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Asymptotic inference for mixture models by using data‐dependent priors

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  • L. Wasserman

Abstract

For certain mixture models, improper priors are undesirable because they yield improper posteriors. However, proper priors may be undesirable because they require subjective input. We propose the use of specially chosen data‐dependent priors. We show that, in some cases, data‐dependent priors are the only priors that produce intervals with second‐order correct frequentist coverage. The resulting posterior also has another interpretation: it is the product of a fixed prior and a pseudolikelihood.

Suggested Citation

  • L. Wasserman, 2000. "Asymptotic inference for mixture models by using data‐dependent priors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 159-180.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:1:p:159-180
    DOI: 10.1111/1467-9868.00226
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    Cited by:

    1. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    2. Sylvia Kaufmann, 2014. "K-state switching models with time-varying transition distributions – Does credit growth signal stronger effects of variables on inflation?," Working Papers 14.04, Swiss National Bank, Study Center Gerzensee.
    3. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    4. Grazian, Clara & Robert, Christian P., 2018. "Jeffreys priors for mixture estimation: Properties and alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 149-163.
    5. Chopin, Nicolas & Pelgrin, Florian, 2004. "Bayesian inference and state number determination for hidden Markov models: an application to the information content of the yield curve about inflation," Journal of Econometrics, Elsevier, vol. 123(2), pages 327-344, December.
    6. repec:dau:papers:123456789/13436 is not listed on IDEAS
    7. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    8. Cathy W. S. Chen & Sangyeol Lee & K. Khamthong, 2021. "Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts," Computational Statistics, Springer, vol. 36(1), pages 261-281, March.
    9. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    10. Blasques, Francisco & Duplinskiy, Artem, 2018. "Penalized indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 34-54.
    11. Lo, Yungtai, 2005. "Likelihood ratio tests of the number of components in a normal mixture with unequal variances," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 225-235, March.
    12. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.
    13. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.
    14. repec:dau:papers:123456789/13437 is not listed on IDEAS
    15. D. A. S. Fraser & N. Reid & E. Marras & G. Y. Yi, 2010. "Default priors for Bayesian and frequentist inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 631-654, November.
    16. Kilchan Choi & Michael Seltzer, 2010. "Modeling Heterogeneity in Relationships Between Initial Status and Rates of Change: Treating Latent Variable Regression Coefficients as Random Coefficients in a Three-Level Hierarchical Model," Journal of Educational and Behavioral Statistics, , vol. 35(1), pages 54-91, February.

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