使用 Python 进行多元分布 [英] Multivariate distributions with Python

问题描述

我计算了一个取决于两个变量的概率密度函数.我想使用这个多元分布来生成一些随机数，这些随机数出现的概率与 PDF 成正比.

I have computed a probability density function that depends on two variables. I want to use this multivariate distribution to generate some random numbers that occur with a probability proportional to the PDF.

看起来，SciPy 目前只支持单变量分布.是否有任何简单的方法或易于使用的包允许 2d 分布?

As it seems, SciPy currently only supports univariate distributions. Are there any simple methods or easy-to-use packages that allow 2d-distributions?

作为一种解决方法，我可能会尝试在感兴趣的域上创建随机数并将其丢弃或保留与我的 PDF 相关的机会，但仍然可能有其他选择.随机数生成不一定要很快.

As a workaround, I might try creating random numbers on the domain of interest and throwing them away or keeping them with a chance related to my PDF, but still there might be other options. The random number generation does not have to be fast.

感谢您的帮助！

根据答案(非常感谢！)，我修改了一些代码，您可能会在 this gist.如果您使用 sin^2*Gauss PDF 运行此示例，则将在 PDF 上绘制满足给定条件(在圆圈内)的 2000 个随机随机变量.也许这对其他人也有帮助.

Based on the answers (thanks a lot!), I hacked in some code the you may find in this gist. If you run this example with a sin^2*Gauss PDF, 2000 random random variates that fulfil a given condition (be inside a circle) will be plotted over the PDF. Maybe that's helpful for others, too.

推荐答案

所以你有一个 PDF F(x,y) 并且你想要生成 x 对> 和 y 根据此 PDF 分发?

So you have a PDF F(x,y) and you want to generate the pairs of x and y distributed according to this PDF?

我会说除非你可以使用多变量版本的反演技术(wiki)，拒绝抽样是要走的路.

I'd say unless you can use the multivariate version of the inversion technique (wiki), the rejection sampling is the way to go.

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