AUTHORS: Lu Shaokui, Pei Yongzhen, Li Changguo

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ABSTRACT: Parameter estimation is crucial for us to analyse the models, and such works of individuals-based models is still in the early stage of development. For the individuals-based models, there is no efficient methods to estimate the parameters due to the observed data with noise produced by inherent randomness of model. This paper, we utilize different methods that are well developed for parameter estimation of determined model which is constituted by ordinary differential equations(ODE) are also adapted to stochastic models. In this article, We use the population changes of aphids as a case study. We want to estimate the birth rate and the mortality of the aphids. An intuitive approach is least square method to estimate the parameters, and this application is very extensive. However, the problem of parameter identification is the most common issue of least square method in estimating parameters. In this article we show the latest progress in parameter estimation for individuals-based models of our study which bases on moment closure approximation technique. The combination of MCMC and likelihood function is a less used method in the estimation of stochastic model parameters. These two methods can overcome the problem of parameter identification in the least square.

KEYWORDS: Parameter estimation, Individuals-based Models, Moment closure, Least squares method, Likelihood function, MCMC

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