Questions tagged [conditioning]
Conditioning is a probabilistic operation that consists in examining the probabilistic properties of a random variable (or of an event) given the realised value of another random variable (or of an event)
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What is the difference between conditioning on regressors vs. treating them as fixed?
Sometimes we assume that regressors are fixed, i.e. they are non-stochastic. I think that means all our predictors, parameter estimates etc. are unconditional then, right? Might I even go so far that ...
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What does the assumption of the Fisher test that "The row and column totals should be fixed" mean?
As this source states, one of the assumptions to perform Fisher's exact test of independence is that the row and column totals should be fixed. However, I find the explanation coming with it pretty ...
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On Fisher's exact test: What test would have been appropriate if the lady hadn't known the number of milk-first cups?
In the famous lady tasting tea experiment by RA Fisher, the lady is informed of how many milk-first/tea-first cups there are (4 for each out of 8 cups). This respects the fixed marginal total ...
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Intuition for Conditional Expectation of $\sigma$-algebra
Let $(\Omega,\mathscr{F},\mu)$ be a probability space, given a random variable $\xi:\Omega \to \mathbb{R}$ and a $\sigma$-algebra $\mathscr{G}\subseteq \mathscr{F}$ we can construct a new random ...
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Meaning of partial correlation
From Wikipedia
Formally, the partial correlation between $X$ and $Y$ given a set of $n$ controlling variables $Z = \{Z_1, Z_2, …, Z_n\}$, written $ρ_{XY·Z}$, is the correlation between the ...
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Investigate correlation conditional on a threshold
I have 3 variables in my data set.
(i) My gut feel says variable1 and variable2 are correlated, only when variable3 >= threshold3. What is the technique I can use to see if this holds true, to ...
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How do you interpret the condition number of a correlation matrix
I have two correlation matrices, one with a condition number of 9 and the other with a condition number of 70. From what i have read, it will appear that the first matrix is better conditioned than ...
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What is the physical significance of cumulative correlation coefficient?
Say, I have 2 parameters, and based on my dataset, I have iteratively calculated the correlation coefficients between them by taking the correlation of the first i terms, where i ranges from 1 to the ...
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Expected number I will be on after drawing cards until I get an ace, 2, 3, and so forth
I am having some trouble solving the following.
You draw cards from a standard 52-card deck without replacement until you get an ace. You draw from what is remaining until you get a 2. You continue ...
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Sample random variables conditional on their sum
Let $(X_1, \dots, X_n)$ be an iid sample of random variables with a known continuous distribution. I would like to simulate such a sample, conditional on the value of its sum, that is:
$$
X_1, \dots, ...
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Conditional Distribution of uniform random variable given Order statistic
I have the following question at hand:
Suppose $U,V$ are iid random variables following Unif$(0,1)$. what is the conditional distribution of $U$ given $Z:=\max(U,V)$ ?
I tried writing $Z=\Bbb{I}\...
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conditional on the total, what is the distribution of negative binomials
If $x_1, x_2, \ldots, x_n$ are i.i.d. negative binomial, then what is the distribution of $(x_1, x_2, \ldots, x_n)$ given
$x_1 + x_2 + \ldots + x_n = N\quad$?
$N$ is fixed.
If $x_1, x_2, \ldots, ...
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Standard normal distribution on a subspace
Let $U \subset \mathbb{R}^n$ be a vector space with $\dim(U)=d$. A standard normal distribution on $U$ is the law of a random vector $X=(X_1, \ldots, X_n)$ taking values in $U$ and such that the ...
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Bayesian statistical conclusions: we implicitly condition on the known values of any covariates, $x$
My Bayesian data analysis textbook says the following:
Bayesian statistical conclusions about a parameter $\theta$, or unobserved data $\tilde{y}$, are made in terms of probability statements. ...
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iterated expectation conditional on two variables
How to prove that $E[Y]=E[E[E[Y|X_1, X_2]]]$ ?
PS. I don't see how $E[E(Y|X_{1},X_{2})|X_{1}]=Y[Y|X_{1}]$ and $E[Y]=E[E(Y|X_{1})]$ can be used here. But it feels close. Please help, I'm stuck
PPS. ...
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What does conditioning on a random variable mean?
What does conditioning on a random variable mean?
For example: in p(X|Y), X and Y are the random variables, so does the conditioning on Y mean Y is fixed (or non-random)?
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Importance sampling in mixed, discrete/continuous variables
Consider the following model
$$
X \sim |\mathcal{N}(X;0,1)|
\qquad
Y|X \sim Q(Y;X)
$$
where I define $Q(Y=-x|X=x)$ with probability mass $\int_{-\infty}^{-x}\mathcal{N}(x;0,1)dx$, $Q(Y=+x|X=x)$ with ...
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Sampling from the conditional distribution assuming sampling from the joint
I am struggling with this question, which I thought it should be easy: suppose we have a method of sampling from the joint distribution of a collection of (discrete ordinal) random variables. We do ...
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Conditional expectation with conditioning on two independent variables
Let $Y_1$ and $Y_2$ be independent r.v.s, and $X$ be another random variable.
What is $E[X|Y_1, Y_2]$? Is $E[X|Y_1, Y_2]$ equivalent to $E[X|Y_1] \cdot E[X|Y_2]$?
More specifically, is there a ...