模型假設對分析變數間因果關係的影響

Abstract

在日常生活或生物基因方面，變數之間總會有影響與被影響的情形發生；在這篇文章中，最主要的目標是希望將變數間有因果關係的資料，經由統計的方法，判斷出因果圖形結構之方向性，及探討模型假設對其結果之影響。 在這個領域之中，有很多科學家及統計學家提出了一些方法如：線性模型(D’haeseleer et al, 1999)、非線性模型(Weaver et al, 1999)、布爾數學邏輯網路模型 (Kauffman 1993, Somogyi and Sniegoski, 1996)等；隨後，Murphy and Mian (1998) 和 Friedman(1999)等人提出貝氏網路模型（Bayesian Network）。在這篇文章中，試著結合貝氏的概念並探討使用概似函數的方法來分析變數間的因果關係，並希望能判斷出變數間圖形之方向性。

In daily life or biological gene, there always exists variables which inference other variables or are influenced by some others. In this paper, our main goal is to analyze the variables which have causality by using statistical methods, to determine the directionality among causality graphs, and to find out the impact of model assumption on those methods.

In this field, lots of scientists and statisticians have proposed several methods, for example, linear models (D’haeseleer et al., 1999), nonlinear models (Weaver et al., 1999), and Boolean networks (Kauffman 1993, Somogyi and Sniegoski, 1996), etc. However, there should be some assumptions in all of these models. Murphy and Mian (1998) and Friedman et al. (1999) have suggested that use Bayesian network models of gene expression networks to get some improvements. In this paper, we discuss the concept of Bayesian’s method and using likelihood functions to analyze the causality between two and three variables. We hope to determine the direction between variables.