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)
118
questions
1
vote
1
answer
42
views
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?
- 13
0
votes
1
answer
39
views
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 ...
- 71
0
votes
0
answers
11
views
Is there an "antipodal" conditional disintegration of the von Mises Fisher distribution?
For more on conditional disintegration, cf. e.g. the references [1] [2], or these questions [a] [b] on math stackexchange.
Question: For the von-Mises Fisher distribution, is there a conditional ...
1
vote
0
answers
18
views
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 ...
- 131
0
votes
0
answers
14
views
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 $H_c(Y;Y')>H_c(Y|X;Y'|X)$?
1
vote
1
answer
39
views
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|...
- 145
1
vote
1
answer
114
views
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 ...
- 11
1
vote
0
answers
72
views
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
$$
\mathbb{E}...
- 212
1
vote
1
answer
27
views
how to view conditioning on a random variable rather than a particular value of that variable
The question is about $P(Y|X)$ versus $P(Y|X=x)$. Is there an alternate way to write $P(Y|X)$
that makes its meaning more clear?
I believe these are correct equations for conditional entropy:
$$
H(Y|...
- 273
1
vote
1
answer
211
views
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 ...
- 13
2
votes
1
answer
42
views
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 ...
- 385
1
vote
1
answer
296
views
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 ...
- 115
0
votes
1
answer
110
views
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 ...
- 268
0
votes
1
answer
122
views
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(...
2
votes
0
answers
77
views
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 ...
1
vote
1
answer
87
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 ...
- 111
7
votes
1
answer
279
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 ...
- 87
3
votes
1
answer
103
views
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. ...
- 2,699
1
vote
0
answers
166
views
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 ...
- 11
2
votes
1
answer
245
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:
$...
- 2,263
1
vote
1
answer
18
views
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 ...
- 6,103
1
vote
1
answer
805
views
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 ...
- 2,377
2
votes
1
answer
1k
views
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 ...
- 4,169
0
votes
1
answer
2k
views
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 ...
- 175
4
votes
1
answer
91
views
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 \...
- 43
1
vote
0
answers
100
views
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
0
answers
22
views
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 ...
- 11
0
votes
0
answers
67
views
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
0
answers
46
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?
$Cov(X, Y | X + Y \geq Z)$
- 21
1
vote
1
answer
174
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 ...
- 657
4
votes
1
answer
122
views
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 ...
- 63.6k
3
votes
1
answer
641
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 ...
- 547
4
votes
1
answer
63
views
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 ...
- 3,063
1
vote
1
answer
107
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(...
- 1,245
7
votes
2
answers
141
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 ...
- 1,045
1
vote
1
answer
50
views
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 ...
user271077
16
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 ...
- 365
2
votes
1
answer
2k
views
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 ...
- 565
0
votes
0
answers
51
views
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 ...
2
votes
1
answer
186
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 ...
- 125
5
votes
1
answer
80
views
Meaning of "for each value $X = x$, the random variable Y can be represented in the form $Y = \beta_0 + \beta_1 x + \epsilon$" in linear regression
In what follows assume $Y: \ \Omega \to \mathbb R$ and $X: \ \Omega \to E$
The following quoute is from page 700 in DeGroot and Schervish - Probability and statistics, introducing a simple linear ...
- 225
2
votes
0
answers
2k
views
Do fixed design prediction/estimation error guarantees translate to random design for linear regression? When and How? [closed]
Suppose I have an independent vector $X$ and a dependent scalar random variable $Y$ and I wish to construct a regression model to predict $Y$ using $X$ given data $\{(x_i,y_i)\}_{i=1}^{n}$. For ...
3
votes
0
answers
123
views
What does "Normal distribution conditioned on $x \mod 1$" mean?
I understand what $Pr[X = x | Y = y]$ means, however, on this paper (Lemma 10 in Appendix A), we have the following:
Let $D_r$ denote the continuous Gaussian distribution of parameter $r$,i.e., the ...
3
votes
2
answers
761
views
Consistent estimator for conditional expectation
Take sequence of random vectors $(Y_i, X_i)_{i=1}^N$ i.i.d.
$X_i$ has finite support. Let $x$ be a point in the support of $X_i$.
Consider $E(Y_i|X_i=x)$. Suppose it exists and is finite.
Is it ...
- 594
0
votes
0
answers
34
views
Conditioning and linear MSE
Let $\sigma_{X|Y}^2$ denote the linear mean squared error in estimating $X$ from $Y$. Then is it always true that additional conditioning cannot increase the LLSE? In other words, is this true?
$$ \...
- 1
1
vote
1
answer
565
views
How time series structure can affect the independence of residuals condition for MLR?
I am going through all four conditions for Multiple Linear Regression and stick with this question: what happens with the independence if we have time series data structure?
- 385
0
votes
1
answer
328
views
Computing Variances by Conditioning
I have trouble with the first part of this problem (Please take a look at the image below). This is an example problem from my old textbook years ago and I have had trouble understanding:
How Y is ...
- 3
1
vote
1
answer
532
views
Law of Iterated Expectations Example
Consider a randomized experiment (AB test), where $n$ units are randomized into the treatment group $T_i=1$ and control group $T_i=0$. Let $M_i\in P$ denote the observed value of a continuous variable ...
- 35
20
votes
3
answers
17k
views
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)?
- 313
2
votes
1
answer
386
views
Is the conditional distribution of Y given X the most we can know about how X "affects" Y?
In his book "Introductory Econometrics", Jeffrey Woolridge states "The most we can know about how X affects Y is contained in the conditional distribution of Y given X".
Is this statement true?
Would ...
- 4,166