A Monte Carlo method for an objective Bayesian procedure
- Yosihiko Ogata
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This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.
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- A Monte Carlo method for an objective Bayesian procedure
Annals of the Institute of Statistical Mathematics
Volume 42, Issue 3 , pp 403-433
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Bayesian likelihood
- posterior mean
- ϕ- and ψ-statistic
- Gibbs distribution
- Metropolis' algorithm, normalizing factor
- potential function
- type II maximum likelihood method
- Industry Sectors
- Yosihiko Ogata (1)
- Author Affiliations
- 1. The Institute of Statistical Mathematies, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan