生成加权随机数 [英] Generating weighted random numbers

问题描述

我正在为基因组学课程编写一些代码，但在某些方面遇到困难.

Hi I'm doing some code for a genomics class and I am having difficulty on a certain part.

我有一组相互排斥的事件 具有概率

I have a set of mutually exclusive events with probabilities

我想模拟以给定的概率对事件进行随机采样n次.

I want to simulate randomly sampling an event n times with the given probability.

输入:概率= {0.3，0.2，0.5}事件{e1，e2，e3} n = 100

input: probabilities = {0.3, 0.2, 0.5} events{e1,e2,e3} n=100

输出:e3应该有〜50个结果，e2应该有〜20个结果，而e1应该有〜30个结果. 请注意，这些可能不完全是50、20、30，因为 经验值不同于理论值...

output: there should be ~50 results for e3, ~20 for e2 and ~30 for e1. Note that these are probably not exactly 50, 20, 30 because empirical values are different from theoretical values...

推荐答案

Python没有内置任何加权采样功能(NumPy/SciPy具备)，但是对于像这样的非常简单的情况，这很简单:

Python doesn't have any weighted sampling functionality built in (NumPy/SciPy does), but for a really simple case like this, it's pretty easy:

import itertools
import random

probabilities = [0.3, 0.2, 0.5]
totals = list(itertools.accumulate(probabilities))

def sample():
    n = random.uniform(0, totals[-1])
    for i, total in enumerate(totals):
        if n <= total:
            return i

---

如果没有Python 3.2+，则没有accumulate函数.如果清单真的很短，您可以用低效率的单线伪造它:

---

If you don't have Python 3.2+, you don't have the accumulate function; you can fake it with an inefficient one-liner if the list really is this short:

totals = [sum(probabilities[:i+1]) for i in range(len(probabilities))]

…，或者您可以编写一个显式循环或丑陋的reduce调用，或从

… or you can write an explicit loop, or an ugly reduce call, or copy the equivalent Python function from the docs.

此外，请注意，如果您可以确定数字加起来为1.0，则random.uniform(0, totals[-1])只是写random.random()的一种更为复杂的方式.

Also, note that random.uniform(0, totals[-1]) is just a more complicated way of writing random.random() if you can be sure that your numbers add up to 1.0.

一种快速的测试方法:

>>> samples = [sample() for _ in range(100000)]
>>> samples.count(0)
29878
>>> samples.count(1)
19908
>>> samples.count(2)
50214

分别接近100000的30％，20％和50％.

Those are pretty close to 30%, 20%, and 50% of 100000, respectively.

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