Monte Carlo profile confidence intervals for dynamic systems. Issue 132 (31st July 2017)

• Record Type: Journal Article
• Authors: Ionides, E. L.; Breto, C.; Park, J.; Smith, R. A.; King, A. A.
• Is Part Of: Journal of the Royal Society interface. Volume 14:Issue 132(2017)
• Publication Date: 2017-07-31
• Subjects: likelihood-based inference -- sequential Monte Carlo -- panel data -- time series -- spatio-temporal data -- phylodynamic inference; Physical sciences -- Research -- Periodicals; Life sciences -- Research -- Periodicals; Interdisciplinary research -- Periodicals; 570.5
• DOI: 10.1098/rsif.2017.0126
• Languages: English
• ISSNs: 1742-5689

Abstract

Abstract : 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.