Definition: Bayesian model averaging
Index: The Book of Statistical Proofs ▷ Model Selection ▷ Bayesian model selection ▷ Bayesian model averaging ▷ Definition
Sources:
Metadata: ID: D89 | shortcut: bma | author: JoramSoch | date: 2020-08-03, 21:34.
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 $m$:
\[\label{eq:BMA} p(\theta|y) = \sum_{i=1}^{M} p(\theta|y,m_i) \cdot p(m_i|y) \; .\]- Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999): "Bayesian Model Averaging: A Tutorial"; in: Statistical Science, vol. 14, no. 4, pp. 382–417, eq. 1; URL: https://projecteuclid.org/euclid.ss/1009212519; DOI: 10.1214/ss/1009212519.
Metadata: ID: D89 | shortcut: bma | author: JoramSoch | date: 2020-08-03, 21:34.