476,179 research outputs found
Gaussian process surrogates for failure detection: a Bayesian experimental design approach
An important task of uncertainty quantification is to identify {the
probability of} undesired events, in particular, system failures, caused by
various sources of uncertainties. In this work we consider the construction of
Gaussian {process} surrogates for failure detection and failure probability
estimation. In particular, we consider the situation that the underlying
computer models are extremely expensive, and in this setting, determining the
sampling points in the state space is of essential importance. We formulate the
problem as an optimal experimental design for Bayesian inferences of the limit
state (i.e., the failure boundary) and propose an efficient numerical scheme to
solve the resulting optimization problem. In particular, the proposed
limit-state inference method is capable of determining multiple sampling points
at a time, and thus it is well suited for problems where multiple computer
simulations can be performed in parallel. The accuracy and performance of the
proposed method is demonstrated by both academic and practical examples
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
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