Abstract
This chapter provides a statistical framework for the estimation of reach set probabilities. For applying Bayesian inference rules in the context of stochastic reachability analysis, the first step is to express reach set probabilities as imprecise probabilities. The main idea is to use the connection between stochastic reachability probabilities and Choquet capacities. The latter concept is widely used in decision theory and robust Bayesian inference. Since under standard assumptions, a stochastic hybrid system evolution defines a specific Markov process, reach set probability as a function of target set gives rise to a nonlinear measure, which is known under the name of Choquet capacity associated to the underlying Markov process. This connection is essential for applying Bayesian statistics for the estimation of reach set probabilities. Notice that we are working with a specialisation of the Bayesian statistics for nonlinear probability measures (imprecise probabilities). Then the Bayesian algorithms have some peculiar characteristics. This is an open research area, and the ideas described in this chapter are closely connected with the so-called statistical model checking, which represents a new research vista in computer science.
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Bujorianu, L.M. (2012). Statistical Methods to Stochastic Reachability. In: Stochastic Reachability Analysis of Hybrid Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2795-6_8
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DOI: https://doi.org/10.1007/978-1-4471-2795-6_8
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