Data_Sheet_1_MCMC Techniques for Parameter Estimation of ODE Based Models in Systems Biology.ZIP

Ordinary differential equation systems (ODEs) are frequently used for dynamical system modeling in many science fields such as economics, physics, engineering, and systems biology. A special challenge in systems biology is that ODE systems typically contain kinetic rate parameters, which are unknown and have to be estimated from data. However, non-linearity of ODE systems together with noise in the data raise severe identifiability issues. Hence, Markov Chain Monte Carlo (MCMC) approaches have been frequently used to estimate posterior distributions of rate parameters. However, designing a good MCMC sampler for high dimensional and multi-modal parameter distributions remains a challenging task. Here we performed a systematic comparison of different MCMC techniques for this purpose using five public domain models. The comparison included Metropolis-Hastings, parallel tempering MCMC, adaptive MCMC, and parallel adaptive MCMC. In conclusion, we found specifically parallel adaptive MCMC to produce superior parameter estimates while benefitting from inclusion of our suggested informative Bayesian priors for rate parameters and noise variance.

常微分方程组（Ordinary differential equation systems, ODEs）被广泛应用于经济学、物理学、工程学以及系统生物学等诸多科学领域的动力学系统建模。系统生物学领域面临的一项特殊挑战在于，常微分方程组通常包含动力学速率参数，这类参数未知且需从实验数据中估算得到。然而，常微分方程组的非线性特性与数据中存在的噪声会引发严重的可辨识性问题。因此，马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）方法常被用于估算速率参数的后验分布。但针对高维且多峰的参数分布设计优质的MCMC采样器，仍是一项颇具难度的工作。本研究基于五个公有领域模型，针对上述需求对多种MCMC技术开展了系统性对比实验，对比涵盖了梅特罗波利斯－黑斯廷斯（Metropolis-Hastings）算法、并行回火MCMC、自适应MCMC以及并行自适应MCMC。最终实验结果表明，结合本文提出的针对速率参数与噪声方差的信息性贝叶斯先验，并行自适应MCMC能够生成更优质的参数估算结果。