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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 do i solve this problem on conditional probability [closed]

Where x~ u(0,4), what is P(X>Y|X<2Y) I know that X lies between Y at the lower bound and 2Y at the upper bound but i am having trouble trying to figure out P(X<2Y) as none of the examples i ...
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How to choose what to integrate out or what to condition on for marginal distributions?

I am trying to work out the Bayesian posteriors of $\theta$, $\tau$ and the $\varepsilon$ in the following model: $$y(t) = \phi(t,\tau)\theta+v(t),$$ where $\{v(t)\}$ is an iid sequence of random ...
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When and how of stratification?

I understand stratification at a novice level. For example, if we want to condition on gender in post experimentation inference, we might stratify or block on gender. As I understand it, we take each ...
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conditional probabilities in chess

Let's say I am analyzing certain chess positions of a chess player (Magnus Carlsen, Lichess games when playing as white). We know that the 'unconditional probability' (empirically speaking) of this ...
Oscar Flores's user avatar
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Distribution of a random variable conditional on its being a maximum or not

Consider the random variables $\epsilon_1,\dots, \epsilon_D$ defined on the probability space $(\Omega, \mathcal{F}, P)$. Assume they are continuous. Let $$ Y=\sum_{d=1}^D d\times \mathbb{1}\{\...
Star's user avatar
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Chain rule conditional entropy

A textbook I am reading states that$$H(X,Y)=H(X)+H(Y|X)$$where $H(X,Y)$ is the joint entropy of random variables $X,Y$, $H(X)$ the entropy of $X$, and $H(Y|X)$ is conditional entropy. It then states ...
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Expectation of the product of two random variables

I recently tried to derive a formula that I saw in a paper. The scenario was a follows: Let $X\in\lbrace 0,1\rbrace $ a.s. be a binary random variable and $Y$ be a continuous random variable. Let $a,b\...
stats19's user avatar
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How to perform conditional poisson regression for a 1:5 matched cohort study?

I have a matched cohort population using data that spans the years 2016-2021. My exposure of interest is continuous dialysis treatment, and my outcome is e.coli infections (count outcome). Each time ...
Poncho's user avatar
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8 votes
2 answers
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When to use fixed effects or multi level models in regression?

Suppose you run an experiment where the treatment is Gatorade and the outcome is one-mile runtime. You’ve stratified on variables such as sex, height and weight so they’re well randomized and have no ...
jbuddy_13's user avatar
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Converse of pairwise Markov property

Random vector $X$ follows a pairwise Markov property on graph $G=(V,E)$ if for any $(i,j) \notin E$, $X_i$ and $X_j$ are conditionally independent given $X_{V \setminus \{i,j\}}$. My question is, why ...
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Constant conditional variance

Let $X$ and $U$ be two independent random variables, and let $Z= X+U$. Under which conditions is $Var(X|Z)$ constant? I know this holds for instance when $X$ and $Z$ are jointly normal. I'm ...
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How does the QR-code monster model for SD controlNet work?

Background Recent trends show cool QR-codes made by the QR-code monster model used in Stable-Diffusion (SD) with ControlNet. Those are also used to create images containing hidden text/hidden images (...
snatchysquid's user avatar
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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 ...
helloworld's user avatar
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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 ...
Chevallier's user avatar
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In probability, if we have an equality, can we condition on an arbitrary event and guarantee that the equality still holds?

I have a question regarding equalities and conditioning probabilities. I was reading through this proof for conditional independence, which can be found here. In the proof, they first state that $p(A|...
Franklin V's user avatar
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MANOVA (SPSS) test - determine control variables in moderation analysis

I am examining the moderating effect of IV1 in the relationship between IV2 and DV using hierarchical regression analysis. The study has 2 demographic variables: gender and age. To determine if it is ...
Thao Truong's user avatar
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Where does the random come in for conditional expectations $\mathbb{E}[X | \mathcal{F}]$?

For continuous random variables $X, Y$ the conditional expectation $\mathbb{E}[X | Y]$ is itself a random variable. I understood this in the sense that for a realisation of $Y$ we can say $$ \mathbb{E}...
lpnorm's user avatar
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how to view conditioning on a random variable rather than a particular value of that variable

The question is about $P(Y|X)$ versus $P(Y|X=x)$. Is there an alternate way to write $P(Y|X)$ that makes its meaning more clear? I believe these are correct equations for conditional entropy: $$ H(Y|...
isolatedstudent's user avatar
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Condition on two random variables

I'm trying to set up the proper assumptions for a proof I'm working on: Given that $P(A|e) = P(A)$ and $P(A|c,e) = P(A|e)$, can we prove that $P(A|c)=P(A)$? I understand that A is independent of e and ...
Kevin D's user avatar
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Conditional Tolerance Interval

With the generous help of people here, I've recently learned about the notion of a Tolerance Interval (Confidence in a range estimate, and +- 2sigma rule of thumb). I am now working on an application ...
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Probability Conditioned on Inequality

Assume that $A \sim \mathcal{N}(0, 1)$, $B \sim \mathcal{N}(0, 1)$. I am trying to calculate $P(A \,|\, A < B)$. For the sake of this problem, we can assume that $A \perp B$, but (for obvious ...
zen_of_python's user avatar
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Is it possible to calculate a bivariate normal density using only the univariate normal density function? [duplicate]

Suppose $(X,Y)$ are two jointly normally distributed random variables. Suppose further that we want to calculate the density of $(X=x,Y=y)$. Is it possible to calculate this density if we do not have ...
Felipe D.'s user avatar
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If P(A) + P(B) = 1, does P(A|C) + P(B|C) = 1?

Just to explain where this is coming from. I was working on question 5(b) from stat 110 on conditional probabilities. I'll put a picture of the question and its solution below I worked on question 5(...
Rockflame's user avatar
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What’s a textbook covering similar content to “Introduction to Probability Models” by Sheldon Ross?

I’m taking a class with a instructor using said textbook, and I find the explanations in it lacking. It’d be great if anyone can offer an alternative book covering similar content (i.e. conditioning ...
2 votes
1 answer
96 views

A regressor performs better under a certain regime -- how to condition that regressor to make regression better?

I ran a regression $Y \sim X_1 + X_2 + .. X_n$. I find out what one regressor , $X_1$'s performance (or correlation with $Y$) depends on another variable $t$ (not in the regression). So basically if I ...
Taylor Fang's user avatar
7 votes
1 answer
299 views

Variance of Bernoulli when success probability varies

Say the success probability $X$ is a random variable with mean $\mu$ and Variance $\sigma^2$ which takes values in $[0,1]$. How can I compute the variance of a random Variable $Y$ which is 1 with ...
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If $e_0$ are the OLS residuals, what is random in $\hat{\beta}_{OLS}|f(e_0) < \hat{\beta} < f^*(e_0)$?

This is a follow up question to the question I've posted here. Suppose $Y \sim N(X\beta, \sigma^2I)$, where $y \in \mathbb{R}^n$. Let $X \in \mathbb{R}^{n \times p}$ denote a full rank design matrix. ...
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Test for conditional dependence

I am trying to find out whether two variables are conditionally dependent on each other. I would like to have a test for B implies A (B->A) or not and one for A implies B (A->B) or not. It is ...
Val.M's user avatar
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2 votes
1 answer
282 views

Find conditional PMF of a multinomial distribution

I am trying to find the conditional PMF of a multinomial analytically and though I know my result is wrong I can't seem to pinpoint where my argument is wrong. Seeking help to find my mistake. Given: $...
figs_and_nuts's user avatar
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Distribution of R|R+T for R,T binomials with the same probability

$$R \sim \mathrm{Bin}(N_R, p)$$ $$T \sim \mathrm{Bin}(N_T, p)$$ What is the distribution of $R$ given particular value of $R + T$? My guess would be that $R | R + T \sim \mathrm{Bin}(R + T, {N_R \over ...
Tomas's user avatar
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1 vote
1 answer
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Gaussian Processes as weighted averages?

I've been wondering if a "weighted average" is a valid means to consider the Gaussian Process, specifically in the context of GP Regression. The kernel (I'll be referring to the common ...
jbuddy_13's user avatar
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3 votes
1 answer
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Expected value of max of two discrete random variables

I'm reading this paper An Efficient PTAS for Stochastic Load Balancing with Poisson Jobs. Which is solving a makespan minimizing job-shop problem for Poisson job sizes. Basically, schedule the minimum ...
Lucas Roberts's user avatar
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Markov transition matrix row sums to 1

I am trying to learn a little bit of Markov Chains through Dobrow's "Introduction to Stochastic Processes with R", but i am struggling with the following: The entries of every Markov ...
Lucas's user avatar
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4 votes
1 answer
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conditional expection gaussian vector

I have got an question on computing conditional expection I was working on the following conditional expectation problem find $$\mathbb{E}[X-Y|2X+Y]$$ where $\begin{bmatrix}X \\ Y \end{bmatrix} \sim \...
ashu24's user avatar
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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 ...
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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 ...
San Han's user avatar
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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 ...
Rafael Hernández Salazar's user avatar
1 vote
0 answers
49 views

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? $Cov(X, Y | X + Y \geq Z)$
zxjroger's user avatar
1 vote
1 answer
189 views

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 ...
Cesare's user avatar
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1 answer
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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 ...
Richard Hardy's user avatar
3 votes
1 answer
857 views

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 ...
Vaaal's user avatar
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4 votes
1 answer
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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 ...
confused's user avatar
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1 vote
1 answer
144 views

generating process of acceptance-rejection algorithm

The acceptance-rejection algorithm is described as follows: suppose you have RVs $X$ and $Y$ with densities $f_X$ and $f_Y$, respectively, and there exists a constant $c$ such that $\frac{f_X(t)}{f_Y(...
user6703592's user avatar
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7 votes
2 answers
167 views

Is there a difference in interpretation between $Y|X = m(X) + \epsilon$ vs. $Y = m(X) + \epsilon$?

I understand that $E(Y|X)$ and $E(Y)$ are different, but difference sources, when $Y$ is a function of other random variables such as $X$, use $Y|X$ and $Y$ to describe this relationship. I'm not sure ...
Yandle's user avatar
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Why condition on either the r.v. $X$ or $Y$ and integrate over a product of pdfs rather a single pdf to find this probability density?

Let $X$ have the probability density $f_{X}(x)=\lambda e^{-\lambda x}, \;\; x>0$ and let $Y$ have the probability density $f_{Y}(y)=\lambda e^{-\lambda x},\;\; y>0.$ Find the probability ...
user avatar
18 votes
1 answer
3k views

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 ...
Astarno's user avatar
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2 votes
1 answer
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conditioning for deep neural networks

What is the best way to do conditioning when working with deep neural nets? For example, say we we want to condition a VAE on the class i.e. CVAE. There exists different ways of adding the class to ...
AnarKi's user avatar
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What is E[X|Y>c] where Y=X+Z, and X, Z are normally distributed rvs? [duplicate]

Suppose X, Z are normally distributed random variables and independent ($X$ follows $N(\mu,\sigma^{2})$ and $Z$ follows $N(0,\sigma_{z}^{2})$), and that Y=X+Z. What is E[X|Y>c], where c is just a ...
CuriousCat's user avatar
2 votes
1 answer
220 views

Find conditional pdf given joint

Let the joint pdf of $X$ and $Y$ be $f(x,y) = 12e^{-4x-3y}, x>0, y>0$. What is the marginal cdf of $X$? of $Y$? Am I just supposed to integrate f(x,y) with respect to $x$ or $y$ to get the ...
Evan Kim's user avatar
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