IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v83y2015icp168-181.html
   My bibliography  Save this article

A Monte Carlo approach to quantifying model error in Bayesian parameter estimation

Author

Listed:
  • White, Staci A.
  • Herbei, Radu

Abstract

Quantifying the discrepancy between two distributions is considered, using the concept of ϕ-divergence. The motivation is a Bayesian inference scenario where one is interested in comparing different posterior distributions. Strongly consistent estimators for the ϕ-divergence between two posterior distributions are developed. The proposed estimators alleviate known computational difficulties with estimating normalizing constants. This approach can be used to study the impact that using an approximate likelihood has on the resulting posterior distribution and also to compare the effectiveness of different model approximations. The methodology is applied to two first-order emulator models and an oceanographic application where evaluation of the likelihood function involves the solution to a partial differential equation.

Suggested Citation

  • White, Staci A. & Herbei, Radu, 2015. "A Monte Carlo approach to quantifying model error in Bayesian parameter estimation," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 168-181.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:168-181
    DOI: 10.1016/j.csda.2014.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314003004
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.10.008?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    2. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    3. 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.
    4. 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.
    5. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    6. Lefebvre, Geneviève & Steele, Russell & Vandal, Alain C., 2010. "A path sampling identity for computing the Kullback-Leibler and J divergences," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1719-1731, July.
    7. Higdon, Dave & Gattiker, James & Williams, Brian & Rightley, Maria, 2008. "Computer Model Calibration Using High-Dimensional Output," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 570-583, June.
    8. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    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. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    2. Won Chang & Murali Haran & Patrick Applegate & David Pollard, 2016. "Calibrating an Ice Sheet Model Using High-Dimensional Binary Spatial Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 57-72, March.
    3. Hubin, Aliaksandr & Storvik, Geir, 2018. "Mode jumping MCMC for Bayesian variable selection in GLMM," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 281-297.
    4. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.
    5. Mayer Alvo & Jingrui Mu, 2023. "COVID-19 Data Analysis Using Bayesian Models and Nonparametric Geostatistical Models," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    6. Massimo Bilancia & Giacomo Demarinis, 2014. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 71-94, March.
    7. Douglas R. M. Azevedo & Marcos O. Prates & Dipankar Bandyopadhyay, 2021. "MSPOCK: Alleviating Spatial Confounding in Multivariate Disease Mapping Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 464-491, September.
    8. Drignei, Dorin, 2011. "A general statistical model for computer experiments with time series output," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 460-467.
    9. Vitoratou, Silia & Ntzoufras, Ioannis & Moustaki, Irini, 2016. "Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions," LSE Research Online Documents on Economics 57685, London School of Economics and Political Science, LSE Library.
    10. I Gede Nyoman Mindra Jaya & Henk Folmer, 2024. "High-Resolution Spatiotemporal Forecasting with Missing Observations Including an Application to Daily Particulate Matter 2.5 Concentrations in Jakarta Province, Indonesia," Mathematics, MDPI, vol. 12(18), pages 1-29, September.
    11. Vidal, Ignacio & Iglesias, Pilar, 2008. "Comparison between a measurement error model and a linear model without measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 92-102, September.
    12. Isabel Martínez-Pérez & Verónica González-Iglesias & Valentín Rodríguez Suárez & Ana Fernández-Somoano, 2021. "Spatial Distribution of Hospitalizations for Ischemic Heart Diseases in the Central Region of Asturias, Spain," IJERPH, MDPI, vol. 18(23), pages 1-10, November.
    13. Maike Tahden & Juliane Manitz & Klaus Baumgardt & Gerhard Fell & Thomas Kneib & Guido Hegasy, 2016. "Epidemiological and Ecological Characterization of the EHEC O104:H4 Outbreak in Hamburg, Germany, 2011," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-19, October.
    14. Zhang, Shen & Liu, Xin & Tang, Jinjun & Cheng, Shaowu & Qi, Yong & Wang, Yinhai, 2018. "Spatio-temporal modeling of destination choice behavior through the Bayesian hierarchical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 537-551.
    15. Zhao, Qing & Boomer, G. Scott & Silverman, Emily & Fleming, Kathy, 2017. "Accounting for the temporal variation of spatial effect improves inference and projection of population dynamics models," Ecological Modelling, Elsevier, vol. 360(C), pages 252-259.
    16. Darren J. Mayne & Geoffrey G. Morgan & Bin B. Jalaludin & Adrian E. Bauman, 2018. "Does Walkability Contribute to Geographic Variation in Psychosocial Distress? A Spatial Analysis of 91,142 Members of the 45 and Up Study in Sydney, Australia," IJERPH, MDPI, vol. 15(2), pages 1-24, February.
    17. Terrance Savitsky & Daniel McCaffrey, 2014. "Bayesian Hierarchical Multivariate Formulation with Factor Analysis for Nested Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 275-302, April.
    18. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    19. Ferreira, Marco A.R. & Porter, Erica M. & Franck, Christopher T., 2021. "Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    20. Yong Li & Zeng Tao & Jun Yu, "undated". "Robust Deviance Information Criterion for Latent Variable Models," Working Papers CoFie-04-2012, Singapore Management University, Sim Kee Boon Institute for Financial Economics.

    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:83:y:2015:i:c:p:168-181. 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.