多維度貝氏分割密度函數估計之回顧

Abstract

本論文的重點在於密度函數的估計，我們運用基於順序重要性抽樣的貝氏順序分割方法去估計1維度和2維度的密度函數並且和內核方法作比較。首先考慮使用座標分割定義的樣本空間中各個區域上的分段常數函數，並且讓這些函數服從某個先驗分佈，再運用閉合形式推導出各個區域相對應的邊際後驗分佈，之後用這些後驗分佈判斷分幾個區域，再基於順序重要性抽樣的方法去估計密度函數，跟傳統的內核方法作比較，此篇論文所用的貝氏順序分割方法能夠更準確的估計密度函數，最後以模擬和實際數據來驗證這觀點。

The purpose of this paper is on the estimation of the density function. We review the Bayesian sequential segmentation method based on sequential importance sampling to estimate the density function of one dimension and two dimension and compare it with kernel method. We first consider using the constant function on each region in the sample space defined by the coordinate segmentation, and let these functions obey a prior distribution, and find the posterior distribution. And then compared with the traditional kernel method. The Bayesian sequential segmentation method used in this paper can estimate the density function more accurately.