Abstract #302307

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JSM 2003 Abstract #302307
Activity Number: 56
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #302307
Title: Nonparametric Bayesian Binary Regression
Author(s): Subhashis Ghosal*+ and Nidhan Choudhuri and Anindya Roy
Companies: North Carolina State University and Case Western Reserve University and University of Maryland, Baltimore County
Address: 2501 Founders Dr., Raleigh, NC, 27695-8203,
Keywords: posterior consistency ; Gaussian process ; logit transformation ; metropolis algorithm ; success probability
Abstract:

We consider the problem of estimating the success probability as function of a covariate in a binary regression. No parametric form of the probability function is assumed. We also do not make the standard assumption of monotonicity of the probability function. We follow a Bayesian approach and put a prior on the logit transform of the probabilities through a Gaussian process. We describe a Markov chain Monte Carlo method to compute the posterior mean. Assuming that the true response probability as a function of the covariate is twice continuously differentiable and bounded away from 0 and 1, we show that the posterior is consistent. A simulation study shows that our method performs well in comparison to other methods of estimation available in the literature. We also apply our method to some real data.

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