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Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…

In many practical and numerical inverse problems, the exact data log-likelihood is not fully accessible, motivating the use of surrogate models. We study heteroscedastic nonparametric nonlinear regression problems with Gaussian errors and…

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…

We derive conditions for posterior consistency when the responses are independent but not identically distributed ($i.n.i.d$) and the model is "misspecified" to be a family of densities parametrized by a possibly infinite dimensional…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

When mapping subnational health and demographic indicators, direct weighted estimators of small area means based on household survey data can be unreliable when data are limited. If survey microdata are available, unit level models can…

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…

A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…

In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

A staple of Bayesian model comparison and hypothesis testing, Bayes factors are often used to quantify the relative predictive performance of two rival hypotheses. The computation of Bayes factors can be challenging, however, and this has…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain…

Linear Mixed Model (LMM) is a common statistical approach to model the relation between exposure and outcome while capturing individual variability through random effects. However, this model assumes the homogeneity of the error term's…