The main contribution of this paper is the characterization of reachability problem associated to stochastic hybrid systems in terms of imprecise probabilities. This provides the connection between reachability problem and Bayesian statistics. Using generalised Bayesian statistical inference, a new concept of conditional reach set probabilities is defined. Then possible algorithms to compute the reach set probabilities are derived

Bujorianu, L.M.

University of Twente Research Information

English

A Mathematical Theory of Evidence”.

A.: Mesures Domin´ ee par une

Bayes’s Theorem for Choquet Capacities.

Computing Posterior Upper Expectations.

Excessive Measures. Birkh¨ auser,

Extended Stochastic Hybrid Systems and their Reachability Problem. In

General Stochastic Hybrid Systems.

H.E.: Bayesian and non-Bayesian Evidential Updating.

Incremental Conditioning of Lower and Upper probabilities.

J.B.: A Representation of Partially Ordered Preferences.

Lower Probability Models for Uncertainty and nondeterministic Processes.

Markov Models and Optimization”.

Markov Processes and Potential Theory.

Markov Processes with Equal Capacities,

Minimax Tests and the Neyman-Pearson Lemma for Capacities.

Reachability Questions

Sensitivity in Bayesian Statistics the Prior and the Likelihood.

Statistical Decision Theory and Bayesian Analysis”.

Statistical Reasoning with Imprecise Probabilities”.

Stochastic Hybrid Control.

Stochastic Hybrid Models: An Overview with applications to Air Trafﬁc Management. ADHS, Analysis and Design of Hybrid System,

Subjective Probability and Expected Utility Without Additivity.

The Enterprise of Knowledge”.

The Foundations of Statistics.

The Measurement of Belief.

Theory of Capacities. Annales de l’Institut Fourier,

Upper and Lower Probabilities Induced by a Multivalued Mapping.

A statistical inference method for the stochastic reachability analysis.