Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic framework for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty. Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternative approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

中文翻译：

---

使用 Multifidelity Sequential Tempered Markov Chain Monte Carlo 的随机反应网络的贝叶斯推理

随机反应网络模型通常用于解释和预测单细胞中基因调控的动态。这些模型通常涉及几个参数，例如化学反应的动力学速率，这些参数不能直接测量，必须从实验数据中推断出来。贝叶斯推理提供了一个严格的概率框架，用于通过找到能够捕捉其不确定性的后验参数分布来识别这些参数。用于解决推理问题的传统计算方法，例如基于经典 Metropolis-Hastings 算法的马尔可夫链蒙特卡罗方法，涉及对似然函数的大量串行评估，而这又需要昂贵的化学主方程 (CME) 正向解。我们提出了一种基于顺序回火马尔可夫链蒙特卡罗 (ST-MCMC) 采样器的多保真扩展的替代方法。该算法建立在 Sequential Monte Carlo 基础上，通过将贝叶斯推理问题分解为一系列有效解决的子问题来解决贝叶斯推理问题，这些子问题逐渐增加模型保真度和观察数据的影响。我们重新制定了有限状态投影 (FSP) 算法，这是一种众所周知的用于求解 CME 的方法，以生成要在此多保真方案中使用的代理主方程的层次结构。为了确定适当的保真度，我们引入了一种新的信息论标准，旨在从层次结构中的每个模型中提取有关最终​​贝叶斯后验的最多信息，而不会引起显着的偏差。