在僅能觀測到部分資料的情形下，ODE model的參數估計

Parameter Estimation for Partially Observed ODE and its Applications

彭瑋翔(Wei-Hsiang Peng)

指導教授 ： 陳賢修

國立臺灣師範大學/理學院/數學系/碩士(2013年)

摘要

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。

關鍵字

參數估計 ； 微分方程模型 ； 類Hindmarsh-Rose模型

並列摘要

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.

並列關鍵字

parameter estimation ； ordinary differential equations ； Hindmarsh-Rose Type model ； partially observed model

參考文獻

1. Brunel (2008). Parameter estimation of ODE's via nonparametric estimators

2. Gugushvili. consistent parameter estimation for systems of ODEs: Bypassing numerical integration via smoothing

4. Ramsay (2007). Parameter estimation for differential equations a generalized smoothing approach

3. Nadaraya E. A. (1964). "On Estimating Regression". Theory of Probability and its Applications 9 (1): 141–2.