運用貝氏定理下的模型選擇

Abstract

本篇文章主要是在討探在多母體下的模型選擇。在這裡我們使用無母數的方法來做分析。我們想要找到一個判別準則有效率的辨別一群資料中任意一個資料點屬於哪一個母體。在這裡用的是貝氏的區分法則，建立在貝氏定理的基礎上。而且我們建立兩種估計的方法來決定兩種判別法則，也就是density estimation和logistic regression。現在的重點是找到一個方法能有效的增加這估計函數的準確度，而提升判別法則的精準度。在本文採用local likelihood density estimation和local logistic regression來估計未知函數，所以有兩種判別準則。藉由的帶寬選擇，以最小的AIC當做選取的標準能充份的對未知模型做選擇。在本文的模擬中顯示，只要樣本點數足夠多，此方法的確能有效改進選擇的成功率。

This paper is concerned with the problem of model selection among multiple populations. Here we use a nonparametric approach. We would like to find a decision rule to effectively identify which population each data comes from. We create a decision rule, based on Bayesian theorem, called Bayesian discriminant rule. Furthermore, we construct two estimated methods to decide the decision rule – density estimation and logistic regression. An unknown density function has to be estimated in the decision rule. Now it is vital to find an accurate way to estimate this density function or logistic probability to arise the classification rate. By using bandwidth selection for local likelihood density estimation or local logistic regression that minimizes AIC criterion does improve the results of model selection. A small simulation shows that for a large enough sample size, the method performs well.