A differential equation model of a dynamical system is a nonlinear parameterized model that is created to match realistic scenarios and occasionally it might be associated with some data, obtained from the system or through simulation. Once there is reasonable level of confidence in the correctness of the model, the task that remains is to estimate the parameters of the model. Due to the structure of parameter estimation problems in dynamical models, statistics and machine learning techniques are an ideal choice for determining the parameters. During the course of the summer I will be implementing some statistical algorithms, including Stochastic Approximation Expectation Maximization(SAEM) and Maximum A Posteriori Estimation (MAP), for parameter estimation of a dynamic model. I will also work on extending support for parameter estimation in Stochastic Differential Equations (SDEs) by adding first differences distribution to generalized Log-Likelihood. These would be quite important additions to the suite of methods in JuliaDiffEq and would be of great use to scientific community involved in systems biology, HIV-AIDS study, and drug dosage estimation.

Organization

Student

Vaibhav Dixit

Mentors

  • Vijay Ivaturi
  • Mike Innes
  • Christopher Rackauckas
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2018