Statistics Seminars: Imprecise Predictive Inference for Logistic Regression
5 December 2011 14:00 in CM221
Logistic regression is a commonly used technique for modelling and predicting the probability of an outcome of interest as a function of explanatory variables. Under a Bayesian paradigm, predictive probabilities incorporate the uncertainty in the estimates of the model parameters but depend on a precise specification of the prior distribution. Walley has proposed an inferential paradigm that applies Bayes theorem to a family of prior distributions, yielding interval posterior probabilities. He suggested a family of Dirichlet priors on multinomial parameters as a practical way of implementing such imprecise inference. For logistic regression, we assume Dirichlet priors on the increments of response probabilities at selected values of the explanatory variable, thereby allowing for prior dependence.
Alternatively, we consider a family of normal priors on the regression parameters. Priors on the response probabilities induce priors on the model parameters and vice versa, but these different parametrizations of prior uncertainty are not equivalent. We compare the effects of these models on prediction using both analytic and simulation techniques.
(This is joint work with Osama Bataineh)
Contact Ian Jermyn