# Questions tagged [conditional-probability]

The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

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### Understanding error in bayesian inference

Let us say we have: Data $X$ Parameter that we are trying to estimate is $\Theta$ The Bayesian estimation method is to Assume a prior on $\Theta$ Sample $x$ from $X$ Use Bayes theorem. Compute the ...
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Does $E(X|X\in A)=\frac{E(X\mathbf{1}(X\in A))}{Pr(X\in A)}$ hold? (Here $\mathbf{1}(\cdot)$ is the indicator function). To me it seems that it holds. Here is the proof: $E(X|X\in A)=\int_{-\infty}^{\... • 1,734 1 vote 1 answer 22 views ### Conditional Distribution of Normally distributed random variable Let$x \sim \mathcal{N}\left(0,\sigma^2\right)$and$y = x+\epsilon$where$\epsilon\sim \mathcal{N}\left(0,\sigma^2_\epsilon\right)$and independent of$x$. We know that the conditional distribution ... • 11 8 votes 3 answers 510 views ### Which metric to use to evaluate Quantile Regression? I have a prediction problem for which I want to predict the 75% Quantile using Quantile Regression. I am a little bit confused on how to evaluate this model (and also compare different models). If I ... • 301 0 votes 0 answers 11 views ### How to apply the the conditional probability and chain rule formulas in a multivariable case? I'm learning about Bayesian Fusion and have a question regarding an expression that I wasn't able to prove. It poses the following statement: Assume$y_1, y_2, y_3$are three observations which are ... 1 vote 1 answer 32 views ### Understanding conditional notation Which is the correct way to describe the conditional probability distribution of X conditioned upon Y where X = a, Y = b $$P_{X \mid Y}(a \mid b) \tag1$$ or $$P_{X \mid Y}(a,b) \tag2$$ What is the ... • 1,683 0 votes 0 answers 8 views ### What is the exact role of model$p_\thetain Diffusion models for the reverse process? I'm reading this interesting blog post explaining Diffusion probabilistic models and trying to understand the following. In order to compute the reverse process, we need to consider the posterior ... • 437 0 votes 0 answers 15 views ### How can we expand the following probability? Suppose we have a predictive regression of the form \begin{align} y_t=\beta x_{t-1}+u_t\\ x_t=\rho x_{t-1}+\varepsilon_t, \end{align} fort=1,\cdots,T$, such that$cov(x_{t-1},u_t)=0$for all$t$, ... • 1,030 1 vote 0 answers 48 views ### Given all conditional probabilities, find joint probability For two random variables$A$and$B$, if we know$\mathbb{P}(A|B)$for all possible values of$A$given all possible values of$B$respectively, and$\mathbb{P}(B|A)$for all possible values of$B$... • 367 1 vote 0 answers 34 views ### Intuition about the relation between joint distribution, marginal distribution, and conditional distribution The wording "intuition" might be a bit imprecise. I want to discuss how we visualize in our head going from one to another among the joint PDF, marginal PDF, and conditional PDF. To make the ... • 367 0 votes 1 answer 29 views ### Finding the conditional distribution from given normal distributions using Bayes' theorem Background This question is related to my previous question: Describing the measurement of a random variable as another random variable, but I've narrowed and clarified my question. I think I've ... -1 votes 1 answer 53 views ### calculate combination of matrix of probabilities (win rate ranking in game) Let imagine we have a game with 4 players. And after playing game, we will get ranking of 4 players based on their score, rank 1 is the best, rank 4 is the worst. I have created a model for predicting ... • 150 0 votes 0 answers 16 views ### Describing the measurement of a random variable as another random variable Background Suppose we have a box of resistors. The manufacturer rates these resistors at 100 ohms, but they have some variability. Let$x$be the true resistance of a resistor chosen from the box at ... 2 votes 1 answer 500 views ### is P(notB|A) same as not(P(B|A)) [closed] is P(notB|A) same as not(P(B|A)) if not then what is the difference between them? this is taken from bayes question. • 37 0 votes 0 answers 14 views ### Under what condition the left stochastic matrix P(X|Y) is an invertible matrix? Say we have two random variables$X$,$Y$. They are discrete variables (or discretization of continuous variables), both with$k$categories. Define the left stochastic matrix as$P(X|Y)_{ij}:=p(x_i|...
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While I am studying Kalman filter, I saw the following equation P(A, B, C) = P(A, B)P(C|A) Is this right? if right, I am wondering why this equation holds. Thank you :)
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### Expand conditional by marginalisation and drop terms from conditional

I have come across this conditional expansion a few times, and I can't seem to make sense of it. $$p(z|y) = \int{p(z|f)p(f|y)df}$$ I would go about it like this: \begin{align} \require{cancel} p(z|y) &...
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### Margin Distribution N-dimensional random vector

I have this exercise on my textbook and I can't understand how I have to do it. I tried to compute the posterior but I don't understand if it's what the exercise requires. Thanks This is what I did ...
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### Precise Definition of $\mathbb{E}[X\mid \sigma(A)]$ Conditional Expectation of Random Variable given Sigma Algebra generated by a set

I want to define precisely, exhaustively and constructively the conditional expectation of a random variable given the sigma algebra generated by a set. This question has some discussion on it but the ...
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### Central Limit Theorem with Exponential and Uniform Distributions

The waiting time of a customer in a customer service telephone line in company number 1 has the exponential distribution with an expected value of 2.2 minutes. The waiting time of company 2 has the ...
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### Can you have a "PMF-PDF" Together?

This is a question I have always struggled to understand: For a discrete random variable, you can have a "Probability Mass Function" (PMF) : For several discrete random variables, you can ...
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### Matrix Factorization for Recommendation System vs just calculating Conditional Probabilities

I have a matrix factorization model (using Lightfm, without user-features) to recommend items to users, based on a user-item matrix. Context A particular recommendation stuck out to me as curious, ...
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### Demonstration and Interpretation between a Fisher matrix and its dual space which is covariance matrix

I have a simple (maybe not) issue about the interpretation of the link between Fisher information matrix and its inverse which is the covariance matrix. How to formulate that a line of Covariance ...
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### Consecutive coin flips, what is the appropriate statistical test for this word problem? [closed]

I was listening to a podcast by NDGT (Neil deGrasse Tyson, a prominent scientist) and he posed a simple thought experiment to illustrate the susceptibilities to cognitive bias. What I've come here to ...
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### Conditioning of join gaussian over a line

I need to compute the conditional probability of bivariate normal distribution over a line. Let's suppose that X and Y both are normal distributions and that they are independent. Let's suppose that ...
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### Probability Notation Confusion

In the following image, taken from paper on Variational Autoencoders by Dr. Kingma and Dr. Welling, it is mentioned that probability of the data points given the parameters factorizes into product of ...
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### Logistics model on variable with values 1, 2, 3?

I have a dataset containing traffic crash information. One variable in the set is the number of fatalities that resulted in the crash, which has the values 0, 1, 2, and 3. I am working in R and want ...
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### Estimating conditional mutual informations from 2D histograms

I have binned marginal and joint distributions of two event features X and Y, i.e. p(X), p(Y) and p(X,Y) where the marginal distributions in X and Y are obtained by summing p(X,Y) over the bins of the ...
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### Inference on a Gaussian random field / undirected graph?

Assume I have an undirected graph with $D$ nodes, and a $D$-by-$D$ matrix with edge strengths between $0$ (implying conditional indepedence given all other nodes), and $1$ (implying complete ...
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### What's wrong with this conditional probability working?

A past exam paper for my course (BSc Mathematics, second-year module in statistical inference and modelling, unpublished) has a question, Let $(X,Y)^T$ be a bivariate random variable with joint ...
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### Sample uniformly from unit square conditioned on sum and product

Consider the following conditional distributions: \begin{align} X, Y \stackrel{\text{iid}}{\sim} U(0, 1) &\mid X + Y = a & a \in [0, 2] \\ X, Y \stackrel{\text{iid}}{\sim} U(0, 1) &\mid X ...
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