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Sparsity of the solution of a linear regression model is a common requirement, and many prior distributions have been designed for this purpose. A combination of the sparsity requirement with smoothness of the solution is also common in…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

In this article, a model is proposed using Bayesian techniques to account for the high correlation between many observed set of contingency tables. In many real life data this high correlation is encountered. Simulation studies are also…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

Within the Hamiltonian formulation of Lattice gauge theories, prepotentials, belonging to the fundamental representation of the gauge group and defined locally at each site of the lattice, enables us to construct local loop operators and…

Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling…

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…

A Bayes factor is proposed for testing whether the effect of a key predictor variable on the dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) when one is interested in…

We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to…

Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental observations are necessary to calibrate certain simulator…

I present all the details in calculating the posterior distribution of the conjugate Normal-Gamma prior in Bayesian Linear Models (BLM), including correlated observations, prediction, model selection and comments on efficient numeric…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…

Extrapolating treatment effects from related studies is a promising strategy for designing and analyzing clinical trials in situations where achieving an adequate sample size is challenging. Bayesian methods are well-suited for this…

We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian…

Transformed Generalized Autoregressive Moving Average (TGARMA) models were recently proposed to deal with non-additivity, non-normality and heteroscedasticity in real time series data. In this paper, a Bayesian approach is proposed for…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the…

Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…