Evolution of the Dependence of Residual Lifetimes

We investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given

Bayesian dynamic financial networks with time-varying predictors

We propose a Bayesian nonparametric model including time-varying predictors in dynamic network inference. The model is applied to infer the dependence structure among financial markets during the global financial crisis, estimating effects of verbal and material cooperation efforts. We interestingly learn contagion effects, with increasing influence of verbal relations during the financial crisis and opposite results during the United States housing bubble

Nonparametric Bayes dynamic modeling of relational data

Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in 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 probability matrix space to the latent relational space, we obtain a flexible and computational tractable formulation. Employing P\`olya-Gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide some theoretical results on flexibility of the model, and illustrate performance via simulation experiments. We also consider an application to co-movements in world financial markets

Locally Adaptive Dynamic Networks

Our focus is on realistically modeling and forecasting dynamic networks of face-to-face contacts among individuals. Important aspects of such data that lead to problems with current methods include the tendency of the contacts to move between periods of slow and rapid changes, and the dynamic heterogeneity in the actors' connectivity behaviors. Motivated by this application, we develop a novel method for Locally Adaptive DYnamic (LADY) network inference. The proposed model relies on a dynamic latent space representation in which each actor's position evolves in time via stochastic differential equations. Using a state space representation for these stochastic processes and P\'olya-gamma data augmentation, we develop an efficient MCMC algorithm for posterior inference along with tractable procedures for online updating and forecasting of future networks. We evaluate performance in simulation studies, and consider an application to face-to-face contacts among individuals in a primary school

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

Locally adaptive factor processes for multivariate time series

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to mis-calibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a locally adaptive factor process for characterizing multivariate mean-covariance changes in continuous time, allowing locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions evolving in time through nested Gaussian processes and linearly related to the observed data with a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application

Nonparametric Bayes Modeling of Populations of Networks

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections 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 which 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