Control Variates for Stochastic Simulation of Chemical Reaction Networks

Abstract

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires the generation of a large number of simulation runs, which is computationally expensive. To reduce the number of necessary runs, we propose a variance reduction technique based on control variates. We exploit constraints on the statistical moments of the stochastic process to reduce the estimators' variances. We develop an algorithm that selects appropriate control variates in an on-line fashion and demonstrate the efficiency of our approach on several case studies.

Analysis of Markov Jump Processes under Terminal Constraints

“…Most methods for the estimation of rare event probabilities rely on importance sampling [26,14]. For other queries, alternative variance reduction techniques such as control variates are available [5]. Apart from sampling-based approaches, dynamic finite-state projections have been employed by Mikeev et al [34], but are lacking automated truncation schemes.…”

“…We call each γ(•, t) a bridging distribution. From the Kolmogorov equations (5) and (7) we can obtain both the forward probabilities π(•, t) and the backward probabilities β(•, t) for t < T . We can easily extend this procedure to deal with hitting times constrained by a finite time-horizon by making the goal state x g absorbing.…”

“…This is due to the assumption of a uniform distribution inside the macro-states. Using this Q-matrix, we can compute the forward and backward solution using the respective Kolmogorov equations (5) and (7).…”

“…A finite state-space truncation covering the same area as the initial lumping approximation would contain 25,600 states. 5 The standard approach would be to build up the entire state-space for such a model [27]. Even using a conservative truncation threshold δ = 1e-5, our method yields an accurate estimate using only about a fifth (5450) of this accumulated over all intermediate lumped approximations.…”

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

“…The dynamics of these processes is therefore well described by stochastic Markov processes in continuous time with discrete state space [15,22,42]. While few-component or linear-kinetics systems [16] allow for exact analysis, in more complex system one often uses approximative methods [12], such as moment closure [4], linear-noise approximation [3,9], hybrid formulations [25,26,33], and multi-scale techniques [38,39].…”