School Seminars and Colloquia

Locally Adaptive Nonparametric Binary Regression

Applied Statistics Seminar

by Dr Sally Wood

Institution: Australian Graduate School of Management
Date: Fri 30th September 2005
Time: 4:15 PM
Location: Theatre 2, Old Geology Building, University of Melbourne

Abstract: This article presents a Bayesian method for estimating a binary regression without assuming that its functional form is known. The estimator is locally adaptive by which we mean that it can be smooth in one
part of the covariate space and quite wiggly in another part. This is achieved by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression having a thin plate spline prior with its own smoothing parameter and with the mixture weights depending on the covariates. Our approach allows for models with differing numbers of components.
Our final estimate is a weighted average of the estimates obtained
from each model where weights are the posterior probability of each model. To ensure that our model is parsimonious in the number of components we introduce an important constraint on the
parameter space called the component dominance condition. The results of a simulation study show that the posterior mean estimator obtained by our method outperforms the single spline estimator when the function requires a locally adaptive estimator
and is as good as the single spline estimator when it does not.
The methodology is illustrated by applying it to estimate the probability that a Pima Indian woman develops diabetes. All the estimation is carried out using Markov chain Monte Carlo simulation.

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