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Title: Simulation-based inference for high dimensional implicit models and application to partially observed processes Authors:  Joonha Park - University of Kansas (United States) [presenting]
Abstract: In many applications, a probabilistic model for a given system is defined implicitly by a simulation algorithm. Such implicit models can be simulated at any parameter value, but often the probability density function cannot be evaluated. We consider the case where the system described by an implicit model is partially observed. Parameter estimation for such partially observed, implicit models can, in principle, be carried out by repeated Monte Carlo simulations at various parameter values and comparing the log measurement densities of the observed data. However, the average of log measurement densities has a downward Jensen bias, which increases with increasing model dimensions. Under certain asymptotic assumptions, we develop methods for constructing Monte Carlo confidence intervals for the log-likelihood of data and the maximum likelihood estimate given the data. Furthermore, for models that satisfy local asymptotic normality (LAN), we develop a method for constructing a confidence interval for the unknown parameter value. We show that our methods can enable likelihood-based inference for partially observed, high-dimensional, mechanistic models for stochastic processes using numerical experiments.