Speaker
Description
Estimating confidence regions for parameters in stochastic epidemic models is challenging when the likelihood is intractable. In continuous-time Markov chain (CTMC) formulations of compartmental models such as SIR, the likelihood cannot be evaluated directly due to the intractability of the Kolmogorov forward equations. Existing approaches rely on simplifying assumptions, such as Gaussian approximations or ad hoc noise models, which can lead to inaccurate inference.
We develop a fully frequentist framework for constructing confidence regions without explicit likelihood evaluation. Our method uses empirical moments from CTMC simulations and Monte Carlo approximations of a Mahalanobis-type test statistic, producing confidence sets with nominal coverage. However, the computational burden of Monte Carlo simulation limits dense exploration of the parameter space. To address this, we introduce a neural network–based pipeline that learns the mapping from parameters to the mean and covariance of the CTMC and estimates key quantiles (0.68, 0.80, 0.90, 0.95) using coverage-based stopping criteria.
We apply our method to SIR and SEIR models and additionally test the models on the English boarding school influenza dataset. Results show that our approach yields narrow, well-calibrated confidence regions when data are modeled as stochastic realizations of CTMC dynamics rather than observations with additive noise.
