# Questions tagged [conjugate-prior]

A prior distribution in Bayesian statistics that is such that, when combined with the likelihood, the resulting posterior is from the same family of distributions.

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### Alternating between Hamiltonian Monte Carlo and sampling from conjugate posterior in large models

For Bayesian models with a large number of parameters and pieces that have conditionally closed form solutions for drawing samples, when is it worth it to use these closed form updates instead of a ...
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### Estimate covariance given noisy data and the mean

Basically, I'm inferring the parameters of a Gaussian, $\mu$ and $\Sigma$ given observed data $y_i$ that have uncertainties $\sigma^2_i$ associated with them. 1D example: Prior I intend to use the ...
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### Finding prior conjugate for reparametrized model

Let $X_i$ be iid Bernoulli$(\pi)$ for $i=1,...,n$. My task is to find the prior conjugate for $\theta$, where $\theta$ is the natural parameter of the sampling model. The sampling model can be ...
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### Poisson-Gamma conjunction - calculating posterior [duplicate]

How to calculate posterior distribution step-by-step while given: some observed numbers of customers from the last days that number of clients is distributed by Poisson($\lambda$) ($\lambda$ is not ...
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### What distributions are conjugate to themselves, besides the normal?

I know the normal distribution is conjugate to itself; are there others? Is there some sort of intuition behind why a given distribution would be conjugate to itself?
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### MLE vs Binomial - Beta conjugate pairs

I'm trying to understand how to use the conjugate relationship between the Binomial and Beta distributions to update the parameters of the Beta distribution. Specifically, I am imagining a series of ...