Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are modelled using a continuous-time stochastic process, and, depending on the application area of interest, this will typically take the form of a Markov jump process or an It\^o diffusion process. Widespread use of these models is typically precluded by their computational complexity. In particular, performing exact fully Bayesian inference in either modelling framework is challenging due to the intractability of the observed data likelihood, necessitating the use of computationally intensive techniques such as particle Markov chain Monte Carlo (particle MCMC). We propose to increase the computational and statistical efficiency of this approach by leveraging the tractability of an inexpensive surrogate derived directly from either the jump or diffusion process. The surrogate is used in three ways: in the design of a gradient-based parameter proposal, to construct an appropriate bridge construct and in the first stage of a delayed-acceptance step. We find that the resulting approach offers substantial gains in efficiency over a standard particle MCMC implementation.
翻译:在流行病学、人口生态学和系统生物学等领域,物种数量采用连续时间随机过程,并视感兴趣的应用领域而定,通常采用Markov跳跃过程或It ⁇ o扩散过程的形式。这些模型通常因其计算复杂性而无法广泛使用。特别是,由于观测到的数据可能性的可忽略性,在任何建模框架中精确地全面进行巴耶斯式推断具有挑战性,因此需要使用Markov MonteCarlo粒子链(MMC)等计算密集技术。我们提议,通过利用直接从跳跃或扩散过程获得的廉价代孕的可移动性,提高这一方法的计算和统计效率。在设计基于梯度的参数提案时,以建造适当的桥梁,并在延迟接受步骤的第一阶段,以三种方式使用代孕门。我们发现,由此形成的方法在标准粒子MC的实施上取得了显著的效率。