The Imprecise Logit-Normal Model and its Application to Estimating Hazard Functions

Given data on inter-arrival times, the imprecise Dirichlet model can be used to determine upper and lower values on the survival function. Similar bounds on the hazard function can be quite irregular without some structural assumptions. To address this problem, a family of prior distributions for a binomial success probability is contructed by assuming that the logit of the probability has a normal distribution. Posterior distributions so defined form a three-dimensional exponential family of which the beta family is a limiting case. This family is extended to the multivariate case, which provides for the inclusion of prior information about autocorrelation in the parameters. By restricting the hyperparameters to a suitably chosen subset, this model is proposed as an alternative to the usual imprecise Dirichlet model of Walley, having the advantage of providing smoother estimates of the hazard function. The methods are applied to data on inter-occurrence times of pandemic influenza.