Nonparametric Bayes Applications to Biostatistics
نویسنده
چکیده
1. Introduction Biomedical research has clearly evolved at a dramatic rate in the past decade, with improvements in technology leading to a fundamental shift in the way in which data are collected and analyzed. Before this paradigm shift, studies were most commonly designed to be simple and to focus on relationships among a few variables of primary interest. For example, in a clinical trial, patients may be randomized to receive either the drug or placebo, with the analysis focusing on a comparison of means between the two groups. However, with emerging biotechnology tools, scientists are increasingly interested in studying how patients vary in their response to drug therapies, and what factors predict this variability. Such questions are of fundamental interest in personalizing medicine, so that the physician prescribes the most appropriate therapy given the patient's history, genetics and lifestyle factors. Given this focus , it has become routine to collect large amounts of information for each study subject, with the statistician's challenge then being to perform inferences and develop predictive models based on the massive amount of data available. Clinical trials and personalized medicine are just one example of a growing trend in biomedicine towards embracing emerging technologies for collection, storage and analysis of massive amounts of data. To address big problems of this type, it is crucial for statisticians to have an appropriate toolbox at their disposal. Certainly, classical statistical methods were developed with simpler data structures and problems in mind. Hence, it has become necessary to consider new statistical paradigms that perform well in characterizing complex data from a broad variety of study designs. In complex settings, it is seldom if ever the case that one has a defensible parametric model at their disposal, and it can be very challenging to check mod-eling assumptions in high-dimensions. Hence, non-or semiparametric models seem required. However, classical nonparametric methods often perform poorly in complex settings due to the curse of dimensionality and to difficulties in accommodating complicating features of the data, such as censoring and missing data. Nonparametric Bayes methods provide a widely useful paradigm that gains some key advantages of a fully model-based probabilistic framework, while being highly flexible and adaptable. In addition, a key to the success of nonparametric Bayes methods in applications is the incorporation of a sparseness-favoring structure, which combats the curse of dimensionality. This is accomplished automatically through the Bayesian penalty for model complexity (Jeffreys and …
منابع مشابه
A nonparametric empirical Bayes framework for large-scale multiple testing.
We propose a flexible and identifiable version of the 2-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the nonnull cases. We use a computationally efficient predictive recursion (PR) marginal likelihood procedure to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonp...
متن کاملSpecies sampling priors for modeling dependence: an application to the detection of chromosomal aberrations
We discuss a class of Bayesian nonparametric priors that can be used to model local dependence in a sequence of observations. Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, common exchangeability assumptions may not be appropriate. We discuss a generalization of species sampling sequences, where...
متن کاملWavelet-based Nonparametric Bayes Methods
In this chapter, we will provide an overview of the current status of research involving Bayesian inference in wavelet nonparametric problems. In many statistical applications, there is a need for procedures to (i) adapt to data and (ii) use prior information. The interface of wavelets and the Bayesian paradigm provide a natural terrain for both of these goals.
متن کاملBayesian nonparametric regression and density estimation using integrated nested Laplace approximations.
Integrated nested Laplace approximations (INLA) are a recently proposed approximate Bayesian approach to fit structured additive regression models with latent Gaussian field. INLA method, as an alternative to Markov chain Monte Carlo techniques, provides accurate approximations to estimate posterior marginals and avoid time-consuming sampling. We show here that two classical nonparametric smoot...
متن کاملA New Nonparametric Regression for Longitudinal Data
In many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. Regression is the most common tool in this situation. If we have some assumptions for such normality for response variable, we could use it. In this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus ...
متن کامل