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Bayesian online learning provides a coherent framework for sequential inference. However, its theoretical understanding remains limited, particularly in the one-pass setting. Existing theoretical guarantees typically require the mini-batch…

Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…

This paper presents three hyperspectral mixture models jointly with Bayesian algorithms for supervised hyperspectral unmixing. Based on the residual component analysis model, the proposed general formulation assumes the linear model to be…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…

The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…

The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior…

A method for implicit variable selection in mixture of experts frameworks is proposed. We introduce a prior structure where information is taken from a set of independent covariates. Robust class membership predictors are identified using a…

Probabilistic model-based diagnosis computes the posterior probabilities of failure of components from the prior probabilities of component failure and observations of system behavior. One problem with this method is that such priors are…

We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…

A sparse Dirichlet prior is proposed for estimating the abundance vector of hyperspectral images with a nonlinear mixing model. This sparse prior is led to an unmixing procedure in a semi-supervised scenario in which exact materials are…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Comparing composite models for multi-component observational data is a prevalent scientific challenge. When fitting composite models, there exists the potential for systematics from a poor fit of one model component to be absorbed by…

We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…

We propose a structure of a semiparametric two-component mixture model when one component is parametric and the other is defined through L-moments conditions. Estimation of a two-component mixture model with an unknown component is very…