Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Random-effects Bayesian model selection ▷ Exceedance probabilities

Definition: Let $p(y,m,r)$ with data sets $y = \left\lbrace y_1, \ldots, y_N \right\rbrace$, generative models $m \in \left\lbrace 0, 1 \right\rbrace^{N \times K}$ and model frequencies $r \in [0, 1]^K$ be the joint likelihood function of the model specified by random-effects Bayesian model selection and let $p(r \vert y)$ be the posterior distribution resulting from estimation of this model.

Then, the posterior exceedance probability of the $j$-th model frequency $r_j$, i.e. the probability that, given the data, the $j$-th model is more frequent than any other model, is called the exceedance probability of model $j$:

\[\label{eq:excprob} \mathrm{EP}_j = \varphi_{p(r|y)}(r_j) = \mathrm{Pr}\left( \forall i \in \left\lbrace 1, \ldots, n | i \neq j \right\rbrace: \, r_j > r_i \, \vert \, y \right) \; .\]
 
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Metadata: ID: D238 | shortcut: excprob | author: JoramSoch | date: 2026-06-29, 17:53.