# 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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### 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 ...
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### 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
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### 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 ...
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### What is the exact role of model $p_\theta$ in 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 ...
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### How do you calculate the probability of seeing the same image in a set of 5 when the set is drawn randomly?

Given a webpage that displays 5 images drawn at random And given a pool of 70 images And assuming each image has an equally likely chance of being drawn And assuming if an image is drawn for 1 of the ...
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### Conditional Probability on Disease

A man living in a country where only 1 out of 1000 people has the virus A. There is a test available that gives a positive result 5% of the time when the patient does not have virus A and a negative ...
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### 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 ...
1 vote
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### In this Bayesian network, where does this posterior probability come from?

I'm reading Building Intelligent Interactive Tutors (Woolf, 2009) on student models for ITSs. On page 261, the author presents an example for a simple Bayesian network ($S \rightarrow E$), where $S$ ...
1 vote
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### 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 $B$ ...
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### 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} for $t=1,\cdots,T$, such that $cov(x_{t-1},u_t)=0$ for all $t$, ...
1 vote
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### 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 ...
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### 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 ...
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### What's the conditional variance of the chain X -> Y -> Z?

If I have a cascade of 3 random variables, represented as a Bayesian Graph: $X\rightarrow Y \rightarrow Z$, is there a simple formula for $\sigma_{X|Z}$? Further, assume all the variables are normal, ...
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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 ...
1 vote
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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 ...