Abel Rodriguez

The Nested Dirichlet Process

In multicenter studies, subjects in different centers may have different outcome distributions. This article is motivated by the problem of nonparametric modeling of these distributions, borrowing information across centers while also allowing centers to be clustered. Starting with a stick-breaking representation of the Dirichlet process (DP), we replace the random atoms with random probability measures drawn from a DP. This results in a nested DP prior, which can be placed on the collection of distributions for the different centers, with centers drawn from the same DP component automatically clustered together. Theoretical properties are discussed, and an efficient Markov chain Monte Carlo algorithm is developed for computation. The methods are illustrated using a simulation study and an application to quality of care in U.S. hospitals.

Nonparametric Bayesian models through probit stick-breaking processes

We describe a novel class of Bayesian nonparametric priors based on stick-breaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology.

Bayesian Inference for General Gaussian Graphical Models With Application to Multivariate Lattice Data

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using a simulated example and a real-world application which concerns cancer mortality surveillance. Supplementary materials with computer code and the datasets needed to replicate our numerical results together with additional tables of results are available online.

Early Onset Prion Disease from Octarepeat Expansion Correlates with Copper Binding Properties

Insertional mutations leading to expansion of the octarepeat domain of the prion protein (PrP) are directly linked to prion disease. While normal PrP has four PHGGGWGQ octapeptide segments in its flexible N-terminal domain, expanded forms may have up to nine additional octapeptide inserts. The type of prion disease segregates with the degree of expansion. With up to four extra octarepeats, the average onset age is above 60 years, whereas five to nine extra octarepeats results in an average onset age between 30 and 40 years, a difference of almost three decades. In wild-type PrP, the octarepeat domain takes up copper (Cu2+) and is considered essential for in vivo function. Work from our lab demonstrates that the copper coordination mode depends on the precise ratio of Cu2+ to protein. At low Cu2+ levels, coordination involves histidine side chains from adjacent octarepeats, whereas at high levels each repeat takes up a single copper ion through interactions with the histidine side chain and neighboring backbone amides. Here we use both octarepeat constructs and recombinant PrP to examine how copper coordination modes are influenced by octarepeat expansion. We find that there is little change in affinity or coordination mode populations for octarepeat domains with up to seven segments (three inserts). However, domains with eight or nine total repeats (four or five inserts) become energetically arrested in the multi-histidine coordination mode, as dictated by higher copper uptake capacity and also by increased binding affinity. We next pooled all published cases of human prion disease resulting from octarepeat expansion and find remarkable agreement between the sudden length-dependent change in copper coordination and onset age. Together, these findings suggest that either loss of PrP copper-dependent function or loss of copper-mediated protection against PrP polymerization makes a significant contribution to early onset prion disease.

Sparse covariance estimation in heterogeneous samples

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era.

Latent Stick-Breaking Processes

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same cluster. We develop an efficient and straightforward Markov chain Monte Carlo (MCMC) algorithm for computation and discuss applications in financial econometrics and ecology. This article has supplementary material online.

Stochastic volatility models including open, close, high and low prices

Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility models that uses opening and closing prices along with the minimum and maximum prices within a trading period to infer the dynamics underlying the volatility process of asset prices and compare it with similar models presented previously in the literature. The paper also discusses sequential Monte Carlo algorithms to fit this class of models and illustrates its features using both a simulation study and real data.

Bayesian semiparametric estimation of covariate-dependent ROC curves

Receiver operating characteristic (ROC) curves are widely used to measure the discriminating power of medical tests and other classification procedures. In many practical applications, the performance of these procedures can depend on covariates such as age, naturally leading to a collection of curves associated with different covariate levels. This paper develops a Bayesian heteroscedastic semiparametric regression model and applies it to the estimation of covariate-dependent ROC curves. More specifically, our approach uses Gaussian process priors to model the conditional mean and conditional variance of the biomarker of interest for each of the populations under study. The model is illustrated through an application to the evaluation of prostate-specific antigen for the diagnosis of prostate cancer, which contrasts the performance of our model against alternative models.

Bayesian hierarchically weighted finite mixture models for samples of distributions

Finite mixtures of Gaussian distributions are known to provide an accurate approximation to any unknown density. Motivated by DNA repair studies in which data are collected for samples of cells from different individuals, we propose a class of hierarchically weighted finite mixture models. The modeling framework incorporates a collection of k Gaussian basis distributions, with the individual-specific response densities expressed as mixtures of these bases. To allow heterogeneity among individuals and predictor effects, we model the mixture weights, while treating the basis distributions as unknown but common to all distributions. This results in a flexible hierarchical model for samples of distributions. We consider analysis of variance-type structures and a parsimonious latent factor representation, which leads to simplified inferences on non-Gaussian covariance structures. Methods for posterior computation are developed, and the model is used to select genetic predictors of baseline DNA damage, susceptibility to induced damage, and rate of repair.

Modeling the dynamics of social networks using Bayesian hierarchical blockmodels

We introduce a new class of dynamic models for networks that extends stochastic blockmodels to settings where the interactions between a group of actors are observed at multiple points in time. Our goal is to identify structural changes in model features such as differential attachment, homophily by attributes, transitivity, and clustering as the network evolves. Our focus is on Bayesian inference, so the models are constructed hierarchically by combining different classes of Bayesian nonparametric priors. The methods are illustrated through a simulation study and two real data sets.