Related papers: Bayesian Prediction under Moment Conditioning

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…

Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Change-plane regression identifies subpopulations through an interpretable linear threshold rule, but likelihood-based inference for the hard-threshold boundary is nonregular: objectives are non-smooth, the boundary is weakly identified…

We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…

Structural estimation in economics often makes use of models formulated in terms of moment conditions. While these moment conditions are generally well-motivated, it is often unknown whether the moment restrictions hold exactly. We consider…

The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

Accurate uncertainty estimates are important in sequential model-based decision-making tasks such as Bayesian optimization. However, these estimates can be imperfect if the data violates assumptions made by the model (e.g., Gaussianity).…

Bayesian Neural Networks (BNNs) extend traditional neural networks to provide uncertainties associated with their outputs. On the forward pass through a BNN, predictions (and their uncertainties) are made either by Monte Carlo sampling…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

We introduce and develop moment propagation for approximate Bayesian inference. This method can be viewed as a variance correction for mean field variational Bayes which tends to underestimate posterior variances. Focusing on the case where…

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…