Tham khảo tài liệu 'progress in biomass and bioenergy production part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Methods for Structural and Parametric Synthesis of Bio-Economic Models 439 unknown parameters 0 we set fY yk fY yk 0 k 0 1 . n and formulate the identification task as minimization of the functional . - In fY0 yo 0 -J N yk 0 u k 1 J subjected to the constraints and . Panel data sample set Let us consider a very typical situation for the bio-economic modeling when the data on the population dynamics X Xt t e t0 t1 are obtained by different observers say there are M observers. In this case the parameters of the stochastic differential equation can be estimated on the basis of the panel Ykk where j 1 2 . M stands for the observer k 0 1 . n refers to the discretization times t0 T0 T1 . Tn t1 and Y0 E Y0j J . It is not difficult to conclude that the hypothesized distribution in the given parametrized family of probability distributions F. . 0 represents the most probable distribution from the given class of distributions having observed Yj j 1 2 . M k 0 1 . n . We suppose that for the stochastic process X Xt te t0 t1 there exists the equivalent stochastic process X Xt t e t0 t which sample paths are continuous on the interval t0 t1 so that both processes have equivalent distributions . FX x Fx x . The empirical estimate of FX x can be found on the basis of Yj as 1 M F yj MJ w Yj where j 1 2 . M k 0 1 . n . For the same estimate of F. x the generated sample paths are required 1 _N ỹk 0 NJ y-JY where N is the number of simulated sample paths of the equivalent stochastic process given by with the set of the parameters 0 . Now the identification task can be solved by means of the testing the hypothesis about the equivalence of the distributions and using for example Kolmogorov-Smirnov s goodness-of-fit test DM Tk 0 sup I FYk ỹk -N ỹk 0 y yeR k 1 for all Tk e t0 t1 . 440 Progress in Biomass and Bioenergy Production The statistic has asymptotic null distribution KS D t 0 .lim p . NMDnm t 0 sD I 1 k N M-Upl
