In many applications, a stochastic system is studied using a model implicitly defined via a simulator. We develop a simulation-based parameter inference method for implicitly defined models. Our method differs from traditional likelihood-based inference in that it uses a metamodel for the distribution of a log-likelihood estimator. The metamodel is built on a local asymptotic normality (LAN) property satisfied by the simulation-based log-likelihood estimator under certain conditions. A method for hypothesis test is developed under the metamodel. Our method can enable accurate parameter estimation and uncertainty quantification where other Monte Carlo methods for parameter inference become highly inefficient due to large Monte Carlo variance. We demonstrate our method using numerical examples including a mechanistic model for the population dynamics of infectious disease.

翻译：在许多应用中，随机系统通过隐式由仿真器定义的模型进行研究。我们针对隐式定义模型开发了一种基于仿真的参数推断方法。该方法与传统基于似然的推断不同，它利用元模型来刻画对数似然估计量的分布。该元模型建立在仿真对数似然估计量在特定条件下满足局部渐近正态性的性质之上。我们在元模型框架下发展了假设检验方法。该方法能够在其他由于蒙特卡洛方差过大而效率低下的参数推断方法中，实现精确的参数估计与不确定性量化。我们通过数值算例（包括传染病种群动力学的机制模型）验证了该方法。