The Annals of Statistics

Bayesian Nonparametric Inference for Quantal Response Data

Larry P. Ammann

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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

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

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

Nonparametric Bayes estimation tolerance distribution quantal response data


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

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