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Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…

We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…

This study introduces the Misclassification Likelihood Matrix (MLM) as a novel tool for quantifying the reliability of neural network predictions under distribution shifts. The MLM is obtained by leveraging softmax outputs and clustering…

Measurement of uncertainty of predictions from machine learning methods is important across scientific domains and applications. We present, to our knowledge, the first such technique that quantifies the uncertainty of predictions from a…

In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. To…

Multivariate methods that relate outcomes to risk factors have been adopted clinically to individualize treatment. This has promoted the belief that individuals have a true or unique risk. The logic of assigning an individual a single risk…

Active consumer participation is seen as an integral part of the emerging smart grid. Examples include demand-side management programs, incorporation of consumer-owned energy storage or renewable energy units, and active energy trading.…

Effective decision making requires understanding the uncertainty inherent in a prediction. In regression, this uncertainty can be estimated by a variety of methods; however, many of these methods are laborious to tune, generate…

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

Decisions in organizations are about evaluating alternatives and choosing the one that would best serve organizational goals. To the extent that the evaluation of alternatives could be formulated as a predictive task with appropriate…

Projection theorems of divergences enable us to find reverse projection of a divergence on a specific statistical model as a forward projection of the divergence on a different but rather "simpler" statistical model, which, in turn, results…

Variational inequalities are modelling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle…

Network economics is the study of a rich class of equilibrium problems that occur in the real world, from traffic management to supply chains and two-sided online marketplaces. In this paper we explore causal inference in network economics,…

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project…

This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…

While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to the same degree. Uncertainty methods are designed to provide…

Network models provide an efficient way to represent many real life problems mathematically. In the last few decades, the field of network optimization has witnessed an upsurge of interest among researchers and practitioners. The network…

Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…

We propose a new approach for solving a class of discrete decision making problems under uncertainty with positive cost. This issue concerns multiple and diverse fields such as engineering, economics, artificial intelligence, cognitive…

In order for reinforcement learning techniques to be useful in real-world decision making processes, they must be able to produce robust performance from limited data. Deep policy optimization methods have achieved impressive results on…