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Adaptive Incremental Mixture Markov Chain Monte Carlo.
- Source :
-
Journal of Computational & Graphical Statistics . Oct-Dec2019, Vol. 28 Issue 4, p790-805. 16p. - Publication Year :
- 2019
-
Abstract
- We propose adaptive incremental mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric proposal kernel with a global rule, AIMM locally adapts a semiparametric kernel. AIMM is based on an independent Metropolis–Hastings proposal distribution which takes the form of a finite mixture of Gaussian distributions. Central to this approach is the idea that the proposal distribution adapts to the target by locally adding a mixture component when the discrepancy between the proposal mixture and the target is deemed to be too large. As a result, the number of components in the mixture proposal is not fixed in advance. Theoretically, we prove that there exists a stochastic process that can be made arbitrarily close to AIMM and that converges to the correct target distribution. We also illustrate that it performs well in practice in a variety of challenging situations, including high-dimensional and multimodal target distributions. Finally, the methodology is successfully applied to two real data examples, including the Bayesian inference of a semiparametric regression model for the Boston Housing dataset. for this article are available online. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10618600
- Volume :
- 28
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Graphical Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 140855932
- Full Text :
- https://doi.org/10.1080/10618600.2019.1598872