Thời gian: 17h00, Thứ 4, ngày 9/12/2015
Địa điểm: Phòng 201, Nhà A5, Viện Toán học, 18 Hoàng Quốc Việt, Cầu Giấy, Hà Nội
Tóm tắt: Mathematical models defined by a system of non-linear differential equations are widely applied to describe dynamic processes in biology and other fields. For instance, the SIR model (Susceptiple- Infected-Recovered) and accompanying system of partial differential equations is one of the basic compartmental models in infectious disease epidemiology, which is widely used and well suited to model many viral infections in childhood. In the field of predictive microbiology, mathematical models defined by differential equations have been developed to predict the growth rate of a microorganism population under a set of environmental conditions.
Ramsay et al (2007) describe a method for estimating parameters in ordinary differential equations that is robust to model misspecification. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. As mentioned by Hooker et al (2011), an advantage of the generalised profiling method is that it provides readily accessible diagnostics for assessing model fit through visual inspection of different type of plots.
In this contribution generalised profiling is extended to account for shape restrictions such as monotonicity constraints, one-sided cross-validation is introduced as an objective way to choose the smoothing parameter, and  a bootstrap method is proposed for inferential purposes, more precisely, for constructing  confidence regions and for formally testing the null hypothesis that a particular parametric model (defined by differential equations) holds. The methodology is applied to estimate the age-dependent seroprevalence of Parvovirus B19 and to estimate growth models for Yersinia Enterocolitica, a species of gram-negative coccobacillus.