#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from thinkbayes import Pmf
pmf = Pmf()
pmf.Set('Bowl 1', 0.5)
pmf.Set('Bowl 2', 0.5)
pmf.Mult('Bowl 1', 0.75)
pmf.Mult('Bowl 2', 0.5)
pmf.Normalize()
print pmf.Prob('Bowl 1')
from thinkbayes import Pmf
# make empty pmf
pmf = Pmf()
pmf.Set('Bowl 1', .5) # P(Bowl 1)
pmf.Set('Bowl 2', .5) # P(Bowl 2)
pmf.Print()
# picks vanilla cookie - update P of bowl with evidence
pmf.Mult('Bowl 1', .75) # P(Vanilla | Bowl 1)
pmf.Mult('Bowl 2', .5) # P(Vanilla | Bowl 2)
pmf.Print()
print pmf.Normalize()
pmf.Print()
# picks chocolate cookie - update the pmf with new evidence
pmf.Mult('Bowl 1', .25) # P(Chocolate | Bowl 1)
pmf.Mult('Bowl 2', .5) # P(Chocolate | Bowl 2)
pmf.Print()
print pmf.Normalize()
pmf.Print()
## based on "Cookie" problem
## http://www.greenteapress.com/thinkbayes/
from thinkbayes import Pmf
pmf = Pmf()
pmf.Set("H1", 1 / 2.0)
pmf.Set("H2", 1 / 2.0)
pmf.Mult("H1", 30 / 40.0)
pmf.Mult("H2", 20 / 40.0)
pmf.Normalize()
for bowl in ["H1", "H2"]:
print bowl, pmf.Prob(bowl)
from thinkbayes import Pmf
pmf = Pmf()
pmf.Set('b1', 0.5)
pmf.Set('b2', 0.5)
print pmf.Items()
pmf.Mult('b1', 0.75)
pmf.Mult('b2', 0.5)
print pmf.Items()
pmf.Normalize()
print pmf.Items()
print pmf.Prob('b1')
def CH2_2():
"""
Cookie Problem (曲奇饼问题)
碗1: 30个香草味 10个巧克力味
碗2: 20个香草味 20个巧克力味
| 碗1 | 碗2 |
| 香草 | 巧克力 | 香草 | 巧克力 |
-------+---------------+---------------+
先验 | 0.5 | 0.5 |
------+---------------+---------------+
似然度| 0.75 | 0.25 | 0.5 | 0.5 |
------+------+--------+----------------
后验 |0.375 | 0.125 | 0.25 | 0.25 |
-------+--^---+--------+----------^----+
| | | | | |
| +---+--------+----------+ |
归一化| 0.6 | | |
0.375 / (0.375 + 0.25)
"""
# 先验
pmf = Pmf()
pmf.Set(x='b1', y=0.5)
pmf.Set(x='b2', y=0.5)
# 乘以似然度 (香草)
pmf.Mult('b1', 0.75)
pmf.Mult('b2', 0.5)
# 归一化
pmf.Normalize(fraction=1.0)
print("b1 = %.3f" % (pmf.Prob('b1', default=0)))
print("b2 = %.3f" % (pmf.Prob('b2', default=0)))
class Cookie(Pmf):
# 似然度
mixes = {
'bow1': {
'vanilla': 0.75,
'chocolate': 0.24
},
'bow2': {
'vanilla': 0.5,
'chocolate': 0.5
}
}
def __init__(self, hypos):
Pmf.__init__(self)
# 先验概率
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
# 计算后验概率
def Update(self, data):
for hypo in self.Values():
# 在该假设的条件下, 计算似然度
like = self.Likelihood(data, hypo)
self.Mult(hypo, like)
return self.Normalize()
def Likelihood(self, data, hypo):
mix = self.mixes[hypo]
return mix[data]
hypos = ["bow1", "bow2"]
data = 'vanilla'
cookie = Cookie(hypos)
# D: 香草
cookie.Update(data)
for hypo, prob in sorted(cookie.Items()):
print('p(%s/%s) = %.3f' % (hypo, data, prob))
# 有放回replace, 取三块
cookie = Cookie(hypos)
dataset = ['vanilla', 'chocolate', 'vanilla']
for data in dataset:
cookie.Update(data)
for hypo, prob in sorted(cookie.Items()):
print('p(%s/%s) = %.3f' % (hypo, dataset, prob))
#===========#
from thinkbayes import Pmf # requires print statement fixes
# build a 6-sided die:
die = Pmf()
for x in range(1, 7):
die.Set(x, 1 / 6.)
# solve the cookie problem
cookies = Pmf()
# set our prior distribution
cookies.Set('Bowl 1', 0.5)
cookies.Set('Bowl 2', 0.5)
# update the distribution based on evidence of a vanilla cookie
cookies.Mult('Bowl 1', 0.75)
cookies.Mult('Bowl 2', 0.5)
# renormalize
cookies.Normalize()
# posterior probability
print(cookies.Prob('Bowl 1'))
# more general tooling for the cookie problem:
class Cookie(Pmf):
def __init__(self, hypos):
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
'''
学习笔记：
贝叶斯
事情A发生的情况下，推测可能导致事件A发生的各条件的概率。
单次贝叶斯的计算逻辑：
各条件下，事件A发生的概率，进行归一化后，则为A发生的情况下，各条件可能导致的概率。
'''
from thinkbayes import Pmf
pmf = Pmf()
#曲奇饼问题
#1.设置先验概率
pmf.Set('Bowl1', 0.5)
pmf.Set('Bowl2', 0.5)
print('***************')
print('Bowl1:' + str(pmf.Prob('Bowl1')))
print('Bowl2:' + str(pmf.Prob('Bowl2')))
#2.设置似然度
pmf.Mult('Bowl1', 0.75) #香菜来自1碗的概率。碗1中香草曲奇饼的出现概率75%；选中1碗且是香草曲奇饼的概率0.375。
pmf.Mult('Bowl2', 0.5) #香草饼干来自2碗的概率。碗2中香草曲奇饼的出现概率25%；选中2碗且是香草曲奇饼的概率0.25。
print('***************')
print('Bowl1:' + str(pmf.Prob('Bowl1')))
print('Bowl2:' + str(pmf.Prob('Bowl2')))
#3.初始化
pmf.Normalize()
print('***************')
print('Bowl1:' + str(pmf.Prob('Bowl1'))) #拿出来了一个香草曲奇饼，来自碗1的概率0.375/0.625
print('Bowl2:' + str(pmf.Prob('Bowl2')))
# _*_ coding: utf-8 _*_
from thinkbayes import Pmf
pmf = Pmf()
pmf.Set('Bow1', 0.5) #碗1的概率
pmf.Set('Bow2', 0.5) #碗2的概率
pmf.Mult('Bow1', 0.75) #碗1香草曲奇概率
pmf.Mult('Bow2', 0.5) #碗2香草曲奇概率
pmf.Normalize() #归一化
t = pmf.Prob('Bow1') #后验概率
print(t)
