Fernando A. Quintana

Nonparametric Bayesian Data Analysis

We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Polya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models and model validation with DP and Polya tree extensions of parametric models.

Random-set methods identify distinct aspects of the enrichment signal in gene-set analysis

A prespecified set of genes may be enriched, to varying degrees, for genes that have altered expression levels relative to two or more states of a cell. Knowing the enrichment of gene sets defined by functional categories, such as gene ontology (GO) annotations, is valuable for analyzing the biological signals in microarray expression data. A common approach to measuring enrichment is by cross-classifying genes according to membership in a functional category and membership on a selected list of significantly altered genes. A small Fishers exact test

A New Class of Skew-Normal Distributions

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Linear mixed models with skew-elliptical distributions: A Bayesian approach

-value, for example, in this

Nonparametric Bayesian Modeling for Multivariate Ordinal Data

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Bayesian Nonparametric Data Analysis

table is indicative of enrichment. Other category analysis methods retain the quantitative gene-level scores and measure significance by referring a category-level statistic to a permutation distribution associated with the original differential expression problem. We describe a class of random-set scoring methods that measure distinct components of the enrichment signal. The class includes Fishers test based on selected genes and also tests that average gene-level evidence across the category. Averaging and selection methods are compared empirically using Affymetrix data on expression in nasopharyngeal cancer tissue, and theoretically using a location model of differential expression. We find that each method has a domain of superiority in the state space of enrichment problems, and that both methods have benefits in practice. Our analysis also addresses two problems related to multiple-category inference, namely, that equally enriched categories are not detected with equal probability if they are of different sizes, and also that there is dependence among category statistics owing to shared genes. Random-set enrichment calculations do not require Monte Carlo for implementation. They are made available in the R package allez.

A Product Partition Model With Regression on Covariates

Abstract We introduce a new family of asymmetric normal distributions that contains Azzalinis skew-normal (SN) distribution as a special case. We study the main properties of this new family, showing in particular that it may be generated via mixtures on the SN asymmetry parameter when the mixing distribution is normal. This property provides a Bayesian interpretation of the new family.

On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions

Normality of random effects and error terms is a routine assumption for linear mixed models. However, such an assumption may be unrealistic, obscuring important features of within- and among-unit variation. A simple and robust Bayesian parametric approach that relaxes this assumption by using a multivariate skew-elliptical distribution, which includes the Skew-t, Skew-normal, t-Student, and Normal distributions as special cases and provides flexibility in capturing a broad range of non-normal and asymmetric behavior is presented. An appropriate posterior simulation scheme is developed and the methods are illustrated with an application to a longitudinal data example.

Model-based clustering for longitudinal data

This article proposes a probability model for k-dimensional ordinal outcomes, that is, it considers inference for data recorded in k-dimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contingency table cell probabilities. We use a variation of the traditional multivariate probit model, with latent scores that determine the observed data. In our model, a mixture of normals prior replaces the usual single multivariate normal model for the latent variables. By augmenting the prior model to a mixture of normals we generalize inference in two important ways. First, we allow for varying local dependence structure across the contingency table. Second, inference in ordinal multivariate probit models is plagued by problems related to the choice and resampling of cutoffs defined for these latent variables. We show how the proposed mixture model approach entirely removes these problems. We illustrate the methodology with two examples, one simulated dataset and one dataset of interrater agreement.

Semiparametric Bayesian classification with longitudinal markers

This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the books structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.