We consider the problem of computing the satisfaction probability of a formula for stochastic models with parametric uncertainty. We show that this satisfaction probability is a smooth function of the model parameters. This enables us to devise a novel Bayesian statistical algorithm which performs model checking simultaneously for all values of the model parameters from observations of truth values of the formula over individual runs of the model at isolated parameter values. This is achieved by exploiting the smoothness of the satisfaction function: by modelling explicitly correlations through a prior distribution over a space of smooth functions (a Gaussian Process), we can condition on observations at individual parameter values to construct an analytical approximation of the function itself. Extensive experiments on non-trivial case studies show that the approach is accurate and several orders of magnitude faster than naive parameter exploration with standard statistical model checking methods.
Abstract. Pattern formation is an important spatio-temporal emergent behaviour in biology. Mathematical models of pattern formation in the stochastic setting are extremely challenging to execute and analyse. Here we propose a formal analysis of the emergent behaviour of stochastic reaction diffusion systems in terms of Signal Spatio-Temporal Logic, a recently proposed logic for reasoning on spatiotemporal systems. We present a formal analysis of the spatio-temporal dynamics of the Bicoid morphogen in Drosophila melanogaster, one of the most important proteins in the formation of the horizontal segmentation in the development of the fly embryo. We use a recently proposed framework for statistical model checking of stochastic systems with uncertainty on parameters to characterise the parametric dependence and robustness of the French Flag pattern, highlighting non-trivial correlations between the parameter values and the emergence of the patterning.
Abstract. Novel applications of formal modelling such as systems biology have highlighted the need to extend formal analysis techniques to domains with pervasive parametric uncertainty. Consequently, machine learning methods for parameter synthesis and uncertainty quantification are playing an increasingly significant role in quantitative formal modelling. In this paper, we introduce a toolbox for parameter synthesis and model checking in uncertain systems based on Gaussian Process emulation and optimisation. The toolbox implements in a user friendly way the techniques described in a series of recent papers at QEST and other primary venues, and it interfaces easily with widely used modelling languages such as PRISM and Bio-PEPA. We describe in detail the architecture and use of the software, demonstrating its application on a case study.
Abstract. Stiffness in chemical reaction systems is a frequently encountered computational problem, arising when different reactions in the system take place at different time-scales. Computational savings can be obtained under time-scale separation. Assuming that the system can be partitioned into slow-and fast-equilibrating subsystems, it is then possible to efficiently simulate the slow subsystem only, provided that the corresponding kinetic laws have been modified so that they reflect their dependency on the fast system. We show that the rate expectation with respect to the fast subsystem's steady-state is a continuous function of the state of the slow system. We exploit this result to construct an analytic representation of the modified rate functions via statistical modelling, which can be used to simulate the slow system in isolation. The computational savings of our approach are demonstrated in a number of non-trivial examples of stiff systems.
Approximate Markov chain aggregation involves the construction of a smaller Markov chain that approximates the behaviour of a given chain. We discuss two different approaches to obtain a nearly optimal partition of the state-space, based on different notions of approximate state equivalence. Both approximate aggregation methods require an explicit representation of the transition matrix, a fact that renders them inefficient for large models. The main objective of this work is to investigate the possibility of compositionally applying such an approximate aggregation technique. We make use of the Kronecker representation of PEPA models, in order to aggregate the state-space of components rather than of the entire model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.