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30
The alive particle filter
, 2013
"... In the following article we develop a particle filter for approximating FeynmanKac models with indicator potentials. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rareevent problems. Such models require the use of a ..."
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Cited by 8 (5 self)
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In the following article we develop a particle filter for approximating FeynmanKac models with indicator potentials. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rareevent problems. Such models require the use of advanced particle filter or Markov chain Monte Carlo (MCMC) algorithms e.g. Jasra et al. (2012), to perform estimation. One of the drawbacks of existing particle filters, is that they may ‘collapse’, in that the algorithm may terminate early, due to the indicator potentials. In this article, using a special case of the locally adaptive particle filter in Lee et al. (2013), which is closely related to Le Gland & Oudjane (2004), we use an algorithm which can deal with this latter problem, whilst introducing a random cost pertime step. This algorithm is investigated from a theoretical perspective and several results are given which help to validate the algorithms and to provide guidelines for their implementation. In addition, we show how this algorithm can be used within MCMC, using particle MCMC (Andrieu et al. 2010). Numerical examples are presented for ABC approximations of HMMs.
Importance splitting for statistical model checking rare properties
 Computer Aided Verification, volume 8044 of LNCS
, 2013
"... Abstract Statistical model checking avoids the intractable growth of states associated with probabilistic model checking by estimating the probability of a property from simulations. Rare properties are often important, but pose a challenge for simulationbased approaches: the relative error of the ..."
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Abstract Statistical model checking avoids the intractable growth of states associated with probabilistic model checking by estimating the probability of a property from simulations. Rare properties are often important, but pose a challenge for simulationbased approaches: the relative error of the estimate is unbounded. A key objective for statistical model checking rare events is thus to reduce the variance of the estimator. Importance splitting achieves this by estimating a sequence of conditional probabilities, whose product is the required result. To apply this idea to model checking it is necessary to define a score function based on logical properties, and a set of levels that delimit the conditional probabilities. In this paper we motivate the use of importance splitting for statistical model checking and describe the necessary and desirable properties of score functions and levels. We illustrate how a score function may be derived from a property and give two importance splitting algorithms: one that uses fixed levels and one that discovers optimal levels adaptively.
Bayesian Subset Simulation: a Krigingbased subset simulation algorithm for the estimation of small probabilities of failure
 IN PROCEEDINGS OF PSAM 11 AND ESREL 2012
, 2012
"... The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method to solve it. Subset simulation has been shown to provid ..."
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Cited by 4 (2 self)
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The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method to solve it. Subset simulation has been shown to provide significant savings in the number of simulations to achieve a given accuracy of estimation, with respect to many other Monte Carlo approaches. The number of simulations remains still quite high however, and this method can be impractical for applications where an expensivetoevaluate computer model is involved. We propose a new algorithm, called Bayesian Subset Simulation, that takes the best from the Subset Simulation algorithm and from sequential Bayesian methods based on kriging (also known as Gaussian process modeling). The performance of this new algorithm is illustrated using a test case from the literature. We are able to report promising results. In addition, we provide a numerical study of the statistical properties of the estimator.
SelfAvoiding Random Dynamics on Integer Complex Systems
"... This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binaryvalued systems, which allows for large moves in the state space. This is achieved by constructing selfavoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC s ..."
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Cited by 4 (4 self)
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This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binaryvalued systems, which allows for large moves in the state space. This is achieved by constructing selfavoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the algorithm SARDONICS, an acronym for SelfAvoiding Random Dynamics on Integer Complex Systems. The algorithm has several free parameters, but we show that Bayesian optimization can be used to automatically tune them. SARDONICS performs remarkably well in a broad number of sampling tasks: toroidal ferromagnetic and frustrated Ising models, 3D Ising models, restricted Boltzmann machines and chimera graphs arising in the design of quantum computers.
MCMC algorithms for subset simulation
 Manuscript, Engineering Risk Analysis Group, TU München
, 2013
"... Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCM ..."
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Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in the standard normal space. Two variants of the algorithm are proposed: A basic variant, which is simpler than existing algorithms with equal accuracy and efficiency, and a more efficient variant with adaptive scaling. It is demonstrated that the proposed algorithm improves the accuracy of Subset Simulation, without the need for additional model evaluations.
Mathematical analysis of adaptive multilevel splitting algorithms
 In preparation
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