Verified Computation with Probabilities

  title={Verified Computation with Probabilities},
  author={Scott Ferson and Jack Siegrist},
Because machine calculations are prone to errors that can sometimes accumulate disastrously, computer scientists use special strategies called verified computation to ensure output is reliable. Such strategies are needed for computing with probability distributions. In probabilistic calculations, analysts have routinely assumed (i) probabilities and probability distributions are precisely specified, (ii) most or all variables are independent or otherwise have well-known dependence, and (iii… 
3 Citations
Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty
An in depth discussion of a recently introduced method for the inverse quantification of spatial interval uncertainty is provided and its performance is illustrated using a case studies taken from literature.
A Survey of Tasks and Visualizations in Multiverse Analysis Reports
Analysing data from experiments is a complex, multi‐step process, often with multiple defensible choices available at each step. While analysts often report a single analysis without documenting how
Sensitivity Analysis of a HIFiRE-6 Design Variant Using Minimum-Resource Statistical Designs
An uncertainty-based simulation work flow is used to automate the prediction of steadystate aerodynamic loads for a design variant of the HIFiRE-6 hypersonic flight research vehicle and it is suggested that for the fixed vehicle being analyzed, variations in axial and normal force coefficients are driven by perturbations in angle of attack and Mach number.


Numerical Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Pascal-Xsc Programs
This book presents an extensive set of sophisticated tools to solve numerical problems with a verification of the results using the features of the scientific computer language PASCAL-XSC to offer a general discussion on arithmetic and computational reliability, analytical mathematics and verification techniques, algorithms, and (most importantly) actual implementations in the form of working computer routines.
Probability boxes as info-gap models
  • S. Ferson, W. T. Tucker
  • Mathematics, Computer Science
    NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society
  • 2008
Ben-Haim's info-gap decision theory is a non-probabilistic decision theory that can address poorly characterized and even unbounded uncertainty and provides a ready calculus for the calculations needed for an info- gap analysis involving probabilistic uncertainty.
Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals
This paper describes a new approach to bounding the results of arithmetic operations on random variables when the dependency relationship between the variables is unspecified, where bounds enclose the space in which the result's distribution function can be.
Finite Element Structural Analysis using Imprecise Probablilities Based on P-Box Representation
Imprecise probability identifies a number of various mathematical frameworks for making decisions when precise probabilities (or PDF) are not known. Imprecise probabilities are normally associated
Uncertainty Arithmetic on Excel Spreadsheets: Add-in for Intervals, Probability Distributions and Probability Boxes
An add-in for Microsoft Excel is described that supports arithmetic on uncertain numbers, which include intervals, probability distributions, and p-boxes and enables native calculations in Excel with these objects and ordinary scalar (real) numbers.
Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds
Applications of interval computations
This paper presents a review of techniques in the Verified Solution of Constrained Global Optimization Problems for Accurate, Self-Validating Arithmetic, and Stimulating Hardware and Software Support for Interval Arithmetic.
Representation and problem solving with Distribution Envelope Determination (DEnv)
Updating Sets of Probabilities
This work shows, by considering an axiomatic account of conditioning given by van Fraassen, that the single-measure and sets-of-measures cases are very different, and shows that vanFraassen's axiomatization for the former case is nowhere near sufficient for updating sets of measures.
The effect of neglecting correlations when propagating uncertainty and estimating the population distribution of risk.
This work makes use of well-known error propagation formulas to develop expressions intended to aid the analyst in situations wherein normally and lognormally distributed variables are linearly correlated.