Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis.

This report summarizes methods to incorporate information (or lack of information) about inter-variable dependence into risk assessments that use Dempster-Shafer theory or probability bounds analysis to address epistemic and aleatory uncertainty. The report reviews techniques for simulating correlated variates for a given correlation measure and dependence model, computation of bounds on distribution functions under a specified dependence model, formulation of parametric and empirical dependence models, and bounding approaches that can be used when information about the intervariable dependence is incomplete. The report also reviews several of the most pervasive and dangerous myths among risk analysts about dependence in probabilistic models

Discrete-Event Simulation in Healthcare Settings: A Review

We review and define the current state of the art as relating to discrete event simulation in healthcare-related systems. A review of published literature over the past five years (2017–2021) was conducted, building upon previously published work. PubMed and EBSCOhost were searched for journal articles on discrete event simulation in healthcare resulting in identification of 933 unique articles. Of these about half were excluded at the title/abstract level and 154 at the full text level, leaving 311 papers to analyze. These were categorized, then analyzed by category and collectively to identify publication volume over time, disease focus, activity levels by country, software systems used, and sizes of healthcare unit under study. A total of 1196 articles were initially identified. This list was narrowed down to 311 for systematic review. Following the schema from prior systematic reviews, the articles fell into four broad categories: health care systems operations (HCSO), disease progression modeling (DPM), screening modeling (SM), and health behavior modeling (HBM). We found that discrete event simulation in healthcare has continued to increase year-over-year, as well as expand into diverse areas of the healthcare system. In addition, this study adds extra bibliometric dimensions to gain more insight into the details and nuances of how and where simulation is being used in healthcare

of Interval Probability Problems

Abstract In many real-life situations, we only have partial information about probabilities. This information is usually described by bounds on moments, on probabilities of certain events, etc.- i.e., by characteristics c(p) which are linear in terms of the unknown probabilities pj. If we know interval bounds on some such characteristics ai < = ci(p) < = ai, and we are interested in a characteristic c(p), then we can find the bounds on c(p) by solving a linear programming problem. In some situations, we also have additional conditions on the probability distribution- e.g., we may know that the two variables x1 and x2 are independent, or that the joint distribution of x1 and x2 is unimodal. We show that adding each of these conditions makes the corresponding interval probability problem NP-hard. 1 Introduction Interval probability problems can be often reduced to linear program-ming (LP). In many real-life situations, in addition to the intervals [ xi, xi]of possible values of the unknowns x1,..., xn, we also have partial informationabout the probabilities of different values within these intervals

Qualitative and quantitative simulation: bridging the gap*

Artificia

Combining Interval, Probabilistic, and Fuzzy Uncertainty: Foundations, Algorithms, Challenges – An Overview

Summary. Since the 1960s, many algorithms have been designed to deal with interval uncertainty. In the last decade, there has been a lot of progress in extending these algorithms to the case when we have a combination of interval, probabilistic, and fuzzy uncertainty. We provide an overview of related algorithms, results, and remaining open problems. 1 Main Problem Why indirect measurements? In many real-life situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. Examples of such quantities are the distance to a star and the amount of oil in a given well. Since we cannot measure y directly, a natural idea is to measure y indirectly. Specifically, we find some easier-to-measure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn); this relation may be a simple functional transformation, or complex algorithm (e.g., for the amount of oil, numerical solution to an inverse problem). Then, to estimate y, we first measure the values of the quantities x1,..., xn, an