以下摘自An Introduction to the Science of Statistics书的第224页
simulate in R to find the distribution of the posterior probability of p = p1p2.
> p1<-rbeta(10000,16,6);p2<-rbeta(10000,18,4)
> p<-p1*p2
We then give a table of deciles for the posterior distribution function and present a histogram.
> data.frame(quantile(p,d))
quantile.p..d.
0% 0.2825593
10% 0.4660896
20% 0.5094321
30% 0.5422747
40% 0.5712765
50% 0.5968341
60% 0.6209610
70% 0.6477835
80% 0.6776208
90% 0.7187307
100% 0.9234834
书中未提供d，其外观如下：
> d<-seq(0, 1, by=0.1)
但是，每次运行得到的结果却完全不同：
> d<-seq(0, 1, by=0.1)
> p1<-rbeta(10000,16,6);p2<-rbeta(10000,18,4)
> p<-p1*p2
> data.frame(quantile(p,d))
quantile.p..d.
0% 0.2522659
10% 0.4715691
20% 0.5141640
30% 0.5463989
40% 0.5722724
50% 0.5982149
60% 0.6230126
70% 0.6507722
80% 0.6794564
90% 0.7211774
100% 0.9136375
>
>
> p1<-rbeta(10000,16,6);p2<-rbeta(10000,18,4)
> p<-p1*p2
> data.frame(quantile(p,d))
quantile.p..d.
0% 0.2492287
10% 0.4680199
20% 0.5122128
30% 0.5462639
40% 0.5740713
50% 0.5984662
60% 0.6233943
70% 0.6489084
80% 0.6800467
90% 0.7190094
100% 0.8674298
>
怎么会有这么大的差异？
已更新：
根据rbeta的文档，这确实是有道理的：
The Beta Random Number Generating Function
Random generation for the beta distribution with parameters shape1 and shape2
rbeta(n, shape1, shape2)
python
from numpy.random import beta
import numpy as np
import pandas as pd
import sys
# pd.set_option('display.max_columns', None)
# pd.set_option('display.expand_frame_repr', False)
# pd.set_option('max_colwidth', -1)
# np.set_printoptions(threshold=sys.maxsize)
p1 = beta(16, 6, 10000)
p2 = beta(18, 4, 10000)
p = p1 * p2
d = np.linspace(0, 1, 11)
df = pd.DataFrame({
'd': ["{0:.0f}%".format(val * 100) for val in d],
'quantile': np.quantile(p, d)
})
print(df)
输出：
d quantile
0 0% 0.247273
1 10% 0.468004
2 20% 0.513628
3 30% 0.544105
4 40% 0.571387
5 50% 0.596308
6 60% 0.620983
7 70% 0.646542
8 80% 0.677496
9 90% 0.716053
10 100% 0.912590