In XiangyunHuang/RcppML: Machine Learning Algorithms Based on Rcpp

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吉布斯采样

例子来自 Rcpp 包

list.files(system.file("examples", "RcppGibbs", package = "Rcpp"))

从如下联合概率密度函数抽样

$$ f(x,y) = x^2\exp(-xy^2 - y^2 + 2y -4x) = x^2 \exp\big[-(y^2+4)x - y^2 + 2y\big] $$ 而 $f(x|y) = \frac{f(x,y)}{f(y)} = \frac{f(x,y)}{\int_{-\infty}^{+\infty} f(x,y)dx}$

伽马分布的密度函数

$$ f(x) = \frac{1}{s^a\Gamma(a)}x^{(a -1)}\exp\big(-\frac{x}{s}\big), x \geq 0, a >0, s > 0 $$ 其中，$\Gamma(a)$ 函数

$$ \begin{align} f(x|y) &= x^2\exp\big[-x(4 + y^2)\big], \ f(y|x) &= \exp\big[-0.52(x + 1)(y^2 - \frac{2y}{x + 1})\big] \end{align} $$

分别是伽马密度函数和正态密度函数的形式

参考文献

1. Rcpp Gallery

2. Rcpp 内置文档

XiangyunHuang/RcppML documentation built on Oct. 31, 2019, 1:16 a.m.