Related papers: Posterior Consistency in Parametric Models via a T…

The consistency of posterior distributions in density estimation is at the core of Bayesian statistical theory. Classical work established sufficient conditions, typically combining KL support with complexity bounds on sieves of high prior…

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 prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…

We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…

Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

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…

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

We study the identifiability of parameters and falsifiability of predictions under the process of model expansion in a Bayesian setting. Identifiability is represented by the closeness of the posterior to the prior distribution and…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…

Under model misspecification, the MLE generally converges to the pseudo-true parameter, the parameter corresponding to the distribution within the model that is closest to the distribution from which the data are sampled. In many problems,…

Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of…