# 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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### Under which probabilistic assumptions is this estimation approach correct?

trying to tackle a problem, I ended up having built a model $p(\boldsymbol{x}_{i}|\boldsymbol{y}_{i,j}, \boldsymbol{x}_{j})$ which gives me for different $\boldsymbol{y}_{i,j}$ observations made ...
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### How are category theory and probability theory related?

How are category theory and probability theory related ? Category theory seems very useful for understanding objects with definite relationships, whereas probability theory (particular Bayesian ...
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### Normalizing factor for product of Gaussian densities - interpretation with Bayes theorem

The normalizing factor for the product of two multivariate Gaussian densities, $f(x)$ and $g(x)$ with mean vectors $a$ and $b$ respectively, and covariance matrices $A$ and $B$ respectively, is itself ...
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### Optimal control of posterior belief over a finite horizon

$\large \textbf{Preface:}\$ Below I describe a dynamic programming problem I am not sure how to formalize. In short: a (Bayesian-updating) agent sequentially runs costly experiments over a finite ...
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### What are sufficient conditions such that consistency of ML estimate implies consistency of MAP estimate?

I am interested in under what conditions the frequentist consistency of a Maximum-Likelihood estimator is enough to give the consistency of a maximum-a-posteriori point estimate, with the further ...
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### How deep is the connection between Bayesian framework and bra-ket calculus?

As a PhD student in condensed matter physics, I am very familiar with Dirac's bra-ket notation, but not so much with Bayesian inference. One of the first things that struck me when I started studying ...
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### Prove these two conditional probabilities are equivalent

I saw people using such equivalence $$P(X|\mu) P(\mu | D) = P(X,\mu|D)$$ how to prove it is valid? My attempt: \begin{align} P(X|\mu) P(\mu | D) &= P(X|\mu) \frac{P(\mu,D)}{P(D)}\\ &= P(X|\mu)...
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### Question about the extrinsic information in turbo based equalizer

In light of the question given in why only extrinsic information is passed in turbo decoding/equalization, why not a posteriori information? if we have different observation provided to two linear ...
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### Simple example of "Spike-and-Slab Prior" for Bayesian Inference

I would really like to understand how Spike-and-Slab Priors work in relation to Linearized Models. Can somebody provide a toy example of a Spike-and-Slab Prior with a Bernoulli spike and a Gaussian ...
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### Getting a feel for the Normal-Inverse-Wishart conjugate prior to multivariate normal distribution

I am trying to get a feel for the Normal-Inverse-Wishart conjugate prior, which I have started to use, sparingly, in my work, where I am trying to cluster multivariate normal data. As Wikipedia ...
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