Application of variance reduction techniques for tau-leaping systems to particle filters

Maginnis, Peter A.; West, Matthew; Dullerud, Geir E.

doi:10.1109/cdc.2012.6425806

Cited by 3 publications

(7 citation statements)

References 13 publications

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“…The results of this paper pertain to previously published [11] anticorrelated stochastic simulation algorithms for vari ance reduction in discrete time tau-leaping Markov pro cesses. This work focuses primarily on providing rigorous theoretical results to explain numerical behavior observed in the previous paper.…”

Section: Introductionmentioning

confidence: 70%

“…The three examples of this technique that are of interest to this work are antithetic, stratified and hybrid sampling. They are studied in detail in [9] and employed in a particle filtering context in [11]. Briefly, these techniques can be sUlmnarized as follows.…”

Section: A Anticorrelated Stochastic Sampling Algorithmmentioning

confidence: 99%

“…We also prove an algebraic test to determine the potential benefits of the algorithm a priori to stochastic simulation in this linear case. While these algorithms, as shown in [11], are widely applicable to prob lems of estimation (including particle filters for nonlinear systems), here we focus on variance reduction of stochastic simulation.…”

Section: Introductionmentioning

confidence: 99%

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Anticorrelated discrete-time stochastic simulation

Maginnis

West

Dullerud

2013

52nd IEEE Conference on Decision and Control

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Ahstract-We provide the first known rigorous theoretical analysis of previously published anticorrelated variance re duction techniques for tau-leaping systems. These algorithms provide a way to reduce the expected MSE of mean estimators by introducing local negative correlation between Monte Carlo sample paths. We prove a recursive equation governing the evolution of these covariances in both the nonlinear and linear cases. Further, we prove sufficient algebraic conditions for variance reduction in the linear rates case that require no stochastic simulation. Finally, we present an example system to illustrate both the application of these tests and to demonstrate their effectiveness.

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Section: Introductionmentioning

confidence: 70%

Section: A Anticorrelated Stochastic Sampling Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anticorrelated discrete-time stochastic simulation

Maginnis

West

Dullerud

2013

52nd IEEE Conference on Decision and Control

Self Cite

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“…The correlation between simulations is achieved by transforming the stream of the random numbers used for simulations. The theoretical analysis of such technique for the stochastic simulation of biochemical processes with constant rates has been recently developed [39][40][41]. Even though the proposed strategy [41] is able to apply the anticorrelated variance technique to SSA based on the inverse transformation, it is not efficient.…”

Section: Introductionmentioning

confidence: 99%

Efficient anticorrelated variance reduction for stochastic simulation of biochemical reactions

Thanh

2019

IET Systems Biology

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We investigate the computational challenge of improving the accuracy of the stochastic simulation estimation by inducing negative correlation through the anticorrelated variance reduction technique. A direct application of the technique to the stochastic simulation algorithm (SSA), employing the inverse transformation, is not efficient for simulating large networks because its computational cost is similar to the sum of independent simulation runs. We propose in this study a new algorithm that employs the propensity bounds of reactions, introduced recently in their rejection-based SSA, to correlate and synchronise the trajectories during the simulation. The selection of reaction firings by our approach is exact due to the rejection-based mechanism. In addition, by applying the anticorrelated variance technique to select reaction firings, our approach can induce substantial correlation between realisations, hence reducing the variance of the estimator. The computational advantage of our rejection-based approach in comparison with the traditional inverse transformation is that it only needs to maintain a single data structure storing propensity bounds of reactions, which is updated infrequently, hence achieving better performance.

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“…A common problem is the reduction of variance of Monte Carlo estimates of system features. In previous work [8], [7], we have defined and proved several anticorrelated variance reduction techniques for the simulation and estimation of Markov jump processes using a discrete-time tau leaping approximation. In this work, we extend those efforts to an exact, continuous-time domain.…”

Section: Introductionmentioning

confidence: 99%

Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation

Maginnis

West

Dullerud

2014

53rd IEEE Conference on Decision and Control

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Abstract-We provide an exact, continuous time extension to previous work in anticorrelated stochastic process simulation that was performed in an approximate, discrete time setting. These methods reduce the variance of continuous time Monte Carlo for Markov jump process systems. We rigorously construct antithetic Poisson processes and analytically prove the negative correlation between pairs. We then show how these anticorrelated Poisson processes can be used to drive Markov jump processes via a random time change representation. Finally, we provide a sufficient condition for variance reduction in the jump process context as well as demonstrate a simple example.

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Application of variance reduction techniques for tau-leaping systems to particle filters

Cited by 3 publications

References 13 publications

Anticorrelated discrete-time stochastic simulation

Anticorrelated discrete-time stochastic simulation

Efficient anticorrelated variance reduction for stochastic simulation of biochemical reactions

Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation

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