Nonparametric Bayes Estimator Research Articles

Nonparametric Bayes estimation of a distribution under nomination sampling

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some distribution. If the data are ((Y/sub i/, K/sub i/), i=1, . . ., n) where K/sub i/ is the size of sample i, and Y/sub i/ is the maximum of a random sample of size K/sub i/ from an unknown Cdf, F; the Bayes estimator of F is derived by discretizing F over a fixed finite partition of the support of F and taking a Dirichlet distribution as the prior for the probabilities of the partitioning intervals. For the flood data of the Nidd River considered by R.A. Boyles and F.J. Samaniego (J. Am. Stat. Assoc., vol.81, p.1039-45, 1986), the plots of the Bayes estimator of F are obtained for several sets of values of the parameters of the Dirichlet distribution. >

Bayesian Nonparametric Inference for Quantal Response Data

The problem of nonparametric Bayes estimation of a tolerance distribution based on quantal response data has been considered previously with a prior distribution based on the Dirichlet process. In the present article, a broad class of priors is developed for this problem by allowing the hazard function of the tolerance distribution to be a realization of a nonnegative stochastic process with independent increments. This class includes the Dirichlet prior as a special case. In addition, priors over a space of absolutely continuous tolerance distributions, which includes IFR, DFR, and U-shaped failure rate distributions, are constructed by taking the failure rate to be the superposition of two processes with independent increments. Posterior Laplace transforms of the corresponding processes are obtained based on quantal response data with binomial sampling. These posterior Laplace transforms are then used to find Bayes estimates, and examples are given to illustrated the results.