def __init__(self, hypos):
"""Initialize the distribution.
hypos: sequence of hypotheses
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
def __init__(self, hypos):
"""Initialize self.
hypos: sequence of string bowl IDs
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
def __init__(self, hypos):
"""Initialize the distribution.
hypos: sequence of hypotheses
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
def __init__(self, hypos):
"""Initialize self.
hypos: whether you play tennis or not
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, countdict[hypo])
self.Normalize()
def __init__(self, hypos, alpha=1.0):
"""Initializes the hypotheses with a power law distribution.
hypos: sequence of hypotheses
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, hypo**(-alpha))
self.Normalize()
def __init__(self, hypos):
"""Initialize self.
hypos: sequence of string bowl IDs
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
def __init__(self, hypos):
"""Initialize self.
hypos: whether you play tennis or not
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, countdict[hypo])
self.Normalize()
def __init__(self, hypos):
"""UPDATE THIS DOCSTRING
hypos: sequence of hypotheses representing possible company sizes
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, int(max(hypos) / hypo) * hypo)
self.Normalize()
def __init__(self, hypos, alpha=1.0):
"""Initializes hypotheses with a power law distribution.
hypos: sequence of hypotheses
alpha: parameter of the power law prior
"""
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, hypo**(-alpha))
self.Normalize()
def main():
d6 = Die(6)
d8 = Die(8)
d12 = Die(12)
d16 = Die(16)
d20 = Die(20)
mix = Pmf()
for die in [d6, d8, d12, d16, d20]:
for outcome, prob in die.Items():
mix.Incr(outcome, prob)
mix.Normalize()
thinkplot.PrePlot(1)
thinkplot.Pmf(mix)
thinkplot.Save(root='dice_Mix_self1',
xlabel='sum of dice',
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'])
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')
def __init__(self, hypos):
Pmf.__init__(self)
for hypo_k, hypo_v in hypos.items():
self.Set(hypo_k, 1)
self.Normalize()
#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)
# _*_ 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)
from thinkbayes import Pmf
import Pmf
# pmf = Pmf()
#
#
#
# pmf.Set('Bowl 1', 0.5)
# pmf.Set('Bowl 2', 0.5)
# pmf.Incr(2, 0.2)
#
# pmf.Mult('Bowl 1', 0.75)
# pmf.Mult('Bowl 2', 0.5)
#
# pmf.Normalize()
# print (pmf.Prob('Bowl 1'))
hist = Pmf.MakeHistFromList([1, 2, 2, 3, 5])
print(hist.Freq(2))
print("end")
for val in sorted(hist.Values()):
print(val, hist.Freq(val))
def __init__(self, hypos):
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
def __init__(self, hypos):
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, 1)
self.Normalize()
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))
# body of new data, D.
# p(H | D) = [p(H) p(D | H)] / p(D)
### p(H) := is the probability of the hypothesis before we see the data,called the prior probability, or just 'prior'.
### p(H|D) := is what we want to compute, the probability of the hypothesis after we see the data, called the 'posterior'.
### p(D|H) := is the probability of the data under the hypothesis, called the 'likelihood'.
### p(D) := is the probability of the data under any hypothesis, called the 'normalizing constant'.
# Sometimes the 'prior' can be computed based on background information
# Here we will use the probability mass function on the cookie problem.
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'))
print('\n')
print('The Cookie Problem: ')
# The Cookie problem #
# In the following class a Cookie object is a Pmf that maps from hypotheses to their probabilities.
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')
"""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', 0.5)
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'))
def __init__(self, hypo, alpha=1.0):
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, hypo**(-alpha))
self.Normalize()
def __init__(self, bowls): Pmf.__init__(self) self.bowls = bowls for hypo in bowls.keys(): self.Set(hypo, 1) self.Normalize()
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()
def __init__(self, hypos, alpha = 1.0):
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo, hypo**(-alpha))
self.Normalize()
## 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)
def __init__(self, sides):
Pmf.__init__(self)
for side in xrange(1, sides + 1):
self.Set(side, 1)
self.Normalize()
def __init__(self):
Pmf.__init__(self)
self.Set('goodsinger', 0.05)
self.Set('badsinger', 0.95)
self.Normalize()
#!/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))
def __init__(self,hypos):
Pmf.__init__(self)
for hypo in hypos:
self.Set(hypo,1)
"""
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'))
#!/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())
# =========================
#
# 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'))
def MakePmf(self,xs):
pmf = Pmf()
for x in xs:
pmf.Set(x, self.Density(x))
pmf.Normalize()
return pmf
'''
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')))
def __init__(self, hypos):
Pmf.__init__(self)
for who, prob in hypos.iteritems():
self.Set(who, prob)
self.Normalize()
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'])
#!/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')
def __init__(self, sides):
Pmf.__init__(self)
for x in xrange(1, sides+1):
self.Set(x, 1)
self.Normalize()