# 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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### How to obtain marginal density [x], given [y|x] and [y]

I came across a problem knowing density of Y, conditional density of Y given X, how would I obtain density of X? Or would this even unique?
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### Maximum change in entropy when conditioning on an event

Let $P_{XYZ}$ be the joint distribution of discrete RVs $X,Y,Z$ where $Z$ is binary-valued. Let $Q_{XY}=P_{XY|Z=0}$, i.e. the distribution of $XY$ conditioned on $Z=0$. Are there lower/upper bounds on ...
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### Is there an "antipodal" conditional disintegration of the von Mises Fisher distribution?

For more on conditional disintegration, cf. e.g. the references  , or these questions [a] [b] on math stackexchange. Question: For the von-Mises Fisher distribution, is there a conditional ...
1 vote
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### Wishart conditionned by the determinant

I am interested in the density of the Wishart distribution under the constraint that the determinant of the outcome is 1. It suffice do divide the density of the Wishart by the marginal density of the ...
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### Conditioning decreases cross-entropy

I know conditioning decreases the normal entropy: $H(Y)>H(Y|X)$. But does it hold for the cross entropy? Do we have $H_c(Y;Y')>H_c(Y|X;Y'|X)$?
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### How conditioning happens?

F. Elwert and C. Winship in the paper "Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable" (content available here) discuss conditioning on different types of ...
1 vote
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### Observational study comparing 2 products with different (but overlapping) feature coverage

I have two software products $A$ and $B$ which form treatment $X$. $B$ is a new version of $A$ and in development. So $B$ does not have all the features that $A$ has. However, $B$ is designed to make ...
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### Graphical representation of unconditional expected value

First, let tell you that I've being struggling with the concept of unconditional expectation for linear regression. For conditional expectation is easier: We know that the conditional expectation ...
1 vote
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### Covariance of X and Y conditional on X+Y>Z? [closed]

Suppose that $X$, $Y$, and $Z$ are three independent random variables. Is there a way to compute the following conditional covariance? $Cov(X, Y | X + Y \geq Z)$
1 vote
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### How to notate joint conditional probability

Given $X = \{ x_1, x_2, \dots, \}$ and $Y = \{ y_1, y_2, \dots \}$ let $P(X,Y)$ be their joint probability. Conditioning $P(X, Y)$ on $y \in Y$ corresponds to looking at the distribution of the ...
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### Definition of covariate-specific effect: why after, not before intervention?

Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 70 contains the following text regarding conditional interventions and covariate-specific effects: [S]uppose a doctor ...
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### Gibbs sampling for Multivariate: how to update?

In this page of Murphy's 'Machine Learning: a Probabilistic Perspective' it's explained how to do Gibbs sampling on a Gaussian Mixture Model. Reading this, I was trying to understand when to update ...
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### Typo in Deepleariningbook.org or am I misunderstanding Bayesian stats?

This is on page 133 of the book: https://www.deeplearningbook.org/contents/ml.html#pf10 In the above, it says that the data set is directly observed and so is not random If that data we observe ...
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