The DOI matches its Crossref record; 34 of the 34 references it cites were found in a registry or an index.
Marginal Likelihood Estimation via Power Posteriors
Abstract
Summary: Model choice plays an increasingly important role in statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. However, this is typically a difficult task since it amounts to integrating over all model parameters. The aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling. We show how the marginal likelihood can be computed via Markov chain Monte Carlo methods on modified posterior distributions for each model. This then allows Bayes factors or posterior model probabilities to be calculated. We show that this approach requires very little tuning and is straightforward to implement. The new method is illustrated in a variety of challenging statistical settings.
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Cites
(2005) · Technometrics · doi:10.1198/tech.2005.s303 · Cited by 17,923
Spatial Interaction and the Statistical Analysis of Lattice Systems
Besag, J. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00999.x · Cited by 6,067
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
GREEN, P. J. (1995) · Biometrika · doi:10.1093/biomet/82.4.711 · Cited by 5,930
Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118 · cited 1×
“From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model.”
BackgroundMonte Carlo Strategies in Scientific Computing
Liu, J. S. (2004) · Springer Series in Statistics · doi:10.1007/978-0-387-76371-2 · Cited by 2,690
Marginal Likelihood from the Gibbs Output
Chib, S. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476635 · Cited by 1,905
Monte Carlo Strategies in Scientific Computing
Hesterberg, T. (2002) · Technometrics · doi:10.1198/tech.2002.s85 · Cited by 1,409
A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion
Kass, R. E., & Wasserman, L. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476592 · Cited by 1,253
Neal, R. M. (2001) · Statistics and Computing · doi:10.1023/a:1008923215028 · Cited by 1,172
Marginal Likelihood From the Metropolis–Hastings Output
Chib, S., & Jeliazkov, I. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501750332848 · Cited by 1,062
Cited by
Improving Marginal Likelihood Estimation for Bayesian Phylogenetic Model Selection
Xie, W., Lewis, P. O., Fan, Y., Kuo, L., & Chen, M.-H. (2011) · Systematic Biology · doi:10.1093/sysbio/syq085 · Cited by 1,050
Approximate Bayesian computational methods
Marin, J.-M., Pudlo, P., Robert, C. P., & Ryder, R. J. (2012) · Statistics and Computing · doi:10.1007/s11222-011-9288-2 · Cited by 818
Accurate Model Selection of Relaxed Molecular Clocks in Bayesian Phylogenetics
Baele, G., Li, W. L. S., Drummond, A. J., Suchard, M. A., & Lemey, P. (2012) · Molecular Biology and Evolution · doi:10.1093/molbev/mss243 · Cited by 594
A Nondegenerate Code of Deleterious Variants in Mendelian Loci Contributes to Complex Disease Risk
Blair, D. R., Lyttle, C. S., Mortensen, J. M., Bearden, C. F., Jensen, A. B., Khiabanian, H., Melamed, R., Rabadan, R., Bernstam, E. V., Brunak, S., et al. (2013) · Cell · doi:10.1016/j.cell.2013.08.030 · Cited by 215
Bayesian ranking of biochemical system models
Vyshemirsky, V., & Girolami, M. A. (2008) · Bioinformatics · doi:10.1093/bioinformatics/btm607 · Cited by 181
Metadata
- Authors
- Friel, N., & Pettitt, A. N.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2008-04-10
- Volume
- 70
- Issue
- 3
- Pages
- 589-607
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2158128575
- Cited by
- 353
- References
- 34
- FWCI
- 9.93
- Type
- journal article
- Language
- en
- Open access
- closed
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