The Annals of Statistics

Bayesian Nonparametric Inference for Quantal Response Data

Larry P. Ammann

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 12, Number 2 (1984), 636-645.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346511

Digital Object Identifier
doi:10.1214/aos/1176346511

Mathematical Reviews number (MathSciNet)
MR740917

Zentralblatt MATH identifier
0576.62051

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G99: None of the above, but in this section

Keywords
Nonparametric Bayes estimation tolerance distribution quantal response data

Citation

Ammann, Larry P. Bayesian Nonparametric Inference for Quantal Response Data. Ann. Statist. 12 (1984), no. 2, 636--645. doi:10.1214/aos/1176346511. https://projecteuclid.org/euclid.aos/1176346511


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