Bayesian nonparametric inference for quantal response data
type: Item
instance of: scholarly article
title: Bayesian nonparametric inference for quantal response data
zbMATH Open document ID: 0576.62051
author: Larry P. Ammann
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62G99
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 3921746
zbMATH Keywords: tolerance distribution
zbMATH Keywords: quantal response data
zbMATH Keywords: hazard function
zbMATH Keywords: failure rate
zbMATH Keywords: nonnegative valued stochastic process
zbMATH Keywords: independent increments
zbMATH Keywords: Dirichlet process
zbMATH Keywords: superposition of two processes
zbMATH Keywords: Posterior Laplace transforms
zbMATH Keywords: binomial sampling
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346511
OpenAlex ID: W2030712844
DOI: 10.1214/AOS/1176346511
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description: scientific article; zbMATH DE number 3921746