在僅能觀測到部分資料的情形下，ODE model的參數估計

Abstract

在物理、化學、生物的領域上，我們常常會用微分方程模型去描述自然的現象。而對於這樣一個微分方程模型，我們可能僅能觀測到裡面的其中某幾個參數。在這樣的情形底下，我們該如何去做微分方程模型的參數估計？這就是我們要討論的議題。在考慮到電腦計算的速度以及參數估計的精確度，本文以Hindmarsh-Rose Type model做為例子，提供了一套參數估計的方法。In physics, chemistry and biology, many researcher try to describe natural phenomena by ordinary differential equations (ODE) due to the fact that a lot of elegant theorem can be found in ODE and its nonlinear properties. With the observed information and some prior knowledge for a potential model, parameter estimation of an ODE model often requires a lot of computation works, such as a numerical integration of the ODE system and minimization of the log-likelihood function. In this paper, we consider a partially observed ODE model: 2D-HR type model. With the partially information, we present a simple way (iterative estimation process) without too mach computation to estimate the parameters in this model.