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Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…

Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…

Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…

Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution…

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation…

The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First,…

We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence…