Development of noninformative priors for Bayesian analysis

Ruoyong Yang, Purdue University

Abstract

The reference priors, initiated in Bernardo (1979) and further developed in Berger and Bernardo (1992a, b, c), are applied to several statistical models. These include the AR(1) model, estimation of a covariance matrix, and the random coefficient regression model. Invariance of the reference prior is also established under transformations which preserve a specified ordering and grouping pattern of the parameters. For the models mentioned above, other common noninformative priors, including the Jeffreys priors and Uniform priors, are compared with the reference priors, from a decision theoretic point of view, involving risk performance. Frequentist coverage probabilities of the resulting posteriors are also simulated and compared for different noninformative priors. Bayesian testing for a unit root in the AR(1) model is also carried out. Computation of reference posteriors is accomplished by Monte Carlo simulation, either by importance sampling or by Markov Chain sampling. The Metropolisized Hit-and-Run Sampler and Hybrid Markov Chain Sampling are used in the computation of covariance matrix related posterior expectations.

Degree

Ph.D.

Advisors

Berger, Purdue University.

Subject Area

Statistics

COinS