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What is the difference between Metropolis-Hastings, Gibbs, Importance, and Rejection sampling?

As detailed in our book with George Casella, Monte Carlo statistical methods, these methods are used to produce samples from a given distribution, with density $f$ say, either to get an idea about ...
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When would one use Gibbs sampling instead of Metropolis-Hastings?

Firstly, let me note [somewhat pedantically] that There are several different kinds of MCMC algorithms: Metropolis-Hastings, Gibbs, importance/rejection sampling (related). importance and ...
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Conditional distribution of $\exp(-|x|-|y|-a \cdot |x-y|)$

Disclaimer: although there is nothing to complain about Ben's answer (!), except maybe that the normalising constant of the conditional is not of direct use, here is what I wrote while being off-...
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Marginal Likelihood from the Gibbs Output

There is a slight programming mistake in the prior ...
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