# Questions tagged [bayesian]

The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.

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### Stuck on the proof conditional probability theorem

Given a random vector $\mathbb{X}$ with joint density $f$, and a set $A=\{\mathbb{X}\in B\}$ with $B\in \mathscr{B}(\mathbb{R})$ Prove that:\ $$f_{(x|A)}=\frac{f(x)}{\mathbb{P}(A)}\text{ if } x\in B$$...
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### Covariance for Optimal Bayes Estimator using Gaussian distributions

Lemma : If we have a Bayesian linear model: $$y = X\beta + w$$ where $\beta \sim N(0, I_d)$ (prior parameter) and $w \sim N(0,I_n)$, then $\beta$ conditioned on $y$ (posterior parameter) is Gaussian ...
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### Unscented Kalman filter and measurement function

Suppose I have a nonlinear system with states $x$ and measurements $z$. I don't have a measurement function for $z=h(x)+n$ where n is my gaussian noise term. However I do have the sufficient ...
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### Probability of choosing M out of N Groups given that all A elements are inside M

Assuming I have A number of individuals who are randomly distributed into N number of groups. What is the probability of finding A (or any number a <= A) by picking M number of groups within N? I ...
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### If the attrition rate of the customer is 5% every year, what is the probability the customer will not be there in year 3?

I want to find out what is the error in my logic: P(employee not being there in year 3) = P (employee dropping out in year 2 or dropping out in year 3) . Note she cannot drop out in year 1 as per the ...
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### Does Bayesian inference imply a contradiction?

Suppose that there have been $n$ days and that the sun has risen on all of them. What’s the chance that the sun will rise tomorrow? Assuming that we start with a uniform prior on the probability that ...
Suppose that I have a prior distribution $\pi_0(\theta)$ on $\mathbb{R}^k$ and a "naively chosen" sample distribution $f_0(x|\theta)$ on $\mathbb{R}^n$. I would like to online-update both of these ...