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Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions

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  • S. P. Brooks
  • P. Giudici
  • G. O. Roberts

Abstract

The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of proposal. The first group of methods is based on an analysis of acceptance probabilities for jumps. Essentially, these methods involve a Taylor series expansion of the acceptance probability around certain canonical jumps and turn out to have close connections to Langevin algorithms. The second group of methods generalizes the reversible jump algorithm by using the so-called saturated space approach. These allow the chain to retain some degree of memory so that, when proposing to move from a smaller to a larger model, information is borrowed from the last time that the reverse move was performed. The main motivation for this paper is that, in complex problems, the probability that the Markov chain moves between such spaces may be prohibitively small, as the probability mass can be very thinly spread across the space. Therefore, finding reasonable jump proposals becomes extremely important. We illustrate the procedure by using several examples of reversible jump Markov chain Monte Carlo applications including the analysis of autoregressive time series, graphical Gaussian modelling and mixture modelling. Copyright 2003 Royal Statistical Society.

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  • S. P. Brooks & P. Giudici & G. O. Roberts, 2003. "Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 3-39.
  • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:3-39
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    1. S. P. Brooks & N. Friel & R. King, 2003. "Classical model selection via simulated annealing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 503-520.
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    2. VĂ­ctor Enciso-Mora & Peter Neal & T. Subba Rao, 2009. "Efficient order selection algorithms for integer-valued ARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 1-18, January.
    3. Liqun Wang & James Fu, 2007. "A practical sampling approach for a Bayesian mixture model with unknown number of components," Statistical Papers, Springer, vol. 48(4), pages 631-653, October.
    4. David I. Hastie & Peter J. Green, 2012. "Model choice using reversible jump Markov chain Monte Carlo," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 309-338, August.
    5. Ho, Remus K.W. & Hu, Inchi, 2008. "Flexible modelling of random effects in linear mixed models--A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1347-1361, January.
    6. Kobayashi, Genya, 2014. "A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 167-183.
    7. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607.
    8. D. Fouskakis & I. Ntzoufras & D. Draper, 2009. "Population-based reversible jump Markov chain Monte Carlo methods for Bayesian variable selection and evaluation under cost limit restrictions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 383-403.
    9. Sridhar Narayanan, 2013. "Bayesian estimation of discrete games of complete information," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 39-81, March.
    10. Pandolfi, Silvia & Bartolucci, Francesco & Friel, Nial, 2014. "A generalized multiple-try version of the Reversible Jump algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 298-314.
    11. Azari Soufiani, Hossein & Diao, Hansheng & Lai, Zhenyu & Parkes, David C., 2013. "Generalized Random Utility Models with Multiple Types," Scholarly Articles 12363923, Harvard University Department of Economics.
    12. repec:gam:jecnmx:v:5:y:2017:i:3:p:43-:d:112377 is not listed on IDEAS
    13. Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
    14. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.
    15. Overstall, Antony M. & King, Ruth, 2014. "conting: An R Package for Bayesian Analysis of Complete and Incomplete Contingency Tables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i07).
    16. Streftaris, George & Worton, Bruce J., 2008. "Efficient and accurate approximate Bayesian inference with an application to insurance data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2604-2622, January.
    17. Helen Armstrong & Christopher K. Carter & Kevin K. F. Wong & Robert Kohn, 2007. "Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models," Discussion Papers 2007-13, School of Economics, The University of New South Wales.
    18. Rigat, F. & Mira, A., 2012. "Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1450-1467.
    19. Oedekoven, C.S. & King, R. & Buckland, S.T. & Mackenzie, M.L. & Evans, K.O. & Burger, L.W., 2016. "Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 79-90.
    20. repec:bla:scjsta:v:44:y:2017:i:3:p:765-779 is not listed on IDEAS
    21. Chen, Langnan & Luo, Jiawen & Liu, Hao, 2013. "The determinants of liquidity with G-RJMCMC-VS model: Evidence from China," Economic Modelling, Elsevier, vol. 35(C), pages 192-198.
    22. Alexander Meyer-Gohde & Daniel Neuhoff, 2015. "Generalized Exogenous Processes in DSGE: A Bayesian Approach," SFB 649 Discussion Papers SFB649DP2015-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    23. Tsung-I Lin & Hsiu Ho & Pao Shen, 2009. "Computationally efficient learning of multivariate t mixture models with missing information," Computational Statistics, Springer, vol. 24(3), pages 375-392, August.

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