Related papers: Asymptotic Properties of Approximate Bayesian Comp…

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of…

Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…

Bayesian inference provides a framework to combine various model components with shared parameters, allowing joint uncertainty estimation and the use of all available data sources. Unfortunately, misspecification of any part of the model…

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…

Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

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…

The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations…

We discuss an approach for deriving robust posterior distributions from $M$-estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use $M$-estimating functions to construct suitable summary statistics…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…