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Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed.
This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants.
A tuned...
The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.
Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate
clinical attack rates in children much higher than in adults. Non-medical interventions
such as school closings are constrained by their large socio-economic costs. Here we
develop a mathematical model to ascertain the roles of pre-symptomatic influenza
transmission as well as symptoms surveillance of children to assess the utility of school
closures. Our model analysis...
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