Polya 樹過程

Abstract

Polya 樹過程為一隨機測量之先驗分配，其中包含了Dirichlet 過程，亦即 Dirichlet 過程為Polya 樹過程的一個特例。此外，Polya 樹過程跟Dirichlet 過程一樣，都具有共軛分配的特質。但Polya 樹過程有兩點特徵與Dirichlet 過程不同，其一，Polya 樹過程具有大量參數共同決定分配，作為分配廣大的支撐；其二， Polya 樹過程具有近似連續分配的性質。

Polya tree process is a large class of prior distributions, which Dirichlet process is included as a special case of Polya trees process. Like Dirichlet prior, the Polya tree prior also able to form a conjugate class for the posterior distributions. However, Polya tree process is different from Dirichlet process in two aspects: First, the Polya tree process is determined by a large collection of parameters and thus provide means to incorporate a wide range of beliefs. Second, some Polya trees assign probability 1 to the set of continuous distributions by (Kraft, 1964).