Bayesian Models

Abstract

As seen in the previous three chapters, parametric inference from record-breaking data can be quite challenging, and nonparametric inference is perhaps even more so. Even for the case of complete random samples, Bayesian inference can be quite complex and require highly sophisticated computational methods, such as Markov chain Monte Carlo, to obtain posterior distributions. It is not surprising then that very little research has been done on Bayesian estimation from record-breaking data. Initial research from this perspective can be found in Dunsmore (1983) who provided Bayesian predictive distributions for X _m − X _n for an exponential distribution (both the one-parameter and the two-parameter models). This was followed by the work of Basak and Bagchi (1990) who developed an approximation for the predictive distribution of a future record using past records, based on Laplace approximation. Tiwari and Zalkikar (1991) considered the general problem of nonparametric Bayesian inference from record-breaking data. They derived the nonparametric Bayes and the empirical Bayes estimators of the underlying survival function for such data under a Dirichlet process prior and squared-error loss function. In this chapter, all of the work done on Bayesian inference from record-breaking data is summarized, starting with the work of Dunsmore (1983).