Definition: Uniform-prior log model evidence

Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Model evidence ▷ Uniform-prior log model evidence

Definition: Assume a generative model $m$ with likelihood function $p(y \vert \theta, m)$ and a uniform prior distribution $p_{\mathrm{uni}}(\theta \vert m)$. Then, the log model evidence of this model is called “log model evidence with uniform prior” or “uniform-prior log model evidence” (upLME):

\[\label{eq:upLME} \mathrm{upLME}(m) = \log \int p(y \vert \theta, m) \, p_{\mathrm{uni}}(\theta \vert m) \, \mathrm{d}\theta \; .\]

 

Sources:

• Wikipedia (2020): "Lindley's paradox"; in: Wikipedia, the free encyclopedia, retrieved on 2020-11-25; URL: https://en.wikipedia.org/wiki/Lindley%27s_paradox#Bayesian_approach.

Metadata: ID: D113 | shortcut: uplme | author: JoramSoch | date: 2020-11-25, 07:28.