Bayesian nonparametric inference for quantal response data
Nonparametric Bayes estimation of the tolerance distribution based on quantal response data is considered with a broad class of priors. If F denotes the distribution function of the tolerance level of an individual to a drug then \(H(t):=-\log (1-F(t))\) is called the hazard function and its derivative is called the failure rate function. In the present paper the hazard function of the tolerance distribution is allowed to be a realization of a nonnegative valued stochastic process with independent increments. This class includes the case when the prior distribution is based on the Dirichlet process. In addition, priors 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 illustrate the results.
scientific article; zbMATH DE number 3921746