**Basic Bayesian Theory**

Recall that for Bayesian inference:

The denominator is the *marginal probability of the data*, averaged over all possible parameter values weighted by their prior distribution. Formally,

where is the parameter space for .

In the original Metropolis algorithm, given a current -value, and a new -value, the new value is accepted with probability:

Read more about this topic: Bayesian Inference In Phylogeny

### Famous quotes containing the words theory and/or basic:

“In the *theory* of gender I began from zero. There is no masculine power or privilege I did not covet. But slowly, step by step, decade by decade, I was forced to acknowledge that even a woman of abnormal will cannot escape her hormonal identity.”

—Camille Paglia (b. 1947)

“Not many appreciate the ultimate power and potential usefulness of *basic* knowledge accumulated by obscure, unseen investigators who, in a lifetime of intensive study, may never see any practical use for their findings but who go on seeking answers to the unknown without thought of financial or practical gain.”

—Eugenie Clark (b. 1922)