Index: The Book of Statistical ProofsModel Selection ▷ Bayesian model selection ▷ Bayesian model averaging ▷ Definition

Definition: Let $m_1, \ldots, m_M$ be $M$ statistical models with posterior model probabilities $p(m_1 \vert y), \ldots, p(m_M \vert y)$ and posterior distributions $p(\theta \vert y, m_1), \ldots, p(\theta \vert y, m_M)$. Then, Bayesian model averaging (BMA) consists in finding the marginal posterior density, conditional on the measured data $y$, but unconditional on the modelling approach $m$:

\[\label{eq:BMA} p(\theta|y) = \sum_{i=1}^{M} p(\theta|y,m_i) \cdot p(m_i|y) \; .\]

Metadata: ID: D89 | shortcut: bma | author: JoramSoch | date: 2020-08-03, 21:34.