IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v80y2014icp167-183.html

A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice

Author

Listed:
  • Kobayashi, Genya

Abstract

When the likelihood functions are either unavailable analytically or are computationally cumbersome to evaluate, it is impossible to implement conventional Bayesian model choice methods. Instead, approximate Bayesian computation (ABC) or the likelihood-free method can be used in order to avoid direct evaluation of the intractable likelihoods. This paper proposes a new Markov chain Monte Carlo (MCMC) method for model choice. This method is based on the pseudo-marginal approach and is appropriate for situations where the likelihood functions for the competing models are intractable. This method proposes jumps between the models with different dimensionalities without matching the dimensionalities. Therefore, it enables the construction of a flexible proposal distribution. The proposal distribution used in this paper is convenient to implement and works well in the context of ABC. Because the posterior model probabilities can be estimated simultaneously, it is expected that the proposed method will be useful, especially when the number of competing models is large. In the simulation study, a comparison between the proposed and existing methods is presented. The method is then applied to the model choice problem for an exchange return model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:167-183
    DOI: 10.1016/j.csda.2014.06.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314002047
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.06.025?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Jean-Michel Marin & Natesh S. Pillai & Christian P. Robert & Judith Rousseau, 2014. "Relevant statistics for Bayesian model choice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(5), pages 833-859, November.
    2. 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, January.
    3. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309.
    4. repec:dau:papers:123456789/7848 is not listed on IDEAS
    5. Peters, G.W. & Sisson, S.A. & Fan, Y., 2012. "Likelihood-free Bayesian inference for α-stable models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3743-3756.
    6. Víctor 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.
    7. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    8. Drovandi, Christopher C. & Pettitt, Anthony N., 2011. "Likelihood-free Bayesian estimation of multivariate quantile distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2541-2556, September.
    9. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    10. Francois Olivier & Laval Guillaume, 2011. "Deviance Information Criteria for Model Selection in Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-25, July.
    11. repec:dau:papers:123456789/5724 is not listed on IDEAS
    12. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    13. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    14. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    15. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    2. Chan, Joshua C.C., 2023. "Comparing stochastic volatility specifications for large Bayesian VARs," Journal of Econometrics, Elsevier, vol. 235(2), pages 1419-1446.
    3. Alzahrani, Naif & Neal, Peter & Spencer, Simon E.F. & McKinley, Trevelyan J. & Touloupou, Panayiota, 2018. "Model selection for time series of count data," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 33-44.
    4. Ye Yang & Osman Dogan & Suleyman Taspinar & Fei Jin, 2023. "A Review of Cross-Sectional Matrix Exponential Spatial Models," Papers 2311.14813, arXiv.org.
    5. Xing Ju Lee & Christopher C. Drovandi & Anthony N. Pettitt, 2015. "Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets," Biometrics, The International Biometric Society, vol. 71(1), pages 198-207, March.
    6. Warne, Anders & Droumaguet, Matthieu & Woźniak, Tomasz, 2015. "Granger causality and regime inference in Bayesian Markov-Switching VARs," Working Paper Series 1794, European Central Bank.
    7. Woźniak, Tomasz, 2015. "Testing causality between two vectors in multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 876-894.
    8. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    9. Li, J. & Nott, D.J. & Fan, Y. & Sisson, S.A., 2017. "Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 77-89.
    10. Hall, Jamie, 2012. "Consumption dynamics in general equilibrium," MPRA Paper 43933, University Library of Munich, Germany.
    11. Mikael Sunnåker & Alberto Giovanni Busetto & Elina Numminen & Jukka Corander & Matthieu Foll & Christophe Dessimoz, 2013. "Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-10, January.
    12. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.
    13. Frank Schorfheide, 2005. "Learning and Monetary Policy Shifts," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 392-419, April.
    14. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.
    15. Oskar Gustafsson & Mattias Villani & Pär Stockhammar, 2023. "Bayesian optimization of hyperparameters from noisy marginal likelihood estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 577-595, June.
    16. Fiorentini, G. & Planas, C. & Rossi, A., 2012. "The marginal likelihood of dynamic mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2650-2662.
    17. Christopher A. Sims & Tao Zha, 2004. "MCMC method for Markov mixture simultaneous-equation models: a note," FRB Atlanta Working Paper 2004-15, Federal Reserve Bank of Atlanta.
    18. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    19. Shibata, Akihisa & Shintani, Mototsugu & Tsuruga, Takayuki, 2019. "Current account dynamics under information rigidity and imperfect capital mobility," Journal of International Money and Finance, Elsevier, vol. 92(C), pages 153-176.
    20. Rots, Eyno, 2017. "Imperfect information and the house price in a general-equilibrium model," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 215-231.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:167-183. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.