Related papers: Randomness is inherently imprecise
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…
We revisit empirical Bayes discrimination detection, focusing on uncertainty arising from both partial identification and sampling variability. While prior work has mostly focused on partial identification, we find that some empirical…
Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…
For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…
Most of the methods that produce space weather forecasts are based on deterministic models. In order to generate a probabilistic forecast, a model needs to be run several times sampling the input parameter space, in order to generate an…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
In literature on imprecise probability little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision…
Conditions ensuring optimal parameter estimation in the presence of missing data are well established in inference, typically relying on the Missing-at-Random (MAR) assumption. In prediction, similar principles are often assumed to apply.…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
In a prediction tournament, contestants "forecast" by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE…
In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…