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Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
We propose a new fiducial Markov Chain Monte Carlo (MCMC) method for fitting parametric Gaussian models. We utilize the Cayley transform to decompose the parametric covariance matrix, which in turn allows us to formulate a general data…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for…
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…
We review theory and methodology of the class of simultaneous graphical dynamic linear models (SGDLMs) that provide flexibility, parsimony and scalability of multivariate time series analysis. Discussion includes core theoretical aspects…
Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work,…
Inference for doubly intractable distributions is challenging because the intractable normalizing functions of these models include parameters of interest. Previous auxiliary variable MCMC algorithms are infeasible for multi-dimensional…
Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…
Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
In this article we consider Bayesian inference for partially observed Andersson-Madigan-Perlman (AMP) Gaussian chain graph (CG) models. Such models are of particular interest in applications such as biological networks and financial time…
Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…