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Jeffreys priors for mixture estimation: Properties and alternatives

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  • Grazian, Clara
  • Robert, Christian P.

Abstract

While Jeffreys priors usually are well-defined for the parameters of mixtures of distributions, they are not available in closed form. Furthermore, they often are improper priors. Hence, they have never been used to draw inference on the mixture parameters. The implementation and the properties of Jeffreys priors in several mixture settings are studied. It is shown that the associated posterior distributions most often are improper. Nevertheless, the Jeffreys prior for the mixture weights conditionally on the parameters of the mixture components will be shown to have the property of conservativeness with respect to the number of components, in case of overfitted mixture and it can be therefore used as a default priors in this context.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:149-163
    DOI: 10.1016/j.csda.2017.12.005
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    References listed on IDEAS

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    1. M. Ghosh & B. Carlin & M. Srivastava, 1995. "Probability matching priors for linear calibration," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 333-357, December.
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    Cited by:

    1. Gustavo Alexis Sabillón & Luiz Gabriel Fernandes Cotrim & Daiane Aparecida Zuanetti, 2023. "A data-driven reversible jump for estimating a finite mixture of regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 350-369, March.
    2. Grazian, Clara & Villa, Cristiano & Liseo, Brunero, 2020. "On a loss-based prior for the number of components in mixture models," Statistics & Probability Letters, Elsevier, vol. 158(C).

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