Astrostatistical Challenges for the New Astronomy by Joseph M. Hilbe

Author:Joseph M. Hilbe
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(6.1)

Here, p.(Θ|) is the prior, p(d|Θ; ) the likelihood and p(d |) the model likelihood, or marginal likelihood (usually called “Bayesian evidence by physicists). The Bayesian evaluation of a model’s performance in the light of the data is based on the Bayesian evidence, the normalization integral on the right-hand-side of Bayes’ theorem, Eq. (6.1):

(6.2)

Thus the Bayesian evidence is the average of the likelihood under the prior for a specific model choice. From the evidence, the model posterior probability given the data is obtained by using Bayes’ Theorem to invert the order of conditioning:

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