基於貝氏序列分割的機率密度函數估計

Abstract

貝氏序列分割是一個資料取向的機率密度函數估計的新方法。利用貝氏的方式在資料空間上造出有效的分割，並且在這個分割上建立長條圖。相較於傳統的長條圖，在貝氏序列分割下所造出來的長條圖可以節省很多不必要的切割，並且在高維度達到準確地估計。然而由長條圖所建立的機率密度函數都會是局部常數的不平滑函數; 因此這篇論文探討了基於貝氏序列分割下可行的平滑方法，試著達到更好的機率密度函數估計。

Bayesian Sequential Partitioning (BSP) is a data-driven method on density estimation which partitions the sample space by the Bayesian approach and then constructs the histogram (Lu, Jiang and Wong, 2013). It can reduce unnecessary cuts in the construction of histogram and perform accurate estimation in high dimension. However, the estimated density using BSP is not smooth since it provides the density estimation by a histogram. Therefore, this thesis discusses possible smoothing methods based on BSP to estimate smooth densities.