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I am trying to fit my data to a beta-binomial distribution and estimate the alpha and beta shape parameters. For this distribution, the prior is taken from a beta distribution. Python does not have a fit function for beta-binomial but it does for beta. The python beta fitting and R beta binomial fitting is close but systematically off.

R:

library("VGAM")
x = c(222,909,918,814,970,346,746,419,610,737,201,865,573,188,450,229,629,708,250,508)
y = c(2,18,45,11,41,38,22,7,40,24,34,21,49,35,31,44,20,28,39,17)
fit=vglm(cbind(y, x) ~ 1, betabinomialff, trace = TRUE)
Coef(fit)
   shape1    shape2 
  1.736093 26.870768

python:

import scipy.stats
import numpy as np
x = np.array([222,909,918,814,970,346,746,419,610,737,201,865,573,188,450,229,629,708,250,508], dtype=float)
y = np.array([2,18,45,11,41,38,22,7,40,24,34,21,49,35,31,44,20,28,39,17])
scipy.stats.beta.fit((y)/(x+y), floc=0, fscale=1)
    (1.5806623978910086, 24.031893492546242, 0, 1)

I have done this many times and it seems like python is systematically a little bit lower than the R results. I was wondering if this is an input error on my part or just a difference in the way they are calculated?

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2 回答 2

5

您的问题是拟合 beta-binomial 模型与拟合 Beta 模型的值等于比率不同。我将在此处使用bbmle包进行说明，该包将适合类似的模型VGAM（但我更熟悉）。

预赛：

library("VGAM")  ## for dbetabinom.ab
x <- c(222,909,918,814,970,346,746,419,610,737,
       201,865,573,188,450,229,629,708,250,508)
y <- c(2,18,45,11,41,38,22,7,40,24,34,21,49,35,31,44,20,28,39,17)

library("bbmle")

拟合 beta-二项式模型：

mle2(y~dbetabinom.ab(size=x+y,shape1,shape2),
     data=data.frame(x,y),
     start=list(shape1=2,shape2=30))
## Coefficients:
##    shape1    shape2 
##  1.736046 26.871526

这或多或少与VGAM您引用的结果完全一致。

现在使用相同的框架来拟合 Beta 模型：

mle2(y/(x+y) ~ dbeta(shape1,shape2),
     data=data.frame(x,y),
     start=list(shape1=2,shape2=30))
## Coefficients:
##    shape1    shape2 
## 1.582021 24.060570

这适合您的 Python，beta-fit 结果。（我敢肯定，如果您曾经VGAM适合 Beta，您也会得到相同的答案。）

于 2015-02-10T02:14:27.750 回答
0

您可以使用该conjugate_prior软件包python

请参阅硬币翻转示例的代码：

from conjugate_prior import BetaBinomial
heads = 95
tails = 105
prior_model = BetaBinomial() #Uninformative prior
updated_model = prior_model.update(heads, tails)
credible_interval = updated_model.posterior(0.45, 0.55)
print ("There's {p:.2f}% chance that the coin is fair".format(p=credible_interval*100))
predictive = updated_model.predict(50, 50)
print ("The chance of flipping 50 Heads and 50 Tails in 100 trials is {p:.2f}%".format(p=predictive*100))

从这里获取的代码

于 2017-09-26T10:20:21.673 回答