Scalable simulation-based inference for implicitly defined models using a metamodel for Monte Carlo log-likelihood estimator

Joonha Park

Abstract:

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.