1,721,113 research outputs found
Nonparametric Bayes dynamic modelling of relational data
No full textSymmetric 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 Pólya-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
Bayesian inference and testing of group differences in brain networks
No full textNetwork 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
Convex mixture regression for quantitative risk assessment
Full text linkThere 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
Bayesian dynamic financial networks with time-varying predictors
No full textWe 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
Locally adaptive dynamic networks
No full textOur 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 Pólya-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
Bayesian cumulative shrinkage for infinite factorizations
No full textThe dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data
EXTENDED STOCHASTIC BLOCK MODELS WITH APPLICATION TO CRIMINAL NETWORKS
No full textReliably learning group structures among nodes in network data is challenging in several applications. We are particularly motivated by studying covert networks that encode relationships among criminals. These data are subject to measurement errors, and exhibit a complex combination of an unknown number of core-periphery, assortative and disassortative structures that may unveil key architectures of the criminal organization. The coexistence of these noisy block patterns limits the reliability of routinely-used community detection algorithms, and requires extensions of model-based solutions to realistically characterize the node partition process, incorporate information from node attributes, and provide improved strategies for estimation and uncertainty quantification. To cover these gaps, we develop a new class of extended stochastic block models (esbm) that infer groups of nodes having common connectivity patterns via Gibbs-type priors on the partition process. This choice encompasses many realistic priors for criminal networks, covering solutions with fixed, random and infinite number of possible groups, and facilitates the inclusion of node attributes in a principled manner. Among the new alternatives in our class, we focus on the Gnedin process as a realistic prior that allows the number of groups to be finite, random and subject to a reinforcement process coherent with criminal networks. A collapsed Gibbs sampler is proposed for the whole esbm class, and refined strategies for estimation, prediction, uncertainty quantification and model selection are outlined. The esbm performance is illustrated in realistic simulations and in an application to an Italian mafia network, where we unveil key complex block structures, mostly hidden from state-of-the-art alternatives
Improving Prediction from Dirichlet Process Mixtures via Enrichment
Full text linkFlexible covariate-dependent density estimation can be achieved by modelling the joint density of the response and covariates as a Dirichlet process mixture. An appealing aspect of this approach is that computations are relatively easy. In this paper, we examine the predictive performance of these models with an increasing number of covariates. Even for a moderate number of covariates, we find that the likelihood for x tends to dominate the posterior of the latent random partition, degrading the predictive performance of the model. To overcome this, we suggest using a different nonparametric prior, namely an enriched Dirichlet process. Our proposal maintains a simple allocation rule, so that computations remain relatively simple. Advantages are shown through both predictive equations and examples, including an application to diagnosis Alzheimer's disease
Locally Adaptive Factor Processes for Multivariate Time Series
No full textIn 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 di
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erential 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
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