title: Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.
abstract: Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories.
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, Surrey Campus, 13450, 102nd Ave, Surrey BC, Canada V3T 0A3. Electronic address: dac5@sfu.ca.
authors.forename: D A
authors.initials: DA
authors.lastname: Campbell
authors.forename: O
authors.initials: O
authors.lastname: Chkrebtii
mesh_terms: D004921:Erythropoietin / Q000502:physiology; D053612:Janus Kinases / Q000502:physiology; D007700:Kinetics; D016013:Likelihood Functions; D008954:Models, Biological; D050791:STAT Transcription Factors / Q000502:physiology; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D050791:STAT Transcription Factors; D004921:Erythropoietin; D053612:Janus Kinases
keywords: Delay differential equations; Functional data analysis; JAK-STAT; Model based smoothing; Nonlinear regression