def main():
# d6 = Die(6)
# d8 = Die(8)
d6 = Pmf()
print type(d6)
d6.Set(Die(6), 2)
print type(d6)
d8 = Pmf()
d8.Set(Die(8), 3)
d12 = Pmf()
d12.Set(Die(12), 1)
d20 = Pmf()
d20.Set(Die(20), 1)
mix = Pmf()
for dice in [d6, d8, d12, d20]:
# print type(dice)
for die, weight in dice.Items():
# print type(die)
for outcome, prob in die.Items():
mix.Incr(outcome, weight * prob)
mix.Normalize()
thinkplot.PrePlot(1)
thinkplot.Pmf(mix)
thinkplot.Save(root='dice_Mix_self2',
xlabel='',
ylabel='Probability',
formats=['pdf'])
def main():
pmf_dice = Pmf()
pmf_dice.Set(Die(6),2)
pmf_dice.Set(Die(8),3)
pmf_dice.Set(Die(12),1)
pmf_dice.Set(Die(20),1)
mix = Pmf()
for die, weight in pmf_dice.Items():
for outcome, prob in die.Items():
mix.Incr(outcome, weight*prob)
mix.Normalize()
thinkplot.PrePlot(1)
thinkplot.Pmf(mix)
thinkplot.Save(root='dice_Mix_self3',xlabel='',ylabel='Probability',formats=['pdf'])
#!/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')
#p(H|D)，在D的条件下H发生的概率
#先验概率PH
#似然度p(D|H)
#p(H)p(D|H)
#后验概率p(H|D)
#p(A|B) = p(A)p(B|A) / p(B)
from thinkbayes import Pmf
pmf = Pmf()
for x in [1,2,3,4,5,6]:
pmf.Set(x, 1/6.0)
print(pmf)
def MakePmf(self,xs):
pmf = Pmf()
for x in xs:
pmf.Set(x, self.Density(x))
pmf.Normalize()
return pmf
#!/usr/bin/env python
# -*- coding: utf-8 -*-
from thinkbayes import Pmf
pmf1 = Pmf()
for x in range(1, 6 + 1):
pmf1.Set(x, 1 / 6.0)
pmf1.Print()
print("曲奇饼问题")
pmf2 = Pmf()
pmf2.Set('Bowl1', 0.5)
pmf2.Set('Bowl2', 0.5)
pmf2.Mult('Bowl1', 0.75)
pmf2.Mult('Bowl2', 0.5)
pmf2.Normalize()
print pmf2.Probs(pmf2.Values())
## 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)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Nov 17 11:21:39 2020
@author: isajarspector
"""
from thinkbayes import Pmf
pmf = Pmf()
for x in [1, 2, 3, 4, 5, 6]:
pmf.Set(x, 1 / 6)
print(pmf.Prob(1))
"""This file contains code for use with "Think Bayes",
by Allen B. Downey, available from greenteapress.com
Copyright 2012 Allen B. Downey
License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
"""
from thinkbayes import Pmf
pmf = Pmf()
pmf.Set('Bowl 1', 0.50)
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()
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))
"""
PMF - probability mass function
"""
from thinkbayes import Pmf
from thinkbayes import Suite
# introducing pmf.
pmf = Pmf()
for x in [1, 2, 3, 4, 5, 6]:
pmf.Set(x, 1./6)
# re-introducing pmf.
word_list = ['atirei', 'o', 'pau', 'atirei', 'gato', 'gato']
pmf = Pmf()
for word in word_list:
pmf.Incr(word, 1)
pmf.Normalize()
print(pmf.Prob('gato'))
# p(H|D) = p(H) * p(D|H) / p(D)
#
# posterior = prior * likelihood / normalizing constant
# "Suite": a MECE set of hypotheses
#===========#
# Chapter 2 #
#===========#
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'))
from thinkbayes import Pmf
'''
pmf1 =Pmf()
for x in [1,2,3,4,5,6]:
pmf1.Set(x, 1/6.0)
#print pmf1.Normalize()
#print pmf1.Prob(1)
'''
pmf2 = Pmf()
pmf2.Set('Bowl1', 0.5)
pmf2.Set('Bowl2', 0.5)
pmf2.Mult('Bowl1', 0.75)
pmf2.Mult('Bowl2', 0.5)
pmf2.Normalize()
print pmf2.Prob('Bowl1')
print pmf2.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)
