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Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…
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…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the…
Bayesian inference is optimal when the statistical model is well-specified, while outside this setting Bayesian inference can catastrophically fail; accordingly a wealth of post-Bayesian methodologies have been proposed. Predictively…
We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…
The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of…
Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a…
In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…
Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural…
Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of…
Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…
This paper considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, $n$, and the number of time periods, $T$, are large. We first clarify the probability…
We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…
We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…