
An evaluation of estimation techniques for probabilistic reachability
We evaluate numericallyprecise Monte Carlo (MC), QuasiMonte Carlo (QMC...
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A Scrambled Method of Moments
QuasiMonte Carlo (qMC) methods are a powerful alternative to classical ...
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An improvement of Koksma's inequality and convergence rates for the quasiMonte Carlo method
When applying the quasiMonte Carlo (QMC) method of numerical integratio...
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Density estimation by Randomized QuasiMonte Carlo
We consider the problem of estimating the density of a random variable X...
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Adaptive sparse grids and quasiMonte Carlo for option pricing under the rough Bergomi model
The rough Bergomi (rBergomi) model, introduced recently in (Bayer, Friz,...
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Geometrically Convergent Simulation of the Extrema of Lévy Processes
We develop a novel Monte Carlo algorithm for the simulation from the joi...
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Statistical approach to detection of signals by Monte Carlo singular spectrum analysis: Multiple testing
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Full version: An evaluation of estimation techniques for probabilistic reachability
We evaluate numericallyprecise Monte Carlo (MC), QuasiMonte Carlo (QMC) and Randomised QuasiMonte Carlo (RQMC) methods for computing probabilistic reachability in hybrid systems with random parameters. Computing reachability probability amounts to computing (multidimensional) integrals. In particular, we pay attention to QMC methods due to their theoretical benefits in convergence speed with respect to the MC method. The KoksmaHlawka inequality is a standard result that bounds the approximation of an integral by QMC techniques. However, it is not useful in practice because it depends on the variation of the integrand function, which is in general difficult to compute. The question arises whether it is possible to apply statistical or empirical methods for estimating the approximation error. In this paper we compare a number of interval estimation techniques based on the Central Limit Theorem (CLT), and we also introduce a new approach based on the CLT for computing confidence intervals for probability near the borders of the [0,1] interval. Based on our analysis, we provide justification for the use of the developed approach and suggest usage guidelines for probability estimation techniques.
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