A Bayesian Multiresolution Hazard Model with Applicationt An AIDS Reporting Delay Study

Thanks to advances in MCMC methodology, Bayesian curve estimation has become an increasingly popular subject both in practice and in theoretical research. Prior specification for curves is a more challenging task than for usual scalar or multivariate parameters. Besides using fully parametric curves, common strategies include using a stochastic process or discretizing the curve, each with its own advantages and pitfalls. In this paper we adopt the second strategy, primarily for its practicality for general users, in the context of hazard (and survival) curve estimation. We adapt a multiresolution modeling approach from the engineering literature, which provides a resolution-invariant prior for hazard increments, with their {\em a priori} dependence conveniently specified via tuning a few hyperparameters. We also investigate a hierarchical mixing strategy to combat a pitfall of the multiresolution approach: that nearby cells may exhibit lower dependence than cells that are far apart due to the fact that the multiresolution approach is based on a binary tree construction and not the usual Euclidean topology. Our investigations include both simulated and textbook data, as well as a comparison to the first strategy based on a Beta process prior. The paper concludes with a detailed application of the proposed method for an AIDS reporting delay estimation for New York City, from data provided by the Centers for Disease Control and Prevention (CDC).