Related papers: Confidence Intervals for Stochastic Arithmetic
In this article, we consider a stochastic numerical simulator to assess the impact of some factors on a phenomenon. The simulator is seen as a black box with inputs and outputs. The quality of a simulation, hereafter referred to as…
Statistical machine learning often uses probabilistic algorithms, such as Markov Chain Monte Carlo (MCMC), to solve a wide range of problems. Probabilistic computations, often considered too slow on conventional processors, can be…
When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input distributions estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance…
Uncertainty quantification is not yet widely adapted in the design process of engineering components despite its importance for achieving sustainable and resource-efficient structures. This is mainly due to two reasons: 1) Tracing the…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…
Test instability in a floating-point program occurs when the control flow of the program diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by the presence of round-off errors that affect the evaluation of…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Static program analysis today takes an analytical approach which is quite suitable for a well-scoped system. Data- and control-flow is taken into account. Special cases such as pointers, procedures, and undefined behavior must be handled. A…
This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds.…
Simulation techniques are providing with each passing day a deeper insight into the structure and properties of materials. Two main obstacles appear for the cooperation of simulation and experiment: on the one hand, the frequent lack of a…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it's only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential…
Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…
This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
System identification is an important area of science, which aims to describe the characteristics of the system, representing them by mathematical models. Since many of these models can be seen as recursive functions, it is extremely…
In this work, we present a novel inner product design for stochastic computing. Stochastic computing is an emerging computing technique, that encodes a number in the probability of observing a one in a random bit stream. This leads to…
Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization…