Related papers: Asymptotic properties of Bayesian inference in lin…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…

Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

Models of weak-scale supersymmetry offer viable dark matter (DM) candidates. Their parameter spaces are however rather large and complex, such that pinning down the actual parameter values from experimental data can depend strongly on the…

The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong…

We study spike-and-slab priors for generalized linear models with possible grouped sparsity. The main result is an oracle Bernstein--von Mises theorem for the fractional posterior under supportwise likelihood assumptions. The proof develops…

Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…

In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…

Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…

Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…