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We propose a novel approach to estimate the Cox model with temporal covariates. Our new approach treats the temporal covariates as arising from a longitudinal process which is modeled jointly with the event time. Different from the…
We introduce a novel Information Criterion (IC), termed Learning under Singularity (LS), designed to enhance the functionality of the Widely Applicable Bayes Information Criterion (WBIC) and the Singular Bayesian Information Criterion…
Given a random sample from a multivariate population, estimating the number of large eigenvalues of the population covariance matrix is an important problem in Statistics with wide applications in many areas. In the context of Principal…
We develop a framework to quantify systemic risk measures in a class of Wide-Area-Control (WAC) laws in power networks in the presence of noisy and time-delayed sensory data. A closed-form calculation of the risk of phase incoherence in…
Causal discovery from time-series data aims to capture both intra-slice (contemporaneous) and inter-slice (time-lagged) causality between variables within the temporal chain, which is crucial for various scientific disciplines. Compared to…
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…
Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…
Estimating the covariance structure of multivariate time series is a fundamental problem with a wide-range of real-world applications -- from financial modeling to fMRI analysis. Despite significant recent advances, current state-of-the-art…
In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of…
Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
A natural method for approximating out-of-sample predictive evaluation is leave-one-out cross-validation (LOOCV) --- we alternately hold out each case from a full data set and then train a Bayesian model using Markov chain Monte Carlo…
Bayesian filtering aims at tracking sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…
Multivariate time series data comprises various channels of variables. The multivariate forecasting models need to capture the relationship between the channels to accurately predict future values. However, recently, there has been an…
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…
The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional…