  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.
