? | If we want time to be strictly positive, why not make normal distribution with higher mean and very small variance (will have almost no chance to get negative number.)?
Because
that still has a non | Why are survival times assumed to be exponentially distributed?
If we want time to be strictly positive, why not make normal distribution with higher mean and very small variance (will have almost no chance to get negative number.)?
Because
that still has a nonzero probability of being negative, so it's not strictly... | Why are survival times assumed to be exponentially distributed?
If we want time to be strictly positive, why not make normal distribution with higher mean and very small variance (will have almost no chance to get negative number.)?
Because
that still has a non |
6,726 | Is there a name for the opposite of the gambler's fallacy? | That seems to be a typical example of the Ludic Fallacy: https://en.wikipedia.org/wiki/Ludic_fallacy#Example:_Suspicious_coin | Is there a name for the opposite of the gambler's fallacy? | That seems to be a typical example of the Ludic Fallacy: https://en.wikipedia.org/wiki/Ludic_fallacy#Example:_Suspicious_coin | Is there a name for the opposite of the gambler's fallacy?
That seems to be a typical example of the Ludic Fallacy: https://en.wikipedia.org/wiki/Ludic_fallacy#Example:_Suspicious_coin | Is there a name for the opposite of the gambler's fallacy?
That seems to be a typical example of the Ludic Fallacy: https://en.wikipedia.org/wiki/Ludic_fallacy#Example:_Suspicious_coin |
6,727 | Is there a name for the opposite of the gambler's fallacy? | N Blake's answer is great, using the language of cognitive psychology. If you're up for a Bayesian slant, you could treat this as violating Cromwell's rule.
You have a prior certain belief that the coin's probability of giving tails is $f=0.5$. In other words, you believe that $p(f=0.5) = 1$, which is the problem. This... | Is there a name for the opposite of the gambler's fallacy? | N Blake's answer is great, using the language of cognitive psychology. If you're up for a Bayesian slant, you could treat this as violating Cromwell's rule.
You have a prior certain belief that the co | Is there a name for the opposite of the gambler's fallacy?
N Blake's answer is great, using the language of cognitive psychology. If you're up for a Bayesian slant, you could treat this as violating Cromwell's rule.
You have a prior certain belief that the coin's probability of giving tails is $f=0.5$. In other words, ... | Is there a name for the opposite of the gambler's fallacy?
N Blake's answer is great, using the language of cognitive psychology. If you're up for a Bayesian slant, you could treat this as violating Cromwell's rule.
You have a prior certain belief that the co |
6,728 | Is there a name for the opposite of the gambler's fallacy? | Belief perseverance seems to fit - maintaining a belief (that it's a fair coin), despite contrary evidence (100/100 heads). | Is there a name for the opposite of the gambler's fallacy? | Belief perseverance seems to fit - maintaining a belief (that it's a fair coin), despite contrary evidence (100/100 heads). | Is there a name for the opposite of the gambler's fallacy?
Belief perseverance seems to fit - maintaining a belief (that it's a fair coin), despite contrary evidence (100/100 heads). | Is there a name for the opposite of the gambler's fallacy?
Belief perseverance seems to fit - maintaining a belief (that it's a fair coin), despite contrary evidence (100/100 heads). |
6,729 | Is there a name for the opposite of the gambler's fallacy? | It's called a strong prior.
The more enduring your belief in the coin's fairness is, the stronger the prior would be said to be. Might call it an absolute prior if it'd never change.
It's not necessarily a fallacy so much as an approximation, especially if the prior is strong enough that it'd be difficult to meaningfu... | Is there a name for the opposite of the gambler's fallacy? | It's called a strong prior.
The more enduring your belief in the coin's fairness is, the stronger the prior would be said to be. Might call it an absolute prior if it'd never change.
It's not necessa | Is there a name for the opposite of the gambler's fallacy?
It's called a strong prior.
The more enduring your belief in the coin's fairness is, the stronger the prior would be said to be. Might call it an absolute prior if it'd never change.
It's not necessarily a fallacy so much as an approximation, especially if the... | Is there a name for the opposite of the gambler's fallacy?
It's called a strong prior.
The more enduring your belief in the coin's fairness is, the stronger the prior would be said to be. Might call it an absolute prior if it'd never change.
It's not necessa |
6,730 | Is there a name for the opposite of the gambler's fallacy? | This belief was examined in a series of papers on the "gambler's fallacy" and broader methods of binomial prediction under the Bayesian paradigm (see O'Neill and Puza 2005; O'Neill 2012; O'Neill 2015). These papers argue in favour of your view here – that observing more heads in a series of coin-flips should shift you... | Is there a name for the opposite of the gambler's fallacy? | This belief was examined in a series of papers on the "gambler's fallacy" and broader methods of binomial prediction under the Bayesian paradigm (see O'Neill and Puza 2005; O'Neill 2012; O'Neill 2015) | Is there a name for the opposite of the gambler's fallacy?
This belief was examined in a series of papers on the "gambler's fallacy" and broader methods of binomial prediction under the Bayesian paradigm (see O'Neill and Puza 2005; O'Neill 2012; O'Neill 2015). These papers argue in favour of your view here – that obse... | Is there a name for the opposite of the gambler's fallacy?
This belief was examined in a series of papers on the "gambler's fallacy" and broader methods of binomial prediction under the Bayesian paradigm (see O'Neill and Puza 2005; O'Neill 2012; O'Neill 2015) |
6,731 | Is there a name for the opposite of the gambler's fallacy? | I would call that a Type II error, which is anytime in science you fail to reject a null hypothesis even though it is false. If you had no other reason to think the coin is fair other than the flips you've seen, you could calculate draw a conclusion on evidence alone/ If you conclude it is fair just because you think y... | Is there a name for the opposite of the gambler's fallacy? | I would call that a Type II error, which is anytime in science you fail to reject a null hypothesis even though it is false. If you had no other reason to think the coin is fair other than the flips y | Is there a name for the opposite of the gambler's fallacy?
I would call that a Type II error, which is anytime in science you fail to reject a null hypothesis even though it is false. If you had no other reason to think the coin is fair other than the flips you've seen, you could calculate draw a conclusion on evidence... | Is there a name for the opposite of the gambler's fallacy?
I would call that a Type II error, which is anytime in science you fail to reject a null hypothesis even though it is false. If you had no other reason to think the coin is fair other than the flips y |
6,732 | Should parsimony really still be the gold standard? | @Matt's original answer does a great job of describing one of the benefits of parsimony but I don't think it actually answers your question. In reality, parsimony isn't the gold standard. Not now nor has it ever been. A "gold standard" related to parsimony is generalization error. We would like to develop models that d... | Should parsimony really still be the gold standard? | @Matt's original answer does a great job of describing one of the benefits of parsimony but I don't think it actually answers your question. In reality, parsimony isn't the gold standard. Not now nor | Should parsimony really still be the gold standard?
@Matt's original answer does a great job of describing one of the benefits of parsimony but I don't think it actually answers your question. In reality, parsimony isn't the gold standard. Not now nor has it ever been. A "gold standard" related to parsimony is generali... | Should parsimony really still be the gold standard?
@Matt's original answer does a great job of describing one of the benefits of parsimony but I don't think it actually answers your question. In reality, parsimony isn't the gold standard. Not now nor |
6,733 | Should parsimony really still be the gold standard? | Parsimonious models are desirable not just due to computing requirements, but also for generalization performance. It's impossible to achieve the ideal of infinite data that completely and accurately covers the sample space, meaning that non-parsimonious models have the potential to overfit and model noise or idiosyncr... | Should parsimony really still be the gold standard? | Parsimonious models are desirable not just due to computing requirements, but also for generalization performance. It's impossible to achieve the ideal of infinite data that completely and accurately | Should parsimony really still be the gold standard?
Parsimonious models are desirable not just due to computing requirements, but also for generalization performance. It's impossible to achieve the ideal of infinite data that completely and accurately covers the sample space, meaning that non-parsimonious models have t... | Should parsimony really still be the gold standard?
Parsimonious models are desirable not just due to computing requirements, but also for generalization performance. It's impossible to achieve the ideal of infinite data that completely and accurately |
6,734 | Should parsimony really still be the gold standard? | I think the previous answers do a good job of making important points:
Parsimonious models tend to have better generalization characteristics.
Parsimony is not truly a gold standard, but just a consideration.
I want to add a few comments that come out of my day to day job experience.
The generalization of predictive ... | Should parsimony really still be the gold standard? | I think the previous answers do a good job of making important points:
Parsimonious models tend to have better generalization characteristics.
Parsimony is not truly a gold standard, but just a consi | Should parsimony really still be the gold standard?
I think the previous answers do a good job of making important points:
Parsimonious models tend to have better generalization characteristics.
Parsimony is not truly a gold standard, but just a consideration.
I want to add a few comments that come out of my day to d... | Should parsimony really still be the gold standard?
I think the previous answers do a good job of making important points:
Parsimonious models tend to have better generalization characteristics.
Parsimony is not truly a gold standard, but just a consi |
6,735 | Should parsimony really still be the gold standard? | I think this is a very good question. In my opinion parsimony is overrated. Nature is rarely parsimonious, and so we shouldn't necessarily expect accurate predictive or descriptive models to be so either. Regarding the question of interpretability, if you choose a simpler model that only modestly conforms to reality... | Should parsimony really still be the gold standard? | I think this is a very good question. In my opinion parsimony is overrated. Nature is rarely parsimonious, and so we shouldn't necessarily expect accurate predictive or descriptive models to be so e | Should parsimony really still be the gold standard?
I think this is a very good question. In my opinion parsimony is overrated. Nature is rarely parsimonious, and so we shouldn't necessarily expect accurate predictive or descriptive models to be so either. Regarding the question of interpretability, if you choose a ... | Should parsimony really still be the gold standard?
I think this is a very good question. In my opinion parsimony is overrated. Nature is rarely parsimonious, and so we shouldn't necessarily expect accurate predictive or descriptive models to be so e |
6,736 | Should parsimony really still be the gold standard? | Perhaps have a review of the Akaike Information Criterion, a concept that I only discovered by serendipity yesterday. The AIC seeks to identify which model and how many parameters are the best explanation for the observations at hand, rather than any basic Occam's Razor, or parsimony approach. | Should parsimony really still be the gold standard? | Perhaps have a review of the Akaike Information Criterion, a concept that I only discovered by serendipity yesterday. The AIC seeks to identify which model and how many parameters are the best explana | Should parsimony really still be the gold standard?
Perhaps have a review of the Akaike Information Criterion, a concept that I only discovered by serendipity yesterday. The AIC seeks to identify which model and how many parameters are the best explanation for the observations at hand, rather than any basic Occam's Raz... | Should parsimony really still be the gold standard?
Perhaps have a review of the Akaike Information Criterion, a concept that I only discovered by serendipity yesterday. The AIC seeks to identify which model and how many parameters are the best explana |
6,737 | Should parsimony really still be the gold standard? | Parsimony is not a golden start. It's an aspect in modeling. Modeling and especially forecasting can not be scripted, i.e. you can't just hand a script to a modeler to follow. You rather define principles upon which the modeling process must be based. So, the parsimony is one of these principles, application of which c... | Should parsimony really still be the gold standard? | Parsimony is not a golden start. It's an aspect in modeling. Modeling and especially forecasting can not be scripted, i.e. you can't just hand a script to a modeler to follow. You rather define princi | Should parsimony really still be the gold standard?
Parsimony is not a golden start. It's an aspect in modeling. Modeling and especially forecasting can not be scripted, i.e. you can't just hand a script to a modeler to follow. You rather define principles upon which the modeling process must be based. So, the parsimon... | Should parsimony really still be the gold standard?
Parsimony is not a golden start. It's an aspect in modeling. Modeling and especially forecasting can not be scripted, i.e. you can't just hand a script to a modeler to follow. You rather define princi |
6,738 | Should parsimony really still be the gold standard? | Regarding Neural Networks, this topic has been very nicely covered in a recent NeurIPS 2020 paper entitled
The Pitfalls of Simplicity Bias in Neural Networks (Shah et al.).
I totally recommend reading the paper, I think it is very nicely structured and rigorous. Here is an attempt to summarize its main ideas:
The cor... | Should parsimony really still be the gold standard? | Regarding Neural Networks, this topic has been very nicely covered in a recent NeurIPS 2020 paper entitled
The Pitfalls of Simplicity Bias in Neural Networks (Shah et al.).
I totally recommend reading | Should parsimony really still be the gold standard?
Regarding Neural Networks, this topic has been very nicely covered in a recent NeurIPS 2020 paper entitled
The Pitfalls of Simplicity Bias in Neural Networks (Shah et al.).
I totally recommend reading the paper, I think it is very nicely structured and rigorous. Here ... | Should parsimony really still be the gold standard?
Regarding Neural Networks, this topic has been very nicely covered in a recent NeurIPS 2020 paper entitled
The Pitfalls of Simplicity Bias in Neural Networks (Shah et al.).
I totally recommend reading |
6,739 | Why is the Dirichlet distribution the prior for the multinomial distribution? | The Dirichlet distribution is a conjugate prior for the multinomial distribution. This means that if the prior distribution of the multinomial parameters is Dirichlet then the posterior distribution is also a Dirichlet distribution (with parameters different from those of the prior). The benefit of this is that (a) the... | Why is the Dirichlet distribution the prior for the multinomial distribution? | The Dirichlet distribution is a conjugate prior for the multinomial distribution. This means that if the prior distribution of the multinomial parameters is Dirichlet then the posterior distribution i | Why is the Dirichlet distribution the prior for the multinomial distribution?
The Dirichlet distribution is a conjugate prior for the multinomial distribution. This means that if the prior distribution of the multinomial parameters is Dirichlet then the posterior distribution is also a Dirichlet distribution (with para... | Why is the Dirichlet distribution the prior for the multinomial distribution?
The Dirichlet distribution is a conjugate prior for the multinomial distribution. This means that if the prior distribution of the multinomial parameters is Dirichlet then the posterior distribution i |
6,740 | Why is the Dirichlet distribution the prior for the multinomial distribution? | In addition rather than contradiction to Måns T's answer, I simply point out that there is no such thing as "the prior" in Bayesian modelling! The Dirichlet distribution is a convenient choice because of (a) conjugacy, (b) computing, and (c) connection with non-parametric statistics (since this is the discretised versi... | Why is the Dirichlet distribution the prior for the multinomial distribution? | In addition rather than contradiction to Måns T's answer, I simply point out that there is no such thing as "the prior" in Bayesian modelling! The Dirichlet distribution is a convenient choice because | Why is the Dirichlet distribution the prior for the multinomial distribution?
In addition rather than contradiction to Måns T's answer, I simply point out that there is no such thing as "the prior" in Bayesian modelling! The Dirichlet distribution is a convenient choice because of (a) conjugacy, (b) computing, and (c) ... | Why is the Dirichlet distribution the prior for the multinomial distribution?
In addition rather than contradiction to Måns T's answer, I simply point out that there is no such thing as "the prior" in Bayesian modelling! The Dirichlet distribution is a convenient choice because |
6,741 | XGBoost Loss function Approximation With Taylor Expansion | This is a very interesting question. In order to fully understand what was going on, I had to go through what XGBoost is trying to do, and what other methods we had in our toolbox to deal with it. My answer goes over traditional methods, and how/why XGBoost is an improvement. If you want only the bullet points, there i... | XGBoost Loss function Approximation With Taylor Expansion | This is a very interesting question. In order to fully understand what was going on, I had to go through what XGBoost is trying to do, and what other methods we had in our toolbox to deal with it. My | XGBoost Loss function Approximation With Taylor Expansion
This is a very interesting question. In order to fully understand what was going on, I had to go through what XGBoost is trying to do, and what other methods we had in our toolbox to deal with it. My answer goes over traditional methods, and how/why XGBoost is a... | XGBoost Loss function Approximation With Taylor Expansion
This is a very interesting question. In order to fully understand what was going on, I had to go through what XGBoost is trying to do, and what other methods we had in our toolbox to deal with it. My |
6,742 | Neural network with skip-layer connections | I am very late to the game, but I wanted to post to reflect some current developments in convolutional neural networks with respect to skip connections.
A Microsoft Research team recently won the ImageNet 2015 competition and released a technical report Deep Residual Learning for Image Recognition describing some of t... | Neural network with skip-layer connections | I am very late to the game, but I wanted to post to reflect some current developments in convolutional neural networks with respect to skip connections.
A Microsoft Research team recently won the Ima | Neural network with skip-layer connections
I am very late to the game, but I wanted to post to reflect some current developments in convolutional neural networks with respect to skip connections.
A Microsoft Research team recently won the ImageNet 2015 competition and released a technical report Deep Residual Learning... | Neural network with skip-layer connections
I am very late to the game, but I wanted to post to reflect some current developments in convolutional neural networks with respect to skip connections.
A Microsoft Research team recently won the Ima |
6,743 | Neural network with skip-layer connections | In theory, skip-layer connections should not improve on the network performance. But, since complex networks are hard to train and easy to overfit it may be very useful to explicitly add this as a linear regression term, when you know that your data has a strong linear component. This hints the model in a right directi... | Neural network with skip-layer connections | In theory, skip-layer connections should not improve on the network performance. But, since complex networks are hard to train and easy to overfit it may be very useful to explicitly add this as a lin | Neural network with skip-layer connections
In theory, skip-layer connections should not improve on the network performance. But, since complex networks are hard to train and easy to overfit it may be very useful to explicitly add this as a linear regression term, when you know that your data has a strong linear compone... | Neural network with skip-layer connections
In theory, skip-layer connections should not improve on the network performance. But, since complex networks are hard to train and easy to overfit it may be very useful to explicitly add this as a lin |
6,744 | Neural network with skip-layer connections | My old neural network toolbox (I mostly use kernel machines these days) used L1 regularisation to prune away redundant weights and hidden units, and also had skip-layer connections. This has the advantage that if the problem is essentially linear, the hidden units tend to get pruned and you are left with a linear mode... | Neural network with skip-layer connections | My old neural network toolbox (I mostly use kernel machines these days) used L1 regularisation to prune away redundant weights and hidden units, and also had skip-layer connections. This has the adva | Neural network with skip-layer connections
My old neural network toolbox (I mostly use kernel machines these days) used L1 regularisation to prune away redundant weights and hidden units, and also had skip-layer connections. This has the advantage that if the problem is essentially linear, the hidden units tend to get... | Neural network with skip-layer connections
My old neural network toolbox (I mostly use kernel machines these days) used L1 regularisation to prune away redundant weights and hidden units, and also had skip-layer connections. This has the adva |
6,745 | Neural network with skip-layer connections | An in-depth explanation of skip connections from multiple perspectives can be found here:
https://theaisummer.com/skip-connections/
Here I provide the main point from the article:
Basically, skip connection is a standard module in many convolutional architectures. By using a skip connection, we provide an alternative p... | Neural network with skip-layer connections | An in-depth explanation of skip connections from multiple perspectives can be found here:
https://theaisummer.com/skip-connections/
Here I provide the main point from the article:
Basically, skip conn | Neural network with skip-layer connections
An in-depth explanation of skip connections from multiple perspectives can be found here:
https://theaisummer.com/skip-connections/
Here I provide the main point from the article:
Basically, skip connection is a standard module in many convolutional architectures. By using a s... | Neural network with skip-layer connections
An in-depth explanation of skip connections from multiple perspectives can be found here:
https://theaisummer.com/skip-connections/
Here I provide the main point from the article:
Basically, skip conn |
6,746 | Neural network with skip-layer connections | Based on Bishop 5.1. Feed-forward Network Functions:
[A way to generalize] of the network architecture is to include skip-layer connections, each of which is associated with a corresponding adaptive parameter. For instance, in a two-layer network these would go directly from inputs to outputs. In
principle, a network ... | Neural network with skip-layer connections | Based on Bishop 5.1. Feed-forward Network Functions:
[A way to generalize] of the network architecture is to include skip-layer connections, each of which is associated with a corresponding adaptive | Neural network with skip-layer connections
Based on Bishop 5.1. Feed-forward Network Functions:
[A way to generalize] of the network architecture is to include skip-layer connections, each of which is associated with a corresponding adaptive parameter. For instance, in a two-layer network these would go directly from ... | Neural network with skip-layer connections
Based on Bishop 5.1. Feed-forward Network Functions:
[A way to generalize] of the network architecture is to include skip-layer connections, each of which is associated with a corresponding adaptive |
6,747 | How did scientists figure out the shape of the normal distribution probability density function? | "The Evolution of the Normal Distribution" by SAUL STAHL is the best source of information to answer pretty much all the questions in your post. I'll recite a few points for your convenience only, because you'll find the detailed discussion inside the paper.
This is probably an amateur question
No, it's an interestin... | How did scientists figure out the shape of the normal distribution probability density function? | "The Evolution of the Normal Distribution" by SAUL STAHL is the best source of information to answer pretty much all the questions in your post. I'll recite a few points for your convenience only, bec | How did scientists figure out the shape of the normal distribution probability density function?
"The Evolution of the Normal Distribution" by SAUL STAHL is the best source of information to answer pretty much all the questions in your post. I'll recite a few points for your convenience only, because you'll find the de... | How did scientists figure out the shape of the normal distribution probability density function?
"The Evolution of the Normal Distribution" by SAUL STAHL is the best source of information to answer pretty much all the questions in your post. I'll recite a few points for your convenience only, bec |
6,748 | How did scientists figure out the shape of the normal distribution probability density function? | You seem to assume in your question that the concept of the normal distribution was around before the distribution was identified, and people tried to figure out what it was. It's not clear to me how that would work. [Edit: there is at least one sense it which we might consider there being a "search for a distribution"... | How did scientists figure out the shape of the normal distribution probability density function? | You seem to assume in your question that the concept of the normal distribution was around before the distribution was identified, and people tried to figure out what it was. It's not clear to me how | How did scientists figure out the shape of the normal distribution probability density function?
You seem to assume in your question that the concept of the normal distribution was around before the distribution was identified, and people tried to figure out what it was. It's not clear to me how that would work. [Edit:... | How did scientists figure out the shape of the normal distribution probability density function?
You seem to assume in your question that the concept of the normal distribution was around before the distribution was identified, and people tried to figure out what it was. It's not clear to me how |
6,749 | How did scientists figure out the shape of the normal distribution probability density function? | The "normal" distribution is defined to be that particular distribution.
The question is why would we expect this particular distribution to be common in nature, and why is it so often used as an approximation even when the real data does not exactly follow that distribution? (Real data is often found to have a "fat ta... | How did scientists figure out the shape of the normal distribution probability density function? | The "normal" distribution is defined to be that particular distribution.
The question is why would we expect this particular distribution to be common in nature, and why is it so often used as an appr | How did scientists figure out the shape of the normal distribution probability density function?
The "normal" distribution is defined to be that particular distribution.
The question is why would we expect this particular distribution to be common in nature, and why is it so often used as an approximation even when the... | How did scientists figure out the shape of the normal distribution probability density function?
The "normal" distribution is defined to be that particular distribution.
The question is why would we expect this particular distribution to be common in nature, and why is it so often used as an appr |
6,750 | How did scientists figure out the shape of the normal distribution probability density function? | The Normal Distribution (aka "Gaussian Distribution") has a firm mathematical foundation. The Central Limit Theorem says that if you have a finite set of n independent and identically distributed random variables having a specific mean and variance, and you take the average of those random variables, the distribution ... | How did scientists figure out the shape of the normal distribution probability density function? | The Normal Distribution (aka "Gaussian Distribution") has a firm mathematical foundation. The Central Limit Theorem says that if you have a finite set of n independent and identically distributed ran | How did scientists figure out the shape of the normal distribution probability density function?
The Normal Distribution (aka "Gaussian Distribution") has a firm mathematical foundation. The Central Limit Theorem says that if you have a finite set of n independent and identically distributed random variables having a ... | How did scientists figure out the shape of the normal distribution probability density function?
The Normal Distribution (aka "Gaussian Distribution") has a firm mathematical foundation. The Central Limit Theorem says that if you have a finite set of n independent and identically distributed ran |
6,751 | How did scientists figure out the shape of the normal distribution probability density function? | There are some excellent answers on this thread. I can't help feeling the OP wasn't asking the same question as everyone wants to answer. I get that, though, because this is close to being one of the most exciting questions to answer - I actually found it because I was hoping someone had the question "How do we know ... | How did scientists figure out the shape of the normal distribution probability density function? | There are some excellent answers on this thread. I can't help feeling the OP wasn't asking the same question as everyone wants to answer. I get that, though, because this is close to being one of th | How did scientists figure out the shape of the normal distribution probability density function?
There are some excellent answers on this thread. I can't help feeling the OP wasn't asking the same question as everyone wants to answer. I get that, though, because this is close to being one of the most exciting questio... | How did scientists figure out the shape of the normal distribution probability density function?
There are some excellent answers on this thread. I can't help feeling the OP wasn't asking the same question as everyone wants to answer. I get that, though, because this is close to being one of th |
6,752 | How did scientists figure out the shape of the normal distribution probability density function? | Would also mention Maxwell-Herschel derivation of independent multivariate normal distribution from two assumptions:
Distribution is not affected by rotation of the vector.
Components of the vector are independent.
Here is the exposition by Jaynes | How did scientists figure out the shape of the normal distribution probability density function? | Would also mention Maxwell-Herschel derivation of independent multivariate normal distribution from two assumptions:
Distribution is not affected by rotation of the vector.
Components of the vector a | How did scientists figure out the shape of the normal distribution probability density function?
Would also mention Maxwell-Herschel derivation of independent multivariate normal distribution from two assumptions:
Distribution is not affected by rotation of the vector.
Components of the vector are independent.
Here i... | How did scientists figure out the shape of the normal distribution probability density function?
Would also mention Maxwell-Herschel derivation of independent multivariate normal distribution from two assumptions:
Distribution is not affected by rotation of the vector.
Components of the vector a |
6,753 | Why is the null hypothesis often sought to be rejected? | The purpose of statistical hypothesis testing is largely to impose self-skepticism, making us cautious about promulgating our hypothesis unless there is reasonable evidence to support it. Thus in the usual form of hypothesis testing the null hypothesis provides a "devils advocate", arguing against us, and only promulg... | Why is the null hypothesis often sought to be rejected? | The purpose of statistical hypothesis testing is largely to impose self-skepticism, making us cautious about promulgating our hypothesis unless there is reasonable evidence to support it. Thus in the | Why is the null hypothesis often sought to be rejected?
The purpose of statistical hypothesis testing is largely to impose self-skepticism, making us cautious about promulgating our hypothesis unless there is reasonable evidence to support it. Thus in the usual form of hypothesis testing the null hypothesis provides a... | Why is the null hypothesis often sought to be rejected?
The purpose of statistical hypothesis testing is largely to impose self-skepticism, making us cautious about promulgating our hypothesis unless there is reasonable evidence to support it. Thus in the |
6,754 | Why is the null hypothesis often sought to be rejected? | Karl Popper says "We cannot conclusively affirm a hypothesis, but we can conclusively negate it". So when we do hypothesis testing in statistics, we try to negate (reject) the opposite hypothesis (the null hypothesis) of the hypothesis we are interested in (the alternative hypothesis) and which we can not affirm. Since... | Why is the null hypothesis often sought to be rejected? | Karl Popper says "We cannot conclusively affirm a hypothesis, but we can conclusively negate it". So when we do hypothesis testing in statistics, we try to negate (reject) the opposite hypothesis (the | Why is the null hypothesis often sought to be rejected?
Karl Popper says "We cannot conclusively affirm a hypothesis, but we can conclusively negate it". So when we do hypothesis testing in statistics, we try to negate (reject) the opposite hypothesis (the null hypothesis) of the hypothesis we are interested in (the al... | Why is the null hypothesis often sought to be rejected?
Karl Popper says "We cannot conclusively affirm a hypothesis, but we can conclusively negate it". So when we do hypothesis testing in statistics, we try to negate (reject) the opposite hypothesis (the |
6,755 | Why is the null hypothesis often sought to be rejected? | It is not taken for granted that the null is always to be rejected. In model fit testing, the null is usually that the model fits well, and that is something desirable that we would hate to reject. It is, however, usually true that the sampling distribution of the test statistic is easier to derive under the null, whic... | Why is the null hypothesis often sought to be rejected? | It is not taken for granted that the null is always to be rejected. In model fit testing, the null is usually that the model fits well, and that is something desirable that we would hate to reject. It | Why is the null hypothesis often sought to be rejected?
It is not taken for granted that the null is always to be rejected. In model fit testing, the null is usually that the model fits well, and that is something desirable that we would hate to reject. It is, however, usually true that the sampling distribution of the... | Why is the null hypothesis often sought to be rejected?
It is not taken for granted that the null is always to be rejected. In model fit testing, the null is usually that the model fits well, and that is something desirable that we would hate to reject. It |
6,756 | Why is the null hypothesis often sought to be rejected? | This is a fair and good question. @Tim already gave you all you need to answer your question in a formal way, however if you are not familiar with statistical hypothesis testing you could conceptualize the null hypothesis by thinking about it in a more familiar setting.
Suppose you are being accused of having conduct... | Why is the null hypothesis often sought to be rejected? | This is a fair and good question. @Tim already gave you all you need to answer your question in a formal way, however if you are not familiar with statistical hypothesis testing you could conceptuali | Why is the null hypothesis often sought to be rejected?
This is a fair and good question. @Tim already gave you all you need to answer your question in a formal way, however if you are not familiar with statistical hypothesis testing you could conceptualize the null hypothesis by thinking about it in a more familiar s... | Why is the null hypothesis often sought to be rejected?
This is a fair and good question. @Tim already gave you all you need to answer your question in a formal way, however if you are not familiar with statistical hypothesis testing you could conceptuali |
6,757 | Why is the null hypothesis often sought to be rejected? | The law of parsimony (also known as Occam's razor) is a general principle of science. Under that principle, we assume a simple world until it can be shown that the world is more complicated. So, we assume the simpler world of the null hypothesis until it can be falsified. For example:
We assume treatment A and treatm... | Why is the null hypothesis often sought to be rejected? | The law of parsimony (also known as Occam's razor) is a general principle of science. Under that principle, we assume a simple world until it can be shown that the world is more complicated. So, we | Why is the null hypothesis often sought to be rejected?
The law of parsimony (also known as Occam's razor) is a general principle of science. Under that principle, we assume a simple world until it can be shown that the world is more complicated. So, we assume the simpler world of the null hypothesis until it can be ... | Why is the null hypothesis often sought to be rejected?
The law of parsimony (also known as Occam's razor) is a general principle of science. Under that principle, we assume a simple world until it can be shown that the world is more complicated. So, we |
6,758 | Why is the null hypothesis often sought to be rejected? | If I can draw an analogy to logic, a general way to prove something is to assume the opposite and see if that leads to a contradiction. Here the null hypothesis is like the opposite, and rejecting it (i.e. showing that it is very unlikely) is like deriving the contradiction.
You do it that way because it's a way to mak... | Why is the null hypothesis often sought to be rejected? | If I can draw an analogy to logic, a general way to prove something is to assume the opposite and see if that leads to a contradiction. Here the null hypothesis is like the opposite, and rejecting it | Why is the null hypothesis often sought to be rejected?
If I can draw an analogy to logic, a general way to prove something is to assume the opposite and see if that leads to a contradiction. Here the null hypothesis is like the opposite, and rejecting it (i.e. showing that it is very unlikely) is like deriving the con... | Why is the null hypothesis often sought to be rejected?
If I can draw an analogy to logic, a general way to prove something is to assume the opposite and see if that leads to a contradiction. Here the null hypothesis is like the opposite, and rejecting it |
6,759 | Why is the null hypothesis often sought to be rejected? | The null hypothesis is always formed with the intention to reject it that is the basic idea of hypothesis testing. When you are trying to show that something is likely to be true (e.g. a treatment improves or worsens a disease), then the null hypothesis is the default position (e.g. the treatment does not make a differ... | Why is the null hypothesis often sought to be rejected? | The null hypothesis is always formed with the intention to reject it that is the basic idea of hypothesis testing. When you are trying to show that something is likely to be true (e.g. a treatment imp | Why is the null hypothesis often sought to be rejected?
The null hypothesis is always formed with the intention to reject it that is the basic idea of hypothesis testing. When you are trying to show that something is likely to be true (e.g. a treatment improves or worsens a disease), then the null hypothesis is the def... | Why is the null hypothesis often sought to be rejected?
The null hypothesis is always formed with the intention to reject it that is the basic idea of hypothesis testing. When you are trying to show that something is likely to be true (e.g. a treatment imp |
6,760 | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean? | Causal theory offers another explanation for how two variables could be unconditionally independent yet conditionally dependent. I am not an expert on causal theory and am grateful for any criticism that will correct any misguidance below.
To illustrate, I will use directed acyclic graphs (DAG). In these graphs, edges ... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it | Causal theory offers another explanation for how two variables could be unconditionally independent yet conditionally dependent. I am not an expert on causal theory and am grateful for any criticism t | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?
Causal theory offers another explanation for how two variables could be unconditionally independent yet conditionally dependent. I am not an expert on causal theory and am grateful for any criticism that will corr... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it
Causal theory offers another explanation for how two variables could be unconditionally independent yet conditionally dependent. I am not an expert on causal theory and am grateful for any criticism t |
6,761 | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean? | I think @jthetzel's approach is the right one (+1). In order to interpret these results you will have to think about / have some theory of why the relationships manifest as they do. That is, you will need to think about the pattern of causal relationships that underlies your data. You need to recognize that, as @jth... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it | I think @jthetzel's approach is the right one (+1). In order to interpret these results you will have to think about / have some theory of why the relationships manifest as they do. That is, you wil | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?
I think @jthetzel's approach is the right one (+1). In order to interpret these results you will have to think about / have some theory of why the relationships manifest as they do. That is, you will need to thi... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it
I think @jthetzel's approach is the right one (+1). In order to interpret these results you will have to think about / have some theory of why the relationships manifest as they do. That is, you wil |
6,762 | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean? | Just some visualization that it is possible.
On picture (a) "normal" or "intuitive" regressional situation is shown. This pic is the same as for example found (and explained) here or here.
The variables are drawn as vectors. Angles between them (their cosines) are the variables' correlations. $Y'$ here designates the v... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it | Just some visualization that it is possible.
On picture (a) "normal" or "intuitive" regressional situation is shown. This pic is the same as for example found (and explained) here or here.
The variabl | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?
Just some visualization that it is possible.
On picture (a) "normal" or "intuitive" regressional situation is shown. This pic is the same as for example found (and explained) here or here.
The variables are drawn ... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it
Just some visualization that it is possible.
On picture (a) "normal" or "intuitive" regressional situation is shown. This pic is the same as for example found (and explained) here or here.
The variabl |
6,763 | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean? | I agree with the previous answer but hope I can contribute by giving more details.
The correlation coefficient is just measuring the linear dependence between $X$ and $Y$ and it's not controlling for the fact that other variables might be involved in the relationship as well. In fact the correlation coefficient equals ... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it | I agree with the previous answer but hope I can contribute by giving more details.
The correlation coefficient is just measuring the linear dependence between $X$ and $Y$ and it's not controlling for | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?
I agree with the previous answer but hope I can contribute by giving more details.
The correlation coefficient is just measuring the linear dependence between $X$ and $Y$ and it's not controlling for the fact that... | X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it
I agree with the previous answer but hope I can contribute by giving more details.
The correlation coefficient is just measuring the linear dependence between $X$ and $Y$ and it's not controlling for |
6,764 | Difference between feedback RNN and LSTM/GRU | All RNNs have feedback loops in the recurrent layer. This lets them maintain information in 'memory' over time. But, it can be difficult to train standard RNNs to solve problems that require learning long-term temporal dependencies. This is because the gradient of the loss function decays exponentially with time (calle... | Difference between feedback RNN and LSTM/GRU | All RNNs have feedback loops in the recurrent layer. This lets them maintain information in 'memory' over time. But, it can be difficult to train standard RNNs to solve problems that require learning | Difference between feedback RNN and LSTM/GRU
All RNNs have feedback loops in the recurrent layer. This lets them maintain information in 'memory' over time. But, it can be difficult to train standard RNNs to solve problems that require learning long-term temporal dependencies. This is because the gradient of the loss f... | Difference between feedback RNN and LSTM/GRU
All RNNs have feedback loops in the recurrent layer. This lets them maintain information in 'memory' over time. But, it can be difficult to train standard RNNs to solve problems that require learning |
6,765 | Difference between feedback RNN and LSTM/GRU | Standard RNNs (Recurrent Neural Networks) suffer from vanishing and exploding gradient problems. LSTMs (Long Short Term Memory) deal with these problems by introducing new gates, such as input and forget gates, which allow for a better control over the gradient flow and enable better preservation of “long-range depend... | Difference between feedback RNN and LSTM/GRU | Standard RNNs (Recurrent Neural Networks) suffer from vanishing and exploding gradient problems. LSTMs (Long Short Term Memory) deal with these problems by introducing new gates, such as input and fo | Difference between feedback RNN and LSTM/GRU
Standard RNNs (Recurrent Neural Networks) suffer from vanishing and exploding gradient problems. LSTMs (Long Short Term Memory) deal with these problems by introducing new gates, such as input and forget gates, which allow for a better control over the gradient flow and ena... | Difference between feedback RNN and LSTM/GRU
Standard RNNs (Recurrent Neural Networks) suffer from vanishing and exploding gradient problems. LSTMs (Long Short Term Memory) deal with these problems by introducing new gates, such as input and fo |
6,766 | Difference between feedback RNN and LSTM/GRU | LSTMs are often referred to as fancy RNNs. Vanilla RNNs do not have a cell state. They only have hidden states and those hidden states serve as the memory for RNNs.
Meanwhile, LSTM has both cell states and a hidden states. The cell state has the ability to remove or add information to the cell, regulated by "gates". A... | Difference between feedback RNN and LSTM/GRU | LSTMs are often referred to as fancy RNNs. Vanilla RNNs do not have a cell state. They only have hidden states and those hidden states serve as the memory for RNNs.
Meanwhile, LSTM has both cell stat | Difference between feedback RNN and LSTM/GRU
LSTMs are often referred to as fancy RNNs. Vanilla RNNs do not have a cell state. They only have hidden states and those hidden states serve as the memory for RNNs.
Meanwhile, LSTM has both cell states and a hidden states. The cell state has the ability to remove or add inf... | Difference between feedback RNN and LSTM/GRU
LSTMs are often referred to as fancy RNNs. Vanilla RNNs do not have a cell state. They only have hidden states and those hidden states serve as the memory for RNNs.
Meanwhile, LSTM has both cell stat |
6,767 | Difference between feedback RNN and LSTM/GRU | TL;DR
We can say that, when we move from RNN to LSTM (Long Short-Term Memory), we are introducing
more & more controlling knobs, which control the flow and mixing of
Inputs as per trained Weights. And thus, bringing in more flexibility
in controlling the outputs. So, LSTM gives us the most Control-ability
and thus, Be... | Difference between feedback RNN and LSTM/GRU | TL;DR
We can say that, when we move from RNN to LSTM (Long Short-Term Memory), we are introducing
more & more controlling knobs, which control the flow and mixing of
Inputs as per trained Weights. An | Difference between feedback RNN and LSTM/GRU
TL;DR
We can say that, when we move from RNN to LSTM (Long Short-Term Memory), we are introducing
more & more controlling knobs, which control the flow and mixing of
Inputs as per trained Weights. And thus, bringing in more flexibility
in controlling the outputs. So, LSTM g... | Difference between feedback RNN and LSTM/GRU
TL;DR
We can say that, when we move from RNN to LSTM (Long Short-Term Memory), we are introducing
more & more controlling knobs, which control the flow and mixing of
Inputs as per trained Weights. An |
6,768 | Difference between feedback RNN and LSTM/GRU | I think the difference between regular RNNs and the so-called "gated RNNs" is well explained in the existing answers to this question. However, I would like to add my two cents by pointing out the exact differences and similarities between LSTM and GRU.
The original definitions mostly come in the following form (I omit... | Difference between feedback RNN and LSTM/GRU | I think the difference between regular RNNs and the so-called "gated RNNs" is well explained in the existing answers to this question. However, I would like to add my two cents by pointing out the exa | Difference between feedback RNN and LSTM/GRU
I think the difference between regular RNNs and the so-called "gated RNNs" is well explained in the existing answers to this question. However, I would like to add my two cents by pointing out the exact differences and similarities between LSTM and GRU.
The original definiti... | Difference between feedback RNN and LSTM/GRU
I think the difference between regular RNNs and the so-called "gated RNNs" is well explained in the existing answers to this question. However, I would like to add my two cents by pointing out the exa |
6,769 | How to interpret the coefficient of variation? | In examples like yours when data differ just additively, i.e. we add some constant $k$ to everything, then as you point out the standard deviation is unchanged, the mean is changed by exactly that constant, and so the coefficient of variation changes from $\sigma / \mu$ to $\sigma / (\mu + k)$, which is neither interes... | How to interpret the coefficient of variation? | In examples like yours when data differ just additively, i.e. we add some constant $k$ to everything, then as you point out the standard deviation is unchanged, the mean is changed by exactly that con | How to interpret the coefficient of variation?
In examples like yours when data differ just additively, i.e. we add some constant $k$ to everything, then as you point out the standard deviation is unchanged, the mean is changed by exactly that constant, and so the coefficient of variation changes from $\sigma / \mu$ to... | How to interpret the coefficient of variation?
In examples like yours when data differ just additively, i.e. we add some constant $k$ to everything, then as you point out the standard deviation is unchanged, the mean is changed by exactly that con |
6,770 | How to interpret the coefficient of variation? | Imagine I said "There are 1,625,330 people in this town. Plus or minus five." You'd be impressed by my accurate demographic knowledge.
But if I said "There are five people in this house. Plus or minus five." You'd think I had no clue how many people were in the house.
Same standard deviation, much different CV's. | How to interpret the coefficient of variation? | Imagine I said "There are 1,625,330 people in this town. Plus or minus five." You'd be impressed by my accurate demographic knowledge.
But if I said "There are five people in this house. Plus or minu | How to interpret the coefficient of variation?
Imagine I said "There are 1,625,330 people in this town. Plus or minus five." You'd be impressed by my accurate demographic knowledge.
But if I said "There are five people in this house. Plus or minus five." You'd think I had no clue how many people were in the house.
Sa... | How to interpret the coefficient of variation?
Imagine I said "There are 1,625,330 people in this town. Plus or minus five." You'd be impressed by my accurate demographic knowledge.
But if I said "There are five people in this house. Plus or minu |
6,771 | How to interpret the coefficient of variation? | Normally, you use coefficient of variation for variable of different units of measure or very different scales. You can think of it as noise/signal ratio. For instance, you may want to compare variability of the weight and height of students; variability of GDP of USA and Monaco.
In your case, coefficient of variation ... | How to interpret the coefficient of variation? | Normally, you use coefficient of variation for variable of different units of measure or very different scales. You can think of it as noise/signal ratio. For instance, you may want to compare variabi | How to interpret the coefficient of variation?
Normally, you use coefficient of variation for variable of different units of measure or very different scales. You can think of it as noise/signal ratio. For instance, you may want to compare variability of the weight and height of students; variability of GDP of USA and ... | How to interpret the coefficient of variation?
Normally, you use coefficient of variation for variable of different units of measure or very different scales. You can think of it as noise/signal ratio. For instance, you may want to compare variabi |
6,772 | How to interpret the coefficient of variation? | Sample with higher values has less variation relative to its mean, as the definition ($s / \bar{x} $) suggests. It is actually pretty straight-forward. Coefficient of variation is useful when comparing variation between samples (or populations) of different scales. Consider you are dealing with wages among countries. C... | How to interpret the coefficient of variation? | Sample with higher values has less variation relative to its mean, as the definition ($s / \bar{x} $) suggests. It is actually pretty straight-forward. Coefficient of variation is useful when comparin | How to interpret the coefficient of variation?
Sample with higher values has less variation relative to its mean, as the definition ($s / \bar{x} $) suggests. It is actually pretty straight-forward. Coefficient of variation is useful when comparing variation between samples (or populations) of different scales. Conside... | How to interpret the coefficient of variation?
Sample with higher values has less variation relative to its mean, as the definition ($s / \bar{x} $) suggests. It is actually pretty straight-forward. Coefficient of variation is useful when comparin |
6,773 | How to interpret the coefficient of variation? | In actuality, both statistics can be misleading if you do not know or understand your hypothesis and experiment. Consider this gruesome example... Walking across two high rise buildings on a tightrope as opposed to walking on a plank. Let's say that the tightrope has a 1 inch diameter, whereas the plank is 12 inches wi... | How to interpret the coefficient of variation? | In actuality, both statistics can be misleading if you do not know or understand your hypothesis and experiment. Consider this gruesome example... Walking across two high rise buildings on a tightrope | How to interpret the coefficient of variation?
In actuality, both statistics can be misleading if you do not know or understand your hypothesis and experiment. Consider this gruesome example... Walking across two high rise buildings on a tightrope as opposed to walking on a plank. Let's say that the tightrope has a 1 i... | How to interpret the coefficient of variation?
In actuality, both statistics can be misleading if you do not know or understand your hypothesis and experiment. Consider this gruesome example... Walking across two high rise buildings on a tightrope |
6,774 | How to interpret the coefficient of variation? | CV is a relative variability that is used to compare the variability of different sample dataset.
For a you example, the same standard deviation/variance with smaller mean will generate a smaller CV. it indicates that smaller CV dataset has smaller relative variability.
Assume You earn 10000 monthly, and I earn 100.(... | How to interpret the coefficient of variation? | CV is a relative variability that is used to compare the variability of different sample dataset.
For a you example, the same standard deviation/variance with smaller mean will generate a smaller CV. | How to interpret the coefficient of variation?
CV is a relative variability that is used to compare the variability of different sample dataset.
For a you example, the same standard deviation/variance with smaller mean will generate a smaller CV. it indicates that smaller CV dataset has smaller relative variability.
... | How to interpret the coefficient of variation?
CV is a relative variability that is used to compare the variability of different sample dataset.
For a you example, the same standard deviation/variance with smaller mean will generate a smaller CV. |
6,775 | How to interpret the coefficient of variation? | in this case, cv is not the right statistical tool to explain the result.
depending on the nature of the research carried out hence the objective, researcher has a specific hypothesis or point to proof. He or she must design, execute experiment and analyse data using the best and appropriate statistical tool i.e. if th... | How to interpret the coefficient of variation? | in this case, cv is not the right statistical tool to explain the result.
depending on the nature of the research carried out hence the objective, researcher has a specific hypothesis or point to proo | How to interpret the coefficient of variation?
in this case, cv is not the right statistical tool to explain the result.
depending on the nature of the research carried out hence the objective, researcher has a specific hypothesis or point to proof. He or she must design, execute experiment and analyse data using the b... | How to interpret the coefficient of variation?
in this case, cv is not the right statistical tool to explain the result.
depending on the nature of the research carried out hence the objective, researcher has a specific hypothesis or point to proo |
6,776 | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row? | Below we compute the probability in four ways:
Computation with Markov Chain 0.473981098314993
Computation with generating function 0.473981098314988
Estimation false method 0.536438013618686
Estimation correct method 0.473304632462677
The first two are exact methods and differ o... | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a ro | Below we compute the probability in four ways:
Computation with Markov Chain 0.473981098314993
Computation with generating function 0.473981098314988
Estimation false method | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row?
Below we compute the probability in four ways:
Computation with Markov Chain 0.473981098314993
Computation with generating function 0.473981098314988
Estimation false method 0.536438013618686... | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a ro
Below we compute the probability in four ways:
Computation with Markov Chain 0.473981098314993
Computation with generating function 0.473981098314988
Estimation false method |
6,777 | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row? | I got a different result from the accepted answer and would like to know where I've gone wrong.
I assumed a fair, 6-sided die, and simulated 1000 runs of 1000 rolls each. When the result of a roll matches the results of the previous 4 rolls, a flag is set to TRUE. The mean of this flag column and the mean of the runs i... | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a ro | I got a different result from the accepted answer and would like to know where I've gone wrong.
I assumed a fair, 6-sided die, and simulated 1000 runs of 1000 rolls each. When the result of a roll mat | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row?
I got a different result from the accepted answer and would like to know where I've gone wrong.
I assumed a fair, 6-sided die, and simulated 1000 runs of 1000 rolls each. When the result of a roll matches the results ... | A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a ro
I got a different result from the accepted answer and would like to know where I've gone wrong.
I assumed a fair, 6-sided die, and simulated 1000 runs of 1000 rolls each. When the result of a roll mat |
6,778 | Is cosine similarity identical to l2-normalized euclidean distance? | For $\ell^2$-normalized vectors $\mathbf{x}, \mathbf{y}$,
$$||\mathbf{x}||_2 = ||\mathbf{y}||_2 = 1,$$
we have that the squared Euclidean distance is proportional to the cosine distance,
\begin{align}
||\mathbf{x} - \mathbf{y}||_2^2
&= (\mathbf{x} - \mathbf{y})^\top (\mathbf{x} - \mathbf{y}) \\
&= \mathbf{x}^\top \math... | Is cosine similarity identical to l2-normalized euclidean distance? | For $\ell^2$-normalized vectors $\mathbf{x}, \mathbf{y}$,
$$||\mathbf{x}||_2 = ||\mathbf{y}||_2 = 1,$$
we have that the squared Euclidean distance is proportional to the cosine distance,
\begin{align} | Is cosine similarity identical to l2-normalized euclidean distance?
For $\ell^2$-normalized vectors $\mathbf{x}, \mathbf{y}$,
$$||\mathbf{x}||_2 = ||\mathbf{y}||_2 = 1,$$
we have that the squared Euclidean distance is proportional to the cosine distance,
\begin{align}
||\mathbf{x} - \mathbf{y}||_2^2
&= (\mathbf{x} - \m... | Is cosine similarity identical to l2-normalized euclidean distance?
For $\ell^2$-normalized vectors $\mathbf{x}, \mathbf{y}$,
$$||\mathbf{x}||_2 = ||\mathbf{y}||_2 = 1,$$
we have that the squared Euclidean distance is proportional to the cosine distance,
\begin{align} |
6,779 | Is cosine similarity identical to l2-normalized euclidean distance? | Standard cosine similarity is defined as follows in a Euclidian space, assuming column vectors $\mathbf{u}$ and $\mathbf{v}$:
$$
\cos(\mathbf{u}, \mathbf{v}) = \frac{\langle \mathbf{u}, \mathbf{v} \rangle}{\|\mathbf{u}\| \cdot \|\mathbf{v}\|} = \frac{\mathbf{u}^T\mathbf{v}}{\|\mathbf{u}\| \cdot \|\mathbf{v}\|} \in [-1,... | Is cosine similarity identical to l2-normalized euclidean distance? | Standard cosine similarity is defined as follows in a Euclidian space, assuming column vectors $\mathbf{u}$ and $\mathbf{v}$:
$$
\cos(\mathbf{u}, \mathbf{v}) = \frac{\langle \mathbf{u}, \mathbf{v} \ra | Is cosine similarity identical to l2-normalized euclidean distance?
Standard cosine similarity is defined as follows in a Euclidian space, assuming column vectors $\mathbf{u}$ and $\mathbf{v}$:
$$
\cos(\mathbf{u}, \mathbf{v}) = \frac{\langle \mathbf{u}, \mathbf{v} \rangle}{\|\mathbf{u}\| \cdot \|\mathbf{v}\|} = \frac{\... | Is cosine similarity identical to l2-normalized euclidean distance?
Standard cosine similarity is defined as follows in a Euclidian space, assuming column vectors $\mathbf{u}$ and $\mathbf{v}$:
$$
\cos(\mathbf{u}, \mathbf{v}) = \frac{\langle \mathbf{u}, \mathbf{v} \ra |
6,780 | What are the most common biases humans make when collecting or interpreting data? | I think in academia, p-values are very commonly misinterpreted. People tend to forget that the p-value expresses a conditional probability. Even if an experiment has been perfectly conducted and all requisites of the chosen statistical test are met, the false discovery rate is typically much higher than the significanc... | What are the most common biases humans make when collecting or interpreting data? | I think in academia, p-values are very commonly misinterpreted. People tend to forget that the p-value expresses a conditional probability. Even if an experiment has been perfectly conducted and all r | What are the most common biases humans make when collecting or interpreting data?
I think in academia, p-values are very commonly misinterpreted. People tend to forget that the p-value expresses a conditional probability. Even if an experiment has been perfectly conducted and all requisites of the chosen statistical te... | What are the most common biases humans make when collecting or interpreting data?
I think in academia, p-values are very commonly misinterpreted. People tend to forget that the p-value expresses a conditional probability. Even if an experiment has been perfectly conducted and all r |
6,781 | What are the most common biases humans make when collecting or interpreting data? | I would say a general inability to appreciate what true randomness looks like. People seem to expect too few spurious patterns than actually occur in sequences of random events. This also shows up when we try to simulate randomness on our own.
Another fairly common one is not understanding independence, as in the gam... | What are the most common biases humans make when collecting or interpreting data? | I would say a general inability to appreciate what true randomness looks like. People seem to expect too few spurious patterns than actually occur in sequences of random events. This also shows up w | What are the most common biases humans make when collecting or interpreting data?
I would say a general inability to appreciate what true randomness looks like. People seem to expect too few spurious patterns than actually occur in sequences of random events. This also shows up when we try to simulate randomness on o... | What are the most common biases humans make when collecting or interpreting data?
I would say a general inability to appreciate what true randomness looks like. People seem to expect too few spurious patterns than actually occur in sequences of random events. This also shows up w |
6,782 | What are the most common biases humans make when collecting or interpreting data? | It has already been pointed out that many of the behaviors and thought processes labeled "irrational" or "biased" by (behavioral) economists are actually highly adaptive and efficient in the real world. Nonetheless, OP's question is interesting. I think, however, that it may be profitable to refer to more fundamental, ... | What are the most common biases humans make when collecting or interpreting data? | It has already been pointed out that many of the behaviors and thought processes labeled "irrational" or "biased" by (behavioral) economists are actually highly adaptive and efficient in the real worl | What are the most common biases humans make when collecting or interpreting data?
It has already been pointed out that many of the behaviors and thought processes labeled "irrational" or "biased" by (behavioral) economists are actually highly adaptive and efficient in the real world. Nonetheless, OP's question is inter... | What are the most common biases humans make when collecting or interpreting data?
It has already been pointed out that many of the behaviors and thought processes labeled "irrational" or "biased" by (behavioral) economists are actually highly adaptive and efficient in the real worl |
6,783 | What are the most common biases humans make when collecting or interpreting data? | The biggest single factor I can think of is broadly known as "confirmation bias". Having settled upon what I think my study will show, I uncritically accept data that lead to that conclusion, while making excuses for all data points that appear to refute it. I may unconsciously reject as "obvious instrument error" (o... | What are the most common biases humans make when collecting or interpreting data? | The biggest single factor I can think of is broadly known as "confirmation bias". Having settled upon what I think my study will show, I uncritically accept data that lead to that conclusion, while m | What are the most common biases humans make when collecting or interpreting data?
The biggest single factor I can think of is broadly known as "confirmation bias". Having settled upon what I think my study will show, I uncritically accept data that lead to that conclusion, while making excuses for all data points that... | What are the most common biases humans make when collecting or interpreting data?
The biggest single factor I can think of is broadly known as "confirmation bias". Having settled upon what I think my study will show, I uncritically accept data that lead to that conclusion, while m |
6,784 | What are the most common biases humans make when collecting or interpreting data? | Linearity.
I think a common bias during data interpretation/analysis is that people usually are quick to assume linear relations. Mathematically, a regression model assumes that its deterministic component is a linear function of the predictors; unfortunately that is not always true. I recently went to an undergraduat... | What are the most common biases humans make when collecting or interpreting data? | Linearity.
I think a common bias during data interpretation/analysis is that people usually are quick to assume linear relations. Mathematically, a regression model assumes that its deterministic com | What are the most common biases humans make when collecting or interpreting data?
Linearity.
I think a common bias during data interpretation/analysis is that people usually are quick to assume linear relations. Mathematically, a regression model assumes that its deterministic component is a linear function of the pre... | What are the most common biases humans make when collecting or interpreting data?
Linearity.
I think a common bias during data interpretation/analysis is that people usually are quick to assume linear relations. Mathematically, a regression model assumes that its deterministic com |
6,785 | What are the most common biases humans make when collecting or interpreting data? | An intersting case is the discussions of the Gamblers Fallacy.
Should the existing data be included or exluded? If I am already ahead with 6 sixes, are these to be included in my run of a dozen tries? Be clear about prior data.
When should I change from absolute numbers to ratio's? It takes a long time for the advanta... | What are the most common biases humans make when collecting or interpreting data? | An intersting case is the discussions of the Gamblers Fallacy.
Should the existing data be included or exluded? If I am already ahead with 6 sixes, are these to be included in my run of a dozen tries | What are the most common biases humans make when collecting or interpreting data?
An intersting case is the discussions of the Gamblers Fallacy.
Should the existing data be included or exluded? If I am already ahead with 6 sixes, are these to be included in my run of a dozen tries? Be clear about prior data.
When shou... | What are the most common biases humans make when collecting or interpreting data?
An intersting case is the discussions of the Gamblers Fallacy.
Should the existing data be included or exluded? If I am already ahead with 6 sixes, are these to be included in my run of a dozen tries |
6,786 | What are the most common biases humans make when collecting or interpreting data? | I would recommend "Thinking, Fast and Slow" by Daniel Kahneman, which explains many cognitive biases in lucid language.
You may also refer to "http://www.burns-stat.com/review-thinking-fast-slow-daniel-kahneman/" which summarizes some of the biases in the above book.
For more detailed chapter wise summary you may want ... | What are the most common biases humans make when collecting or interpreting data? | I would recommend "Thinking, Fast and Slow" by Daniel Kahneman, which explains many cognitive biases in lucid language.
You may also refer to "http://www.burns-stat.com/review-thinking-fast-slow-danie | What are the most common biases humans make when collecting or interpreting data?
I would recommend "Thinking, Fast and Slow" by Daniel Kahneman, which explains many cognitive biases in lucid language.
You may also refer to "http://www.burns-stat.com/review-thinking-fast-slow-daniel-kahneman/" which summarizes some of ... | What are the most common biases humans make when collecting or interpreting data?
I would recommend "Thinking, Fast and Slow" by Daniel Kahneman, which explains many cognitive biases in lucid language.
You may also refer to "http://www.burns-stat.com/review-thinking-fast-slow-danie |
6,787 | Simple way to algorithmically identify a spike in recorded errors | It has been 5 months since you asked this question, and hopefully you figured something out. I'm going to make a few different suggestions here, hoping that you find some use for them in other scenarios.
For your use-case I don't think you need to look at spike-detection algorithms.
So here goes:
Let's start with a pi... | Simple way to algorithmically identify a spike in recorded errors | It has been 5 months since you asked this question, and hopefully you figured something out. I'm going to make a few different suggestions here, hoping that you find some use for them in other scenari | Simple way to algorithmically identify a spike in recorded errors
It has been 5 months since you asked this question, and hopefully you figured something out. I'm going to make a few different suggestions here, hoping that you find some use for them in other scenarios.
For your use-case I don't think you need to look a... | Simple way to algorithmically identify a spike in recorded errors
It has been 5 months since you asked this question, and hopefully you figured something out. I'm going to make a few different suggestions here, hoping that you find some use for them in other scenari |
6,788 | Simple way to algorithmically identify a spike in recorded errors | +1 for Statistical process control, there's some useful information here on Step Detection.
For SPC it's not too hard to write an implementation of either the Western Electric Rules or the Nelson Rules.
Just make a USP in SQL server that will iterate through a data set and ping each point against the rules using its ne... | Simple way to algorithmically identify a spike in recorded errors | +1 for Statistical process control, there's some useful information here on Step Detection.
For SPC it's not too hard to write an implementation of either the Western Electric Rules or the Nelson Rule | Simple way to algorithmically identify a spike in recorded errors
+1 for Statistical process control, there's some useful information here on Step Detection.
For SPC it's not too hard to write an implementation of either the Western Electric Rules or the Nelson Rules.
Just make a USP in SQL server that will iterate thr... | Simple way to algorithmically identify a spike in recorded errors
+1 for Statistical process control, there's some useful information here on Step Detection.
For SPC it's not too hard to write an implementation of either the Western Electric Rules or the Nelson Rule |
6,789 | Simple way to algorithmically identify a spike in recorded errors | A search for Online detection algorithms would be a start.
More information located on stackoverflow: Peak Dection of measured signal
A python implementation of a naive peak detection routine is to be found at github | Simple way to algorithmically identify a spike in recorded errors | A search for Online detection algorithms would be a start.
More information located on stackoverflow: Peak Dection of measured signal
A python implementation of a naive peak detection routine is to be | Simple way to algorithmically identify a spike in recorded errors
A search for Online detection algorithms would be a start.
More information located on stackoverflow: Peak Dection of measured signal
A python implementation of a naive peak detection routine is to be found at github | Simple way to algorithmically identify a spike in recorded errors
A search for Online detection algorithms would be a start.
More information located on stackoverflow: Peak Dection of measured signal
A python implementation of a naive peak detection routine is to be |
6,790 | Simple way to algorithmically identify a spike in recorded errors | You may want to look at statistical process control. Or time series monitoring. There are tons of work in this direction, and the optimal answer probably depends a lot on what exactly you are doing (do you need to filter out yearly or weekly seasonalities in load before detecting anomalies etc.). | Simple way to algorithmically identify a spike in recorded errors | You may want to look at statistical process control. Or time series monitoring. There are tons of work in this direction, and the optimal answer probably depends a lot on what exactly you are doing (d | Simple way to algorithmically identify a spike in recorded errors
You may want to look at statistical process control. Or time series monitoring. There are tons of work in this direction, and the optimal answer probably depends a lot on what exactly you are doing (do you need to filter out yearly or weekly seasonalitie... | Simple way to algorithmically identify a spike in recorded errors
You may want to look at statistical process control. Or time series monitoring. There are tons of work in this direction, and the optimal answer probably depends a lot on what exactly you are doing (d |
6,791 | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval? | Many frequentist confidence intervals (CIs) are based on the likelihood function.
If the prior distribution is truly non-informative, then the a Bayesian
posterior has essentially the same information as the likelihood function.
Consequently, in practice, a Bayesian probability interval (or credible interval)
may be ve... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv | Many frequentist confidence intervals (CIs) are based on the likelihood function.
If the prior distribution is truly non-informative, then the a Bayesian
posterior has essentially the same information | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
Many frequentist confidence intervals (CIs) are based on the likelihood function.
If the prior distribution is truly non-informative, then the a Bayesian
posterior has essentially the same information as the likeliho... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv
Many frequentist confidence intervals (CIs) are based on the likelihood function.
If the prior distribution is truly non-informative, then the a Bayesian
posterior has essentially the same information |
6,792 | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval? | BruceET's answer is excellent but pretty long, so here's a quick practical summary:
if the prior is flat, likelihood and posterior have the same shape
the intervals, however, are not necessarily the same, because they are constructed in different ways. A standard Bayesian 90% CI covers the central 90% of the posterior... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv | BruceET's answer is excellent but pretty long, so here's a quick practical summary:
if the prior is flat, likelihood and posterior have the same shape
the intervals, however, are not necessarily the | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
BruceET's answer is excellent but pretty long, so here's a quick practical summary:
if the prior is flat, likelihood and posterior have the same shape
the intervals, however, are not necessarily the same, because th... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv
BruceET's answer is excellent but pretty long, so here's a quick practical summary:
if the prior is flat, likelihood and posterior have the same shape
the intervals, however, are not necessarily the |
6,793 | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval? | While one can solve for a prior that yields a credible interval that equals the frequentist confidence interval, it is important to realize how narrow the scope of application is. The entire discussion is assuming that the sample size was fixed and is not a random variable. It assumes that there was only one look at t... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv | While one can solve for a prior that yields a credible interval that equals the frequentist confidence interval, it is important to realize how narrow the scope of application is. The entire discussi | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
While one can solve for a prior that yields a credible interval that equals the frequentist confidence interval, it is important to realize how narrow the scope of application is. The entire discussion is assuming t... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv
While one can solve for a prior that yields a credible interval that equals the frequentist confidence interval, it is important to realize how narrow the scope of application is. The entire discussi |
6,794 | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval? | Likelihood $\neq$ Bayesian with flat prior
The likelihood function, and associated the confidence interval, are not the same (concept) as a Bayesian posterior probability constructed with a prior that specifies a uniform distribution.
In part 1 and 2 of this answer it is argued why likelihood should not be viewed as a ... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv | Likelihood $\neq$ Bayesian with flat prior
The likelihood function, and associated the confidence interval, are not the same (concept) as a Bayesian posterior probability constructed with a prior that | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
Likelihood $\neq$ Bayesian with flat prior
The likelihood function, and associated the confidence interval, are not the same (concept) as a Bayesian posterior probability constructed with a prior that specifies a uni... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv
Likelihood $\neq$ Bayesian with flat prior
The likelihood function, and associated the confidence interval, are not the same (concept) as a Bayesian posterior probability constructed with a prior that |
6,795 | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval? | This is not generally true, but it may seem so because of the most frequently considered special cases.
Consider $X,Y\sim\operatorname{i.i.d}\sim\operatorname{Uniform}[\theta-1/2,\, \theta+1/2].$ The interval $\big(\min\{X,Y\},\max\{X,Y\}\big)$ is a $50\%$ confidence interval for $\theta,$ albeit not one that anyone wi... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv | This is not generally true, but it may seem so because of the most frequently considered special cases.
Consider $X,Y\sim\operatorname{i.i.d}\sim\operatorname{Uniform}[\theta-1/2,\, \theta+1/2].$ The | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
This is not generally true, but it may seem so because of the most frequently considered special cases.
Consider $X,Y\sim\operatorname{i.i.d}\sim\operatorname{Uniform}[\theta-1/2,\, \theta+1/2].$ The interval $\big(\... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv
This is not generally true, but it may seem so because of the most frequently considered special cases.
Consider $X,Y\sim\operatorname{i.i.d}\sim\operatorname{Uniform}[\theta-1/2,\, \theta+1/2].$ The |
6,796 | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval? | From my reading, I thought this statement is true asymptotically, i.e. for large sample size, and if one uses an uninformative prior.
A simple numerical example would seem to confirm this - the 90% profile maximum likelihood intervals and 90% credible intervals of a ML binomial GLM and Bayesian binomial GLM are indeed ... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv | From my reading, I thought this statement is true asymptotically, i.e. for large sample size, and if one uses an uninformative prior.
A simple numerical example would seem to confirm this - the 90% pr | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
From my reading, I thought this statement is true asymptotically, i.e. for large sample size, and if one uses an uninformative prior.
A simple numerical example would seem to confirm this - the 90% profile maximum li... | If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interv
From my reading, I thought this statement is true asymptotically, i.e. for large sample size, and if one uses an uninformative prior.
A simple numerical example would seem to confirm this - the 90% pr |
6,797 | The meaning of "positive dependency" as a condition to use the usual method for FDR control | From your question and in particular your comments to other answers, it seems to me that you are mainly confused about the "big picture" here: namely, what does "positive dependency" refer to in this context at all -- as opposed to what is the technical meaning of the PRDS condition. So I will talk about the big pictur... | The meaning of "positive dependency" as a condition to use the usual method for FDR control | From your question and in particular your comments to other answers, it seems to me that you are mainly confused about the "big picture" here: namely, what does "positive dependency" refer to in this | The meaning of "positive dependency" as a condition to use the usual method for FDR control
From your question and in particular your comments to other answers, it seems to me that you are mainly confused about the "big picture" here: namely, what does "positive dependency" refer to in this context at all -- as opposed... | The meaning of "positive dependency" as a condition to use the usual method for FDR control
From your question and in particular your comments to other answers, it seems to me that you are mainly confused about the "big picture" here: namely, what does "positive dependency" refer to in this |
6,798 | The meaning of "positive dependency" as a condition to use the usual method for FDR control | Great question! Let's step back and understand what Bonferroni did, and why it was necessary for Benjamini and Hochberg to develop an alternative.
It has become necessary and compulsory in recent years to perform a procedure called multiple testing correction. This is due to the increasing numbers of tests being per... | The meaning of "positive dependency" as a condition to use the usual method for FDR control | Great question! Let's step back and understand what Bonferroni did, and why it was necessary for Benjamini and Hochberg to develop an alternative.
It has become necessary and compulsory in recent ye | The meaning of "positive dependency" as a condition to use the usual method for FDR control
Great question! Let's step back and understand what Bonferroni did, and why it was necessary for Benjamini and Hochberg to develop an alternative.
It has become necessary and compulsory in recent years to perform a procedure c... | The meaning of "positive dependency" as a condition to use the usual method for FDR control
Great question! Let's step back and understand what Bonferroni did, and why it was necessary for Benjamini and Hochberg to develop an alternative.
It has become necessary and compulsory in recent ye |
6,799 | The meaning of "positive dependency" as a condition to use the usual method for FDR control | I found this pre-print helpful in understanding the meaning. It should be said that I offer this answer not as an expert in the topic, but as an attempt at understanding to be vetted and validated by the community.
Thanks to Amoeba for very helpful observations about the difference between PRD and PRDS, see comments
P... | The meaning of "positive dependency" as a condition to use the usual method for FDR control | I found this pre-print helpful in understanding the meaning. It should be said that I offer this answer not as an expert in the topic, but as an attempt at understanding to be vetted and validated by | The meaning of "positive dependency" as a condition to use the usual method for FDR control
I found this pre-print helpful in understanding the meaning. It should be said that I offer this answer not as an expert in the topic, but as an attempt at understanding to be vetted and validated by the community.
Thanks to Am... | The meaning of "positive dependency" as a condition to use the usual method for FDR control
I found this pre-print helpful in understanding the meaning. It should be said that I offer this answer not as an expert in the topic, but as an attempt at understanding to be vetted and validated by |
6,800 | The meaning of "positive dependency" as a condition to use the usual method for FDR control | In their paper, Benjamini and Yekutieli provide some examples of how positive regression dependence (PRD) is different from just being positively associated. The FDR control procedure relies on a weaker form of PRD which they call PRDS (i.e. PRD on each one from a subset of variables).
Positive dependency was original... | The meaning of "positive dependency" as a condition to use the usual method for FDR control | In their paper, Benjamini and Yekutieli provide some examples of how positive regression dependence (PRD) is different from just being positively associated. The FDR control procedure relies on a weak | The meaning of "positive dependency" as a condition to use the usual method for FDR control
In their paper, Benjamini and Yekutieli provide some examples of how positive regression dependence (PRD) is different from just being positively associated. The FDR control procedure relies on a weaker form of PRD which they ca... | The meaning of "positive dependency" as a condition to use the usual method for FDR control
In their paper, Benjamini and Yekutieli provide some examples of how positive regression dependence (PRD) is different from just being positively associated. The FDR control procedure relies on a weak |
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