Daniele Durante

Nonparametric Bayes dynamic modelling of relational data

Symmetric binary matrices representing relations are collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being on inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the link probability matrix space to the latent relational space, we obtain a flexible and computationally tractable formulation. Employing Polya-gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide theoretical results on flexibility of the model, and illustrate its performance via simulation experiments. We also consider an application to co-movements in world financial markets.

Nonparametric Bayes Modeling of Populations of Networks

ABSTRACT Replicated network data are increasingly available in many research fields. For example, in connectomic applications, interconnections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model that reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance—compared to state-of-the-art models—in simulations and application to human brain networks. Supplementary materials for this article are available online.

Bayesian inference and testing of group differences in brain networks

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing of group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging a mixture of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel insights on the relationships between human brain networks and creativity.

Bayesian dynamic financial networks with time-varying predictors

We propose a targeted and robust modeling of dependence in multivariate time series via dynamic networks, with time-varying predictors included to improve interpretation and prediction. The model is applied to financial markets, estimating effects of verbal and material cooperations.

A note on the multiplicative gamma process

Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease implementation. This note addresses such aim.

Rejoinder: Nonparametric Bayes Modeling of Populations of Networks

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Bayesian network-response regression.

Motivation: There is increasing interest in learning how human brain networks vary as a function of a continuous trait, but flexible and efficient procedures to accomplish this goal are limited. We develop a Bayesian semiparametric model, which combines low‐rank factorizations and flexible Gaussian process priors to learn changes in the conditional expectation of a network‐valued random variable across the values of a continuous predictor, while including subject‐specific random effects. Results: The formulation leads to a general framework for inference on changes in brain network structures across human traits, facilitating borrowing of information and coherently characterizing uncertainty. We provide an efficient Gibbs sampler for posterior computation along with simple procedures for inference, prediction and goodness‐of‐fit assessments. The model is applied to learn how human brain networks vary across individuals with different intelligence scores. Results provide interesting insights on the association between intelligence and brain connectivity, while demonstrating good predictive performance. Availability and Implementation: Source code implemented in R and data are available at https://github.com/wangronglu/BNRR Contact: rl.wang@duke.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Bayesian semiparametric modelling of contraceptive behaviour in India via sequential logistic regressions

Family planning has been characterized by highly different strategic programmes in India, including method‐specific contraceptive targets, coercive sterilization and more recent target‐free approaches. These major changes in family planning policies over time have motivated considerable interest towards assessing the effectiveness of the different planning programmes. Current studies mainly focus on the factors driving the choice among specific subsets of contraceptives, such as a preference for alternative methods other than sterilization. Although this restricted focus produces key insights, it fails to provide a global overview of the different policies, and of the determinants underlying the choices from the entire range of contraceptive methods. Motivated by this consideration, we propose a Bayesian semiparametric model relying on a reparameterization of the multinomial probability mass function via a set of conditional Bernoulli choices. This binary decision tree is defined to be consistent with the current family planning policies in India, and coherent with a reasonable process characterizing the choice between increasingly nested subsets of contraceptive methods. The model allows a subset of covariates to enter the predictor via Bayesian penalized splines and exploits mixture models to represent uncertainty in the distribution of the state‐specific random effects flexibly. This combination of flexible and careful reparameterizations allows a broader and interpretable overview of the policies and contraceptive preferences in India.

Bayesian inference on group differences in multivariate categorical data

Multivariate categorical data are common in many fields. We are motivated by election polls studies assessing evidence of changes in voters opinions with their candidates preferences in the 2016 United States Presidential primaries or caucuses. Similar goals arise routinely in several applications, but current literature lacks a general methodology which combines flexibility, efficiency, and tractability in testing for group differences in multivariate categorical data at different---potentially complex---scales. We address this goal by leveraging a Bayesian representation which factorizes the joint probability mass function for the group variable and the multivariate categorical data as the product of the marginal probabilities for the groups, and the conditional probability mass function of the multivariate categorical data, given the group membership. To enhance flexibility, we define the conditional probability mass function of the multivariate categorical data via a group-dependent mixture of tensor factorizations, thus facilitating dimensionality reduction and borrowing of information, while providing tractable procedures for computation, and accurate tests assessing global and local group differences. We compare our methods with popular competitors, and discuss improved performance in simulations and in American election polls studies.

Convex mixture regression for quantitative risk assessment: 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.