Monte Carlo profile confidence intervals for dynamic systems.

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, 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 frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally 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 nonlinear time-series and spatio-temporal data.

Infectious Disease Dynamics Inferred from Genetic Data via Sequential Monte Carlo.

Genetic sequences from pathogens can provide information about infectious disease dynamics that may supplement or replace information from other epidemiological observations. Most currently available methods first estimate phylogenetic trees from sequence data, then estimate a transmission model conditional on these phylogenies. Outside limited classes of models, existing methods are unable to enforce logical consistency between the model of transmission and that underlying the phylogenetic reconstruction. Such conflicts in assumptions can lead to bias in the resulting inferences. Here, we develop a general, statistically efficient, plug-and-play method to jointly estimate both disease transmission and phylogeny using genetic data and, if desired, other epidemiological observations. This method explicitly connects the model of transmission and the model of phylogeny so as to avoid the aforementioned inconsistency. We demonstrate the feasibility of our approach through simulation and apply it to estimate stage-specific infectiousness in a subepidemic of human immunodeficiency virus in Detroit, Michigan. In a supplement, we prove that our approach is a valid sequential Monte Carlo algorithm. While we focus on how these methods may be applied to population-level models of infectious disease, their scope is more general. These methods may be applied in other biological systems where one seeks to infer population dynamics from genetic sequences, and they may also find application for evolutionary models with phenotypic rather than genotypic data.