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Modeling Variability Order: A Semiparametric Bayesian Approach

Author

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  • Athanasios Kottas

    (Duke University)

  • Alan E. Gelfand

    (University of Connecticut)

Abstract

In comparing two populations, sometimes a model incorporating a certain probability order is desired. In this setting, Bayesian modeling is attractive since a probability order restriction imposed a priori on the population distributions is retained a posteriori. Extending the work in Gelfand and Kottas (2001) for stochastic order specifications, we formulate modeling for distributions ordered in variability. We work with Dirichlet process mixtures resulting in a fully Bayesian semiparametric approach. The details for simulation-based model fitting and prior specification are provided. An example, based on two small subsets of time intervals between eruptions of the Old Faithful geyser, illustrates the methodology.

Suggested Citation

  • Athanasios Kottas & Alan E. Gelfand, 2001. "Modeling Variability Order: A Semiparametric Bayesian Approach," Methodology and Computing in Applied Probability, Springer, vol. 3(4), pages 427-442, December.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:4:d:10.1023_a:1015420304825
    DOI: 10.1023/A:1015420304825
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Alan Gelfand & Athanasios Kottas, 2001. "Nonparametric Bayesian Modeling for Stochastic Order," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 865-876, December.
    3. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
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    1. Krnjajic, Milovan & Kottas, Athanasios & Draper, David, 2008. "Parametric and nonparametric Bayesian model specification: A case study involving models for count data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2110-2128, January.

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