Simulation techniques are gaining popularity for drawing statistical inference, particularly in the field of practical Bayesian Statistics (e.g. Ann. Statist. 9 (1981), 130-134; J. Amer. Statist. Assoc. 85 (1987), 470-477; J. Amer. Statist. Assoc. 85 (1990), 398-409; J. Roy. Statist. Soc. 56 (1994), 3-48). Smith and Gelfand (Amer. Statist. 46 (1992), 84-88) discussed two sampling-resampling methods for obtaining posterior samples from prior samples. The first is based on the rejection method, the second (the weighted bootstrap) is the sampling importance resampling (SIR) (J. Amer. Statist. Assoc. 82 (1987), 543-546; Bayesian Statistics, Vol. 3, Oxford University Press, 1988). This paper uses an example to illustrate the applicability of these methods. The example is on cosmological data for which maximum likelihood estimates do not exist. The data were analyzed by Chernoff (Comput. Statist. Data Anal. 12 (1991), 159-178) who introduced several non-Bayesian computer intensive methods for analyzing these data. The cosmological data are used to evaluate the two Bayesian computer intensive methods.
- Bayes estimation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics