Models implicitly defined through a random simulator of a process have become widely used in scientific and industrial applications in recent years. However, simulation-based inference methods for such implicit models, like approximate Bayesian computation (ABC), often scale poorly as data size increases. We develop a scalable inference method for implicitly defined models using a metamodel for the Monte Carlo log-likelihood estimator derived from simulations. This metamodel characterizes both statistical and simulation-based randomness in the distribution of the log-likelihood estimator across different parameter values. Our metamodel-based method quantifies uncertainty in parameter estimation in a principled manner, leveraging the local asymptotic normality of the mean function of the log-likelihood estimator. We apply this method to construct accurate confidence intervals for parameters of partially observed Markov process models where the Monte Carlo log-likelihood estimator is obtained using the bootstrap particle filter. We numerically demonstrate that our method enables accurate and highly scalable parameter inference across several examples, including a mechanistic compartment model for infectious diseases.

翻译：近年来，通过随机过程模拟器隐式定义的模型在科学与工业应用中得到了广泛使用。然而，针对此类隐式模型的仿真推断方法（如近似贝叶斯计算）常因数据量增加而面临可扩展性不足的问题。本文提出一种基于元模型的蒙特卡洛对数似然估计器的可扩展推断方法，该估计器通过仿真推导得出。该元模型刻画了对数似然估计器在不同参数值分布中存在的统计随机性与仿真随机性。基于元模型的方法利用对数似然估计器均值函数的局部渐近正态性，以理论完备的方式量化参数估计的不确定性。我们将此方法应用于构建部分可观测马尔可夫过程模型的参数置信区间，其中蒙特卡洛对数似然估计器通过自举粒子滤波器获得。数值实验表明，本方法在包括传染病机制性仓室模型在内的多个案例中，均能实现精确且高度可扩展的参数推断。