Semiparametric inference in mixture models with predictive recursion marginal likelihood

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in the additional unknown structural parameter. As an alternative to existing profile likelihood methods, we treat predictive recursion as a filter approximation to fitting a fully Bayes model, whereby an approximate marginal likelihood of the structural parameter emerges and can be used for inference. We call this the predictive recursion marginal likelihood. Convergence properties of predictive recursion under model mis-specification also lead to an attractive construction of this new procedure. We show pointwise convergence of a normalized version of this marginal likelihood function. Simulations compare the performance of this new marginal likelihood approach that of existing profile likelihood methods as well as Dirichlet process mixtures in density estimation. Mixed-effects models and an empirical Bayes multiple testing application in time series analysis are also considered

On a likelihood interpretation of adjusted profile likelihoods through refined predictive densities.

In this paper a second-order link between adjusted profile likelihoods and refinements of the estimative predictive density is shown. The result provides a new straightforward interpretation for modified profile likelihoods, that complements results in Severini (1998a) and in Pace and Salvan (2006). Moreover, it outlines a form of consistency to second order between likelihood theory and prediction in frequentist inference

Likelihood theory, prediction, model selection: asymptotic connections.

Plug-in estimation and corresponding refinements involving penalisation have been considered in various areas of parametric statistical inference. One major example is adjustment of the profile likelihood for inference in the presence of nuisance parameters. Another important setting is prediction, where improved estimative predictive densities have been recently developed. A third related setting is model selection, where information criteria based on penalisation of maximised likelihood have been proposed starting from the pioneering contribution of Akaike. The seminal contributions in the last setting predate those introducing the former two classes of procedures, and pertinent portions of literature seem to have evolved quite independently. The aim of this paper is to establish some simple asymptotic connections among these classes of procedures. In particular, all the three kinds of penalisations involved can be viewed as bias corrections of plug-in estimates of theoretical target criteria which are shown to be very closely connected. As a by-product, we obtain adjusted profile likelihoods from optimal predictive densities. Links between adjusted procedures in likelihood theory and model selection procedures are also briefly enquired throuh some simulation studies

Convex mixture regression for quantitative risk assessment

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. In addressing this goal, popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose-response relationships. We instead propose a Bayesian convex mixture regression model that allows the entire distribution of the health outcome to be unknown and changing with the dose. To balance flexibility and parsimony, we rely on a mixture model for the density at the extreme doses, and express the conditional density at each intermediate dose via a convex combination of these extremal densities. This representation generalizes classical dose-response models for quantitative outcomes, and provides a more parsimonious, but still powerful, formulation compared to nonparametric methods, thereby improving interpretability and efficiency in inference on risk functions. A Markov chain Monte Carlo algorithm for posterior inference is developed, and the benefits of our methods are outlined in simulations, along with a study on the impact of dde exposure on gestational age

Machine Learning of User Profiles: Representational Issues

As more information becomes available electronically, tools for finding information of interest to users becomes increasingly important. The goal of the research described here is to build a system for generating comprehensible user profiles that accurately capture user interest with minimum user interaction. The research described here focuses on the importance of a suitable generalization hierarchy and representation for learning profiles which are predictively accurate and comprehensible. In our experiments we evaluated both traditional features based on weighted term vectors as well as subject features corresponding to categories which could be drawn from a thesaurus. Our experiments, conducted in the context of a content-based profiling system for on-line newspapers on the World Wide Web (the IDD News Browser), demonstrate the importance of a generalization hierarchy and the promise of combining natural language processing techniques with machine learning (ML) to address an information retrieval (IR) problem.Comment: 6 page

A semi-parametric approach to estimate risk functions associated with multi-dimensional exposure profiles: application to smoking and lung cancer

A common characteristic of environmental epidemiology is the multi-dimensional aspect of exposure patterns, frequently reduced to a cumulative exposure for simplicity of analysis. By adopting a flexible Bayesian clustering approach, we explore the risk function linking exposure history to disease. This approach is applied here to study the relationship between different smoking characteristics and lung cancer in the framework of a population based case control study