Related papers: A general framework for probabilistic model uncert…

The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…

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…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…

Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…

We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

Unquantified sources of uncertainty in observational causal analyses can break the integrity of the results. One would never want another analyst to repeat a calculation with the same dataset, using a seemingly identical procedure, only to…

We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

How do we know how much we know? Quantifying uncertainty associated with our modelling work is the only way we can answer how much we know about any phenomenon. With quantitative science now highly influential in the public sphere and the…

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

Predictive variability due to data ambiguities has typically been addressed via construction of dedicated models with built-in probabilistic capabilities that are trained to predict uncertainty estimates as variables of interest. These…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…