11 research outputs found
Importance Sampling Simulations of Markovian Reliability Systems using Cross Entropy
This paper reports simulation experiments, applying the cross entropy method suchas the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failurebiasing schemes that have been proved to give estimators with bounded relativeerrors. The results from the experiments indicate a considerable improvement ofthe performance of the importance sampling estimators, where performance is mea-sured by the relative error of the estimate, by the relative error of the estimator,and by the gain of the importance sampling simulation to the normal simulation
Asymptotic optimality of the cross-entropy method for Markov chain problems
The correspondence between the cross-entropy method and the zero-variance
approximation to simulate a rare event problem in Markov chains is shown. This
leads to a sufficient condition that the cross-entropy estimator is
asymptotically optimal.Comment: 13 pager; 3 figure
Cross-entropy optimisation of importance sampling parameters for statistical model checking
Statistical model checking avoids the exponential growth of states associated
with probabilistic model checking by estimating properties from multiple
executions of a system and by giving results within confidence bounds. Rare
properties are often very important but pose a particular challenge for
simulation-based approaches, hence a key objective under these circumstances is
to reduce the number and length of simulations necessary to produce a given
level of confidence. Importance sampling is a well-established technique that
achieves this, however to maintain the advantages of statistical model checking
it is necessary to find good importance sampling distributions without
considering the entire state space.
Motivated by the above, we present a simple algorithm that uses the notion of
cross-entropy to find the optimal parameters for an importance sampling
distribution. In contrast to previous work, our algorithm uses a low
dimensional vector of parameters to define this distribution and thus avoids
the often intractable explicit representation of a transition matrix. We show
that our parametrisation leads to a unique optimum and can produce many orders
of magnitude improvement in simulation efficiency. We demonstrate the efficacy
of our methodology by applying it to models from reliability engineering and
biochemistry.Comment: 16 pages, 8 figures, LNCS styl
Improved Cross-Entropy Method for Estimation
The cross-entropy (CE) method is an adaptive importance sampling procedure that has been successfully applied to a diverse range of complicated simulation problems. However, recent research has shown that in some high-dimensional settings, the likelihood ratio degeneracy problem becomes severe and the importance sampling estimator obtained from the CE algorithm becomes unreliable. We consider a variation of the CE method whose performance does not deteriorate as the dimension of the problem increases. We then illustrate the algorithm via a high-dimensional estimation problem in risk management
Runtime Verification of Biological Systems
International audienceComplex computational systems are ubiquitous and their study increasingly important. Given the ease with which it is possible to construct large systems with heterogeneous technology, there is strong motivation to provide automated means to verify their safety, efficiency and reliability. In another context, biological systems are supreme examples of complex systems for which there are no design specifications. In both cases it is usually difficult to reason at the level of the description of the systems and much more convenient to investigate properties of their executions. To demonstrate runtime verification of complex systems we apply statistical model checking techniques to a model of robust biological oscillations taken from the literature. The model demonstrates some of the mechanisms used by biological systems to maintain reliable performance in the face of inherent stochasticity and is therefore instructive. To perform our investigation we use two recently developed SMC platforms: that incorporated in Uppaal and Plasma. Uppaalsmc offers a generic modeling language based on stochastic hybrid automata, while Plasma aims at domain specific support with the facility to accept biological models represented in chemical syntax
Rare Event Simulation for non-Markovian repairable Fault Trees
Dynamic Fault Trees (DFT) are widely adopted in industry to assess the
dependability of safety-critical equipment. Since many systems are too large to
be studied numerically, DFTs dependability is often analysed using Monte Carlo
simulation. A bottleneck here is that many simulation samples are required in
the case of rare events, e.g. in highly reliable systems where components fail
seldomly. Rare Event Simulation (RES) provides techniques to reduce the number
of samples in the case of rare events. We present a RES technique based on
importance splitting, to study failures in highly reliable DFTs. Whereas RES
usually requires meta-information from an expert, our method is fully
automatic: by cleverly exploiting the fault tree structure we extract the
so-called importance function. We handle DFTs with Markovian and non-Markovian
failure and repair distributions (for which no numerical methods exist) and
show the efficiency of our approach on several case studies
Importance Sampling Simulations of Markovian Reliability Systems using Cross Entropy
This paper reports simulation experiments, applying the cross entropy method suchas the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failurebiasing schemes that have been proved to give estimators with bounded relativeerrors. The results from the experiments indicate a considerable improvement ofthe performance of the importance sampling estimators, where performance is mea-sured by the relative error of the estimate, by the relative error of the estimator,and by the gain of the importance sampling simulation to the normal simulation.