AUTHORS: Lu Shaokui, Pei Yongzhen, Li Changguo
Download as PDF
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, MCMCREFERENCES:
 J. H. Matis, T. R. Kiffe, T. I. Matis, D. E. Stevenson, Stochastic modeling of aphid population growth with nonlinear, power-law dynamics,Mathematical Biosciences. 208, 2007, pp. 469–494.
 Johnson, M. L. and Faunt, L. M, Parameter estimation by least-squares methods Methods in Enzymology, 210, 1992.
 Mckinley, Trevelyan and Cook, Alex R and Deardon, Robert, International Journal of Biostatistics, 5, 2009, pp. 24–24.
 Daigle, Bernie J and Min, K Roh and Petzold, Linda R and Niemi, Jarad, Accelerated maximum likelihood parameter estimation for stochastic biochemical systems, Bmc Bioinformatics. 13, 2012, pp. 1–68.
 Hespanha, Jo and Xe, Moment closure for biochemical networks International Symposium on Communications, Control and Signal Processing 2010, pp. 142–147.
 Milner, Peter and Gillespie, Colin S and Wilkinson, Darren J, Moment closure based parameter inference of stochastic kinetic models, FStatistics and Computing. 23, 2013, pp. 287–295.
 Diamond, G. A, Off Bayes: effect of verification bias on posterior probabilities calculated using Bayes’ theorem, Medical Decision Making An International Journal of the Society for Medical Decision Making. 12, 1992, pp. 1–22.
 Arminger, Gerhard and Muthn, Bengt O, A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm, Psychometrika. 63, 1998, pp. 271–300.
 Prajneshu, A nonlinear statistical model for aphid population growth, Journal of the Indian Society of Agricultural Statistic. 51, 1998.
 Matis, J. H. and Kiffe, T. R. and Matis, T. I. and Stevenson, D. E, Application of population growth models based on cumulative size to pecan aphids, Journal of Agricultural Biological and Environmental Statistics. 11, 2006, pp. 425–449.
 Koblents, Eugenia and Młguez, Joaqułn, A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models, Statistics and Computing. 25, 2015, pp. 407–425.
 Golightly, A and Gillespie, C. S, Simulation of stochastic kinetic models, Methods Mol Biol. 1021, 2013, pp. 169–187.
 Daniel T. Gillespie, Exact Stochastic Simulation of Coupled Chemical Reactions, The Journal of chemical physics. 126, 2007.
 Mauro Gasparini, Markov Chain Monte Carlo in Practice, Technometrics. 2, 1999, pp. 9236– 9240.
 Liu, Jun S, Metropolized Independent Sampling with Comparisons to Rejection Sampling and Importance Sampling, Statistics and Computing. 6, 1996, pp. 113–119.
 Geyer, Charles J, Practical Markov Chain Monte Carlo Statistical Science. 7, 1992, pp. 473–483.
 Green, P, Reversible jump MCMC computation and Bayesian model determination Biometrika. 82, 1995, pp. 104–111.
 Kummer, U and Krajnc, B and Pahle, J and Green, A. K. and Dixon, C. J. and Marhl, M, Transition from stochastic to deterministic behavior in calcium oscillations Wiley. 2013.
 Wang, Sichun and Jackson, Brad R. and Inkol, Robert, Hybrid RSS/AOA emitter location estimation based on least squares and maximum likelihood criteria Communications. 2013, pp. 24–29.