Related papers: Implementing Bayesian predictive procedures: The K…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…
Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…
We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…
Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…
The counterfactual distribution models the effect of the treatment in the untreated group. While most of the work focuses on the expected values of the treatment effect, one may be interested in the whole counterfactual distribution or…
In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…
This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance…
I begin by summarizing key ideas of the paper under discussion. Then I will talk about a graphical modeling perspective, posterior contraction rates and alternative methods of aggregation. Moreover, I will also discuss possible applications…
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents…
The prediction interval has been increasingly used in meta-analyses as a useful measure for assessing the magnitude of treatment effect and between-studies heterogeneity. In calculations of the prediction interval, although the…
A general challenge in statistics is prediction in the presence of multiple candidate models or learning algorithms. Model aggregation tries to combine all predictive distributions from individual models, which is more stable and flexible…
We describe a class of algorithms for evaluating posterior moments of certain Bayesian linear regression models with a normal likelihood and a normal prior on the regression coefficients. The proposed methods can be used for hierarchical…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…