Probabilistic Model Checking for Continuous-Time Markov Chains via Sequential Bayesian Inference

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while statistical approaches require a large number of samples to estimate the desired properties with high confidence. Here, we show how model checking of time-bounded path properties can be recast exactly as a Bayesian inference problem. In this novel formulation the problem can be efficiently approximated using techniques from machine learning. Our approach is inspired by a recent result in statistical physics which derived closed form differential equations for the first-passage time distribution of stochastic processes. We show on a number of non-trivial case studies that our method achieves both high accuracy and significant computational gains compared to statistical model checking

Adaptive process and measurement noise identification for recursive Bayesian estimation

The optimality of recursive Bayesian estimators which have been extensively studied and implemented, for problems of state and parameter estimation, as well as for state estimation of systems with unknown inputs, is closely related to the quality of prior information about the process and measurement noise terms. These are typically treated as tuning parameters and therefore adjusted in an ad hoc and rather heuristic manner. Such an approach might be adequate for systems under stable environmental and operational conditions, but is proven insufficient for systems operating in a dynamic environment, where adaptive schemes are required. In this work, a new leave-one-out (LOO) metric is proposed for innovation-based adaptation of noise covariance matrices with the aim of robustly quantifying the actual model errors and properly describing the measurement-related uncertainties.ISSN:2191-5644ISSN:2191-565