R package rjmcmc: reversible jump MCMC using post-processing
Corresponding Author
Nicholas Gelling
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin , 9016 New Zealand
Author to whom correspondence should be addressed.Search for more papers by this authorMatthew R. Schofield
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin , 9016 New Zealand
Search for more papers by this authorRichard J. Barker
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin , 9016 New Zealand
Search for more papers by this authorCorresponding Author
Nicholas Gelling
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin , 9016 New Zealand
Author to whom correspondence should be addressed.Search for more papers by this authorMatthew R. Schofield
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin , 9016 New Zealand
Search for more papers by this authorRichard J. Barker
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin , 9016 New Zealand
Search for more papers by this authorSummary
The rjmcmc package for R implements the post-processing reversible jump Markov chain Monte Carlo (MCMC) algorithm of Barker & Link. MCMC output from each of the models is used to estimate posterior model probabilities and Bayes factors. Automatic differentiation is used to simplify implementation. The package is demonstrated on two examples.
Supporting Information
Filename | Description |
---|---|
anzs12263-sup-0006-results4-19.RDataunknown, 1.5 KB |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
References
- Arlot, S. & Celisse, A. (2010). A survey of cross-validation procedures for model selection. Statistics Surveys 4, 40–79.
10.1214/09-SS054 Google Scholar
- Barker, R.J. & Link, W.A. (2013). Bayesian multimodel inference by RJMCMC: a Gibbs sampling approach. The American Statistician 67, 150–156.
- Basturk, N., Hoogerheide, L., Opschoor, A. & van Dijk, H. (2017). Mixture of Student t Distributions Using Importance Sampling and Expectation Maximization. Available from URL: https://CRAN.R-project.org/package=MitISEM. [Last accessed 3 October 2017]. R package version 1.2.
- Berger, J.O. & Pericchi, L.R. (1998). On Criticisms and Comparisons of Default Bayes Factors for Model Selection and Hypothesis Testing. Durham: Institute of Statistics and Decision Sciences, Duke University.
- Carlin, B.P. & Chib, S. (1995). Bayesian model choice via Markov chain Monte Carlo methods. Journal of the Royal Statistical Society. Series B (Methodological) 57, 473–484.
- Carpenter, B., Hoffman, M.D., Brubaker, M., Lee, D., Li, P. & Betancourt, M. (2015). The Stan Math Library: reverse-mode automatic differentiation in C++. arXiv Preprint arXiv:1509.07164.
- Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis 1, 515–534.
- Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis. Boca Raton, FL: CRC Press.
10.1201/b16018 Google Scholar
- Gill, J. (2014). Bayesian Methods: A Social and Behavioral Sciences Approach. Boca Raton, FL: CRC Press.
10.1201/b17888 Google Scholar
- Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115, 513–583.
10.1098/rstl.1825.0026 Google Scholar
- Green, P.J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732.
- Griewank, A. & Walther, A. (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Philadelphia: SiAM.
- Han, C. & Carlin, B.P. (2001). Markov chain Monte Carlo methods for computing bayes factors: a comparative review. Journal of the American Statistical Association 96, 1122–1132.
- Hoeting, J.A., Madigan, D., Raftery, A.E. & Volinsky, C.T. (1999). Bayesian model averaging: a tutorial. Statistical Science, 382–401.
- Jeffreys, H. (1935). Some tests of significance, treated by the theory of probability. Proceedings of the Cambridge Philosophical Society 31, 203–222.
10.1017/S030500410001330X Google Scholar
- Kass, R.E. & Raftery, A.E. (1995). Bayes factors. Journal of the American Statistical Association 90, 773–795.
- Katsanevakis, S. (2006). Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fisheries Research 81, 229–235.
- Link, W.A. & Barker, R.J. (2009). Bayesian Inference: With Ecological Applications. London: Academic Press.
- Lunn, D.J., Thomas, A., Best, N. & Spiegelhalter, D. (2000). WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and computing 10, 325–337.
- Martin, A.D., Quinn, K.M., Park, J.H., Vieille-dent, G., Malecki, M. & Blackwell, M. (2017). Markov chain Monte Carlo (MCMC) Package. Available from URL: https://CRAN.Rproject.org/package=MCMCpack. [Last accessed 3 October 2017]. R package version 1.4-0.
- Morey, R.D., Rouder, J.N. & Jamil, T. (2015). Computation of Bayes Factors for Common Designs. Available from URL: https://CRAN.R-project.org/package=BayesFactor. [Last accessed 3 October 2017]. R package version 0.9.12-2.
- Ogle, D.H. (2016). FSAdata: Fisheries Stock Analysis, Datasets. R package version 0.3.5.
- Pajor, A. (2017). Estimating the marginal likelihood using the arithmetic mean identity. Bayesian Analysis 12, 261–287.
- Pav, S.E. (2016). madness: Automatic Differentiation of Multivariate Operations. Available from URL: https://github.com/shabbychef/madness. [Last accessed 7 April 2017]. R package version 0.2.0.
- Plummer, M.. (2003). JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing, ed. K. Hornik, F. Leisch and A. Zeileis, vol. 124, pp. 125. Vienna. Available from URL: https://www.rproject.org/conferences/DSC-2003/Proceedings/ [Last accessed 7 April 2017].
- Pritchard, G. & Scott, D.J. (2004). The eigenvalues of the empirical transition matrix of a Markov chain. Journal of Applied Probability 41, 347–360.
- Robert, C.P. & Casella, G. (2004). Monte Carlo Statistical Methods, 2nd edn. Berlin: Springer.
10.1007/978-1-4757-4145-2 Google Scholar
- Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6, 461–464.
- Seber, G.A. (2008). A Matrix Handbook for Statisticians, vol. 15. Hoboken: John Wiley & Sons.
- Su, Y.S. & Yajima, M. (2015). R2jags: Using R to Run ’JAGS’. R package version 0.5-7.
- Von Bertalanffy, L. (1938). A quantitative theory of organic growth (inquiries on growth laws. II). Human Biology 10, 181–213.
- Watanabe, S. (2010). Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research 11, 3571–3594.
- Zeugner, S. (2015). Bayesian Model Averaging Library. Available from URL: https://CRAN.Rproject.org/package=BMS. [Last accessed 3 October, 2017]. R package version 0.3.4.