加速从叠加的截断正态分布中绘制随机值

问题描述

我想从两个截断正态分布之和的分布中抽取 N 个随机样本.我通过从 scipy.stats 子类化 rv_continuous 类并提供一个 pdf 来得到我想要的东西，该 pdf 是两个给定 pdf 的平均值:

I want to draw N random samples from a distribution that is the sum of two truncated normal distributions. I get what I want by subclassing rv_continuous class from scipy.stats and providing a pdf that is the mean of the two given pdfs:

import numpy as np
from scipy import stats

my_lim = [0.05, 7]  # lower and upper limit
my_loc = [1.2, 3]  # loc values of the two truncated normal distributions
my_scale = [0.6, 2]  # scale values of the two truncated normal distributions

class sum_truncnorm(stats.rv_continuous):
    def _pdf(self, x):
        return (stats.truncnorm.pdf(x,
                                    a=(my_lim[0] - my_loc[0]) / my_scale[0],
                                    b=(my_lim[1] - my_loc[0]) / my_scale[0],
                                    loc=my_loc[0],
                                    scale=my_scale[0]) +
                stats.truncnorm.pdf(x,
                                    a=(my_lim[0] - my_loc[1]) / my_scale[1],
                                    b=(my_lim[1] - my_loc[1]) / my_scale[1],
                                    loc=my_loc[1],
                                    scale=my_scale[1]) / 2

但是，使用:

my_dist = sum_truncnorm()
my_rvs = my_dist.rvs(size=10)

非常很慢，每个随机值大约需要 5 秒.

is very slow and takes about 5 seconds per random value.

我确信这可以更快地完成，但我不知道该怎么做.我是否应该将我的分布定义为(非截断的)正态分布的总和，然后强制截断?我在这个方向上做了一些测试，但这只是快了大约 10 倍，因此仍然很慢.

I'm sure that this can be done much faster, but I am not sure how to do it. Should I maybe define my distribution as a sum of (non truncated) normal distributions and force the truncated afterwards? I did some tests in this direction, but this was only about 10x faster and thus still way to slow.

Google 告诉我，我可能需要使用逆变换采样并覆盖 _rvs 方法，但我未能使其适用于我的截断分布.

Google told me that I probably need to use inverse transform sampling and override the _rvs method, but I failed to make this working for my truncated distributions.

推荐答案

首先，您必须确保 _pdf 已规范化.框架不会检查它，否则会默默地产生废话.

First, you'll going to have to make sure _pdf is normalized.The framework does not check it, and silently produces nonsense otherwise.

其次，为了使绘图变量更快，您需要实现一个 _ppf 或 _rvs.仅使用 _pdf，它会通过通用代码路径(数字集成和根查找)，这就是为什么您当前的版本很慢.

Second, to make drawing variates fast, you need to implement a _ppf or _rvs. With just _pdf only, it goes through the generic code path (numeric integration and root-finding) which why your current version is slow.

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