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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Multivariate Pólya distribution ： ウィキペディア英語版 Dirichlet-multinomial distribution In probability and statistics, the Dirichlet-multinomial distribution is a probability distribution for a multivariate discrete random variable. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector $\backslash boldsymbol$, and a set of discrete samples is drawn from the categorical distribution with probability vector p. The compounding corresponds to a Polya urn scheme. In document classification, for example, the distribution is used to represent the distributions of word counts for different document types. ==Probability mass function== Conceptually, we are doing ''N'' independent draws from a categorical distribution with ''K'' categories. Let us represent the independent draws as random categorical variables $z\_n$ for $n\; =\; 1\; \backslash dots\; N$. Let us denote the number of times a particular category $k$ has been seen (for $k\; =\; 1\; \backslash dots\; K$) among all the categorical variables as $n\_k$. Note that $\backslash sum\_k\; n\_k\; =\; N$. Then, we have two separate views onto this problem: # A set of $N$ categorical variables $z\_1,\backslash dots,z\_N$. # A single vector-valued variable $\backslash mathbf=(n\_1,\backslash dots,n\_K)$, distributed according to a multinomial distribution. The former case is a set of random variables specifying each ''individual'' outcome, while the latter is a variable specifying the ''number'' of outcomes of each of the ''K'' categories. The distinction is important, as the two cases have correspondingly different probability distributions. The parameter of the categorical distribution is $\backslash mathbf\; =\; (p\_1,p\_2,\backslash dots,p\_K),$ where $p\_k$ is the probability to draw value $k$; $\backslash mathbf$ is likewise the parameter of the multinomial distribution $P(\backslash mathbf|\backslash mathbf)$. Rather than specifying $\backslash mathbf$ directly, we give it a conjugate prior distribution, and hence it is drawn from a Dirichlet distribution with parameter vector $\backslash boldsymbol\backslash alpha=(\backslash alpha\_1,\backslash alpha\_2,\backslash ldots,\backslash alpha\_K)$. By integrating out $\backslash mathbf$, we obtain a compound distribution. However, the form of the distribution is different depending on which view we take. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dirichlet-multinomial distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.