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Importance Sampling Schemes for Evidence Approximation in Mixture Models
- Source :
- Bayesian Anal. 11, no. 2 (2016), 573-597
- Publication Year :
- 2016
- Publisher :
- International Society for Bayesian Analysis, 2016.
-
Abstract
- The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete exploration by a simulated Markov chain (e.g., a Gibbs sequence) of the collection of posterior modes, a phenomenon also known as lack of label switching, as all possible label permutations must be simulated by a chain in order to converge and hence overcome the bias. In an importance sampling approach, imposing label switching to the importance function results in an exponential increase of the computational cost with the number of components. In this paper, two importance sampling schemes are proposed through choices for the importance function; a MLE proposal and a Rao-Blackwellised importance function. The second scheme is called dual importance sampling. We demonstrate that this dual importance sampling is a valid estimator of the evidence and moreover show that the statistical efficiency of estimates increases. To reduce the induced high demand in computation, the original importance function is approximated but a suitable approximation can produce an estimate with the same precision and with reduced computational workload.<br />24 pages, 5 figures
- Subjects :
- Statistics and Probability
FOS: Computer and information sciences
Mathematical optimization
Bayesian probability
01 natural sciences
Statistics - Computation
Methodology (stat.ME)
010104 statistics & probability
0502 economics and business
0101 mathematics
mixture models
Computation (stat.CO)
Statistics - Methodology
050205 econometrics
Mathematics
Sequence
Markov chain
Applied Mathematics
05 social sciences
Estimator
marginal likelihood
Mixture model
Marginal likelihood
importance sampling
Label switching
model evidence
Importance sampling
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Bayesian Anal. 11, no. 2 (2016), 573-597
- Accession number :
- edsair.doi.dedup.....e11341be0beff40e2a30840637361529