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An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

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  • C. Villa
  • S. G. Walker

Abstract

We present a novel approach to constructing objective prior distributions for discrete parameter spaces. These types of parameter spaces are particularly problematic, as it appears that common objective procedures to design prior distributions are problem specific. We propose an objective criterion, based on loss functions, instead of trying to define objective probabilities directly. We systematically apply this criterion to a series of discrete scenarios, previously considered in the literature, and compare the priors. The proposed approach applies to any discrete parameter space, making it appealing as it does not involve different concepts according to the model. Supplementary materials for this article are available online.

Suggested Citation

  • C. Villa & S. G. Walker, 2015. "An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1072-1082, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:1072-1082
    DOI: 10.1080/01621459.2014.946319
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    Cited by:

    1. Villa, Cristiano & Rubio, Francisco J., 2018. "Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 197-219.
    2. Hinoveanu, Laurentiu C. & Leisen, Fabrizio & Villa, Cristiano, 2019. "Bayesian loss-based approach to change point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 61-78.
    3. Fabrizio Leisen & Luca Rossini & Cristiano Villa, 2018. "Objective bayesian analysis of the Yule–Simon distribution with applications," Computational Statistics, Springer, vol. 33(1), pages 99-126, March.
    4. 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.
    5. Fabrizio Leisen & Luca Rossini & Cristiano Villa, 2020. "Loss-based approach to two-piece location-scale distributions with applications to dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 309-333, June.

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