Related papers: Misspecification in infinite-dimensional Bayesian …

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

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…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

We prove rates of convergence and robustness to prior misspecification within a Generalised Variational Inference (GVI) framework with bounded divergences. This addresses a significant open challenge for GVI and Federated GVI that employ a…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

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 study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the…

We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…

In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…

We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact…

In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…

Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…

Virtually any model we use in machine learning to make predictions does not perfectly represent reality. So, most of the learning happens under model misspecification. In this work, we present a novel analysis of the generalization…

We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…

Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…

We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform…