Expected model frequency

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

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 expected value of the $j$-th model frequency $r_j$ is called the expected frequency of model $j$:

\[\label{eq:expfreq} \mathrm{EF}_j = \mathrm{E}_{p(r|y)}(r_j) \; .\]

Sources:

Stephan KE, Penny WD, Daunizeau J, Moran RJ, Friston KJ (2009): "Bayesian model selection for group studies"; in: NeuroImage, vol. 46, pp. 1004–1017, eq. 15; URL: https://www.sciencedirect.com/science/article/abs/pii/S1053811909002638; DOI: 10.1016/j.neuroimage.2009.03.025.
Soch J, Allefeld C, Haynes JD (2016): "How to avoid mismodelling in GLM-based fMRI data analysis: cross-validated Bayesian model selection"; in: NeuroImage, vol. 141, pp. 469-489, p. 474; URL: https://www.sciencedirect.com/science/article/pii/S1053811916303615; DOI: 10.1016/j.neuroimage.2016.07.047.

Metadata: ID: D236 | shortcut: expfreq | author: JoramSoch | date: 2026-06-29, 17:47.