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Abstract Background A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. Results We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods. Conclusions This work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.

Abstract Background A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. Results We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods. Conclusions This work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.

In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)]. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA-the state-dependent doubly weighted SSA (sdwSSA)-that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In biochemical systems, the occurrence of a rare event can be accompanied by catastrophic consequences. Precise characterization of these events using Monte Carlo simulation methods is often intractable, as the number of realizations needed to witness even a single rare event can be very large. The weighted stochastic simulation algorithm (wSSA) [J. Chem. Phys. 129, 165101 (2008)] and its subsequent extension [J. Chem. Phys. 130, 174103 (2009)] alleviate this difficulty with importance sampling, which effectively biases the system toward the desired rare event. However, extensive computation coupled with substantial insight into a given system is required, as there is currently no automatic approach for choosing wSSA parameters. We present a novel modification of the wSSA-the doubly weighted SSA (dwSSA)-that makes possible a fully automated parameter selection method. Our approach uses the information-theoretic concept of cross entropy to identify parameter values yielding minimum variance rare event probability estimates. We apply the method to four examples: a pure birth process, a birth-death process, an enzymatic futile cycle, and a yeast polarization model. Our results demonstrate that the proposed method (1) enables probability estimation for a class of rare events that cannot be interrogated with the wSSA, and (2) for all examples tested, reduces the number of runs needed to achieve comparable accuracy by multiple orders of magnitude. For a particular rare event in the yeast polarization model, our method transforms a projected simulation time of 600 years to three hours. Furthermore, by incorporating information-theoretic principles, our approach provides a framework for the development of more sophisticated influencing schemes that should further improve estimation accuracy. [ABSTRACT FROM AUTHOR]

The weighted stochastic simulation algorithm (wSSA) was developed by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness. [ABSTRACT FROM AUTHOR]

The weighted stochastic simulation algorithm (wSSA) recently introduced by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] is an innovative variation on the stochastic simulation algorithm (SSA). It enables one to estimate, with much less computational effort than was previously thought possible using a Monte Carlo simulation procedure, the probability that a specified event will occur in a chemically reacting system within a specified time when that probability is very small. This paper presents some procedural extensions to the wSSA that enhance its effectiveness in practical applications. The paper also attempts to clarify some theoretical issues connected with the wSSA, including its connection to first passage time theory and its relation to the SSA. [ABSTRACT FROM AUTHOR]

Oh, S.M.; Roh, M.; Chang, P.-H.; Kim, K.O.; Oh, Y.; Kang, H.-S., and Moon, I.-J., 2023. Impact of data assimilation on KMA's global and regional ocean wave predictions. In: Lee, J.L.; Lee, H.; Min, B.I.; Chang, J.-I.; Cho, G.T.; Yoon, J.-S., and Lee, J. (eds.), Multidisciplinary Approaches to Coastal and Marine Management. Journal of Coastal Research, Special Issue No. 116, pp. 86-90. Charlotte (North Carolina), ISSN 0749-0208. The most efficient and effective way to improve the ocean wave prediction is to assimilate observational data collected in real time. Recently, most institutes are trying to improve the accuracy of ocean wave predictions by assimilating various observation data. In this study, significant wave heights observed from satellites and buoys were assimilated into global and regional ocean wave models of the Korea Meteorological Administration (KMA), and their performance was verified. The KMA global and regional wave data assimilation system uses 2-dimensional optimal interpolation based on WaveWatch-Ⅲ version 6.07 with spatial resolution of 1/4° and 1/30°, respectively. Numerical experiments for boreal summer and winter from June 2020 to February 2021 reveal that the use of data assimilation reduced the Root Mean Square Error (RMSE) by 15% and 44%, respectively, for the initial field of global and regional wave models. In particular, in the case of typhoon Bavi in 2020, when data assimilation was not used, there was a tendency to overestimate the significant wave height at the three ocean research stations, but the use of data assimilation reduced the error by up to105 cm. The assimilated initial fields improved ocean wave predictions by 48 and 12 hours in KMA's global and regional ocean wave models, respectively. [ABSTRACT FROM AUTHOR]