Monte Carlo profile confidence intervals for dynamic systems

Edward Ionides, Carles Breto, Joonha Park, Alex Smith, Aaron A. King

Abstract:

Monte Carlo methods to evaluate and maximize the likelihood function enable
the construction of confidence intervals and hypothesis tests, facilitating scien-
tific investigation using models for which the likelihood function is intractable.
When Monte Carlo error can be made small, by sufficiently exhaustive compu-
tation, then the standard theory and practice of likelihood-based inference
applies. As datasets become larger, and models more complex, situations
arise where no reasonable amount of computation can render Monte Carlo
error negligible. We develop profile likelihood methodology to provide fre-
quentist inferences that take into account Monte Carlo uncertainty. We
investigate the role of this methodology in facilitating inference for computa-
tionally challenging dynamic latent variable models. We present examples
arising in the study of infectious disease transmission, demonstrating our
methodology for inference on nonlinear dynamic models using genetic
sequence data and panel time-series data. We also discuss applicability to non-
linear time-series and spatio-temporal data.