def _test2(show):
# 已知n, f(纪录到的概率), 求k的分布, hypo
n = 150
f = 0.1
# MakeBinomialPmf: 二项分布 0 - n次已经罗列了所有可能, 不需要归一化
pmf = thinkbayes2.MakeBinomialPmf(n, f)
if show:
thinkplot.Clf()
thinkplot.Pmf(pmf)
thinkplot.Show(title="test2",
xlabel='Event Count',
ylabel='Probality')
print("Total: ", pmf.Total())
return pmf
def main():
hypos = range(100, 1001)
suite = Train(hypos)
suite.Update(321)
print('Posterior mean', suite.Mean())
print('Posterior MLE', suite.MaximumLikelihood())
print('Posterior CI 90', suite.CredibleInterval(90))
thinkplot.PrePlot(1)
thinkplot.Pmf(suite)
thinkplot.Show(xlabel='Number of trains',
ylabel='Probability',
legend=False)
def main():
hypos = xrange(1, 1001)
suite = Train(hypos)
suite.label = 'train label'
suite.Update(60)
print suite.Mean()
thinkplot.PrePlot(1)
thinkplot.Pmf(suite)
thinkplot.Save(root='train1',
xlabel='Number of trains',
ylabel='Probability',
formats=['pdf', 'eps'])
def main():
print "1"
hockey1 = Hockey()
# print(type(hockey1))
thinkplot.PrePlot(1)
thinkplot.Pmf(hockey1)
thinkplot.Save(root='hockey_self2_prior',
xlabel='',
ylabel='Probability',
formats=['pdf'])
print(hockey1.Values())
for hypo in hockey1.Values():
print(hockey1.Likelihood(2, hypo))
hockey1.UpdateSet([0, 2, 4, 3, 8])
thinkplot.Pmf(hockey1)
thinkplot.Save(root='hockey_self2_posterior',
xlabel='',
ylabel='Probability',
formats=['pdf'])
print("No error, everything worked fine")
def main():
hypos = range(100, 1001)
suite = Train(hypos)
suite.Update(50)
thinkplot.PrePlot(1)
thinkplot.Pmf(suite)
thinkplot.Show(xlabel='Number of trains',
ylabel='Probability',
legend=False)
for train in [13, 45, 89, 22, 33, 35]:
suite.Update(train)
thinkplot.PrePlot(1)
thinkplot.Pmf(suite)
thinkplot.Show(xlabel='Number of trains',
ylabel='Probability',
legend=False)
print(suite.Mean())
print(suite.MaximumLikelihood())
print(suite.CredibleInterval(90))
def CH7_5():
"""
胜算
"""
go1, go2 = CH7_4(0)
diff_pmf = go1 - go2
thinkplot.Clf()
thinkplot.Pmf(diff_pmf)
thinkplot.Show(title='diff', xlabel='Goals per game', ylabel='Probability')
pwin = diff_pmf.ProbGreater(0)
pmiss = diff_pmf.ProbLess(0)
ptie = diff_pmf.Prob(0, default=0)
print("pwin = %.3f pmiss = %.3f ptie = %.3f" % (pwin, pmiss, ptie))
def CH5_6():
"""
混合分布, 汇总多个分布的贡献
骰子个数 骰子面数
5 4-sides
4 6-sides
3 8-sides
2 12-sides
1 20-sides
"""
thinkplot.PrePlot(num=2)
# (权重, 骰子)
dices = [(5, Die(4)), (4, Die(6)), (3, Die(8)), (2, Die(12)), (1, Die(20))]
mix = thinkbayes.Pmf()
for w, die in dices:
for v, p in die.Items():
mix.Incr(v, w * p)
mix.Normalize()
mix.name = 'mix-1'
thinkplot.Pmf(mix)
# 方法2
pmf_dices = thinkbayes.Pmf()
pmf_dices.Set(Die(4), y=5)
pmf_dices.Set(Die(6), y=4)
pmf_dices.Set(Die(8), y=3)
pmf_dices.Set(Die(12), y=2)
pmf_dices.Set(Die(20), y=1)
pmf_dices.Normalize()
mix = thinkbayes.MakeMixture(pmf_dices, name='mix-2')
mix.name = 'mix-2'
thinkplot.Pmf(mix)
thinkplot.Show()
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'])
def MakePmfPlot(alpha=10):
"""Plots Pmf of location for a range of betas."""
locations = range(0, 31)
betas = [10, 20, 40]
thinkplot.PrePlot(num=len(betas))
for beta in betas:
pmf = MakeLocationPmf(alpha, beta, locations)
pmf.name = 'beta = %d' % beta
thinkplot.Pmf(pmf)
thinkplot.Save('paintball1',
xlabel='Distance',
ylabel='Prob',
formats=FORMATS)
def main():
low = 0.001
high = 1.5
steps = 1001
hypos = [low + (high - low) * i / (steps - 1.0) for i in range(steps)]
suite = Decay(hypos)
data = [1.5, 2, 3, 4, 5, 12]
suite.UpdateSet(data)
print 'Mean of the posterior distribution:', suite.Mean()
# plot the posterior distribution
thinkplot.Pmf(suite)
thinkplot.Show(title='Decay parameter',
xlabel='Parameter (inverse cm)',
ylabel='Posterior probability')
def PlotSurvivalCurve(ts, lams, ss):
"""
ts: times in years
lams: Pmf representing the hazard function
ss: list of values for the survival curve
"""
# scale lams
denom = max(lams.Probs())
lams.MultAll(1 / denom)
thinkplot.Pmf(lams, linewidth=2, linestyle='dashed', color='0.7')
thinkplot.Plot(ts, ss, linewidth=2, color='blue', label='survival')
thinkplot.Save(root='seer1',
title='',
xlabel='Survival time (years)',
ylabel='Probability')
def PredRemaining(self, rem_time, score):
"""Plots the predictive distribution for final number of goals.
rem_time: remaining time in the game in minutes
score: number of goals already scored
"""
# TODO: fill this in
# lam = goals / game
lam_total = 0
for lam, prob in self.Items():
goals_in_remaining_time = lam * rem_time / 90 # convert to goals in remaining time
lam_total += lt * prob
pmf = thinkbayes2.MakePoissonPmf(goals_in_remaining_time, 12)
pmf += score
thinkplot.Pmf(pmf)
thinkplot.Show()
def PlotSurvival(durations):
"""Plots survival and hazard curves.
durations: list of durations
"""
cdf = thinkstats2.MakeCdfFromList(durations)
thinkplot.Cdf(cdf, alpha=0.1)
thinkplot.PrePlot(2)
ts, ss = SurvivalFunction(cdf)
thinkplot.Plot(ts, ss, label="S(t)")
haz_func = HazardFunction(ts, ss)
thinkplot.Pmf(haz_func, label='lam(t)')
thinkplot.Show(xlabel='t (weeks)')
def MakeConditionalPlot(suite):
"""Plots marginal CDFs for alpha conditioned on beta.
suite: posterior joint distribution of location
"""
betas = [10, 20, 40]
thinkplot.PrePlot(num=len(betas))
for beta in betas:
cond = suite.Conditional(0, 1, beta)
cond.name = 'beta = %d' % beta
thinkplot.Pmf(cond)
thinkplot.Save('paintball3',
xlabel='Distance',
ylabel='Prob',
formats=FORMATS)
def main():
data = ReadData()
cols = zip(*data)
price1, price2, bid1, bid2, diff1, diff2 = cols
pdf = thinkbayes.EstimatedPdf(price1)
# print(type(pdf))
low, high = 0, 75000
n = 101
xs = numpy.linspace(low, high, n)
# print(pdf.Density(25000))
pmf = pdf.MakePmf(xs)
thinkplot.PrePlot(1)
thinkplot.Pmf(pmf)
thinkplot.Save(root='price_self2',
xlabel='',
ylabel='Probability_density',
formats=['pdf'])
def ComparePriors():
"""Runs the hypothesis with two different priors and compares them."""
dataset = [60]
high = 1000
thinkplot.Clf()
thinkplot.PrePlot(num=2)
constructors = [Train, Train2]
labels = ['uniform', 'power law']
for constructor, label in zip(constructors, labels):
suite = MakePosterior(high, dataset, constructor)
suite.name = label
thinkplot.Pmf(suite)
thinkplot.Save(root='train4',
xlabel='Number of trains',
ylabel='Probability')
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 MakeHists(live):
"""Plot Hists for live births
live: DataFrame
others: DataFrame
"""
hist = thinkstats2.Hist(np.floor(live.agepreg), label='agepreg')
thinkplot.PrePlot(2, cols=2)
thinkplot.SubPlot(1)
thinkplot.Hist(hist)
thinkplot.Config(xlabel='years', ylabel='frequency', axis=[0, 45, 0, 700])
thinkplot.SubPlot(2)
thinkplot.Pmf(hist)
thinkplot.Save(root='probability_agepreg_hist',
xlabel='years',
axis=[0, 45, 0, 700])
def main():
d6 = Die(6)
dice = [d6] * 3
dice1 = [d6] * 1
print type(d6)
print d6.Items()
print type(dice)
print dice[0].Items()
print dice[1].Items()
print dice[2].Items()
# t1 = RandomSum(dice)
test = SampleSum(dice, 50)
thinkplot.PrePlot(1)
thinkplot.Pmf(test)
thinkplot.Save(root='dice_self2',
xlabel='sum of dice',
ylabel='Probability',
formats=['pdf'])
def main():
d = {
1: 1,
2: 1,
3: 1,
4: 1,
5: 1,
6: 1,
7: 1,
}
# form the pmf
pmf = thinkstats2.MakePmfFromDict(d, 'family size')
print 'mean', pmf.Mean()
print 'var', pmf.Var()
# plot the Pmfs
thinkplot.Pmf(pmf)
thinkplot.Show(xlabel='Family size', ylabel='PMF')
def main():
pmf = Euro(xrange(0, 101))
dataset = 'H' * 140 + "T" * 110
# dataset = 'H' + 'T'
# dataset = 'T'
for data in dataset:
# print(data)
pmf.Update(data)
# print pmf.Items()
# print pmf.Mean()
print pmf.Prob(80)
thinkplot.PrePlot(1)
thinkplot.Pmf(pmf)
thinkplot.Save(root='coin_self1',
xlabel='',
ylabel='Probability',
formats=['pdf'])
def main():
# Create a new Train object with hypotheses 1 (company has one train)
# through 1000 (company has 1000 trains)
train = Train(range(1, 1001))
train.label = "Posterior Probability"
# update the probability mass function with new data (train #60)
train.Update(60)
# train.Print()
print("Mean hypothesis: {}".format(train.Mean()))
# Use Allen Downey's thinkplot module to create a graph
thinkplot.PrePlot(1)
thinkplot.Pmf(train)
thinkplot.Save(root='trains',
xlabel='Number of trains',
ylabel='Probability',
formats=['pdf'])
def main():
'''initializes an instance of a learning styles probability distribution
updates the probability distribution based on data
checks the strength of the evidence that the distribution in hacker school is substantiallly different'''
sensing_data = (2, 0)
sensing_hypo = 50
sensing_ratio = 65
sensing_dist = StyleDist(range(0, 101))
sensing_likelihood = sensing_dist.Likelihood(sensing_data, sensing_hypo)
print('p(D|50%)', sensing_likelihood)
thinkplot.Hist(sensing_dist)
#set p(D|~H)
b_uniform = StyleDist(range(0, 101))
b_uniform.Remove(sensing_ratio)
b_uniform.Normalize()
# %matplotlib inline
thinkplot.Pmf(sensing_dist)
return sensing_dist
def main():
data = 20, 15, 3
probs = numpy.linspace(0, 1, 31)
hypos = []
for n in range(32, 350):
for p1 in probs:
for p2 in probs:
hypos.append((n, p1, p2))
suite = Lincoln(hypos)
suite.Update(data)
n_marginal = suite.Marginal(0)
thinkplot.Pmf(n_marginal, label='n')
thinkplot.Save(root='lincoln1',
xlabel='number of bugs',
ylabel='PMF',
formats=['pdf', 'png'])
print('post mean n', n_marginal.Mean())
print('MAP n', n_marginal.MaximumLikelihood())
p1_marginal = suite.Marginal(1, label='p1')
p2_marginal = suite.Marginal(2, label='p2')
thinkplot.Pdf(p1_marginal)
thinkplot.Pdf(p2_marginal)
thinkplot.Show()
print('post mean p1', p1_marginal.Mean())
print('MAP p1', p1_marginal.MaximumLikelihood())
print('post mean p2', p2_marginal.Mean())
print('MAP p2', p2_marginal.MaximumLikelihood())
print('p1 > p2', p1_marginal > p2_marginal)
print('p1 < p2', p1_marginal < p2_marginal)
def main():
data = 20, 15, 3
probs = numpy.linspace(0, 1, 101)
hypos = []
for n in range(32, 350):
for p1 in probs:
for p2 in probs:
hypos.append((n, p1, p2))
suite = Lincoln(hypos)
suite.Update(data)
n_marginal = suite.Marginal(0)
thinkplot.Pmf(n_marginal, label='n')
thinkplot.Save(root='lincoln1',
xlabel='number of bugs',
ylabel='PMF',
formats=['pdf', 'png'])
print(n_marginal.Mean())
print(n_marginal.MaximumLikelihood())
def main():
pmf_dice = thinkbayes.Pmf()
pmf_dice.Set(Die(4), 5)
pmf_dice.Set(Die(6), 4)
pmf_dice.Set(Die(8), 3)
pmf_dice.Set(Die(12), 2)
pmf_dice.Set(Die(20), 1)
pmf_dice.Normalize()
mix = thinkbayes.Pmf()
for die, weight in pmf_dice.Items():
for outcome, prob in die.Items():
mix.Incr(outcome, weight * prob)
mix = thinkbayes.MakeMixture(pmf_dice)
colors = thinkplot.Brewer.Colors()
thinkplot.Hist(mix, width=0.9, color=colors[4])
thinkplot.Save(root='dungeons3',
xlabel='Outcome',
ylabel='Probability',
formats=FORMATS)
random.seed(17)
d6 = Die(6, 'd6')
dice = [d6] * 3
three = thinkbayes.SampleSum(dice, 1000)
three.name = 'sample'
three.Print()
three_exact = d6 + d6 + d6
three_exact.name = 'exact'
three_exact.Print()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(three)
thinkplot.Pmf(three_exact, linestyle='dashed')
thinkplot.Save(root='dungeons1',
xlabel='Sum of three d6',
ylabel='Probability',
axis=[2, 19, 0, 0.15],
formats=FORMATS)
thinkplot.Clf()
thinkplot.PrePlot(num=1)
# compute the distribution of the best attribute the hard way
# best_attr2 = PmfMax(three_exact, three_exact)
# best_attr4 = PmfMax(best_attr2, best_attr2)
# best_attr6 = PmfMax(best_attr4, best_attr2)
# thinkplot.Pmf(best_attr6)
# and the easy way
best_attr_cdf = three_exact.Max(6)
best_attr_cdf.name = ''
best_attr_pmf = thinkbayes.MakePmfFromCdf(best_attr_cdf)
best_attr_pmf.Print()
thinkplot.Pmf(best_attr_pmf)
thinkplot.Save(root='dungeons2',
xlabel='Sum of three d6',
ylabel='Probability',
axis=[2, 19, 0, 0.23],
formats=FORMATS)
# In[53]: width=200000 axis = [0, 800, 0, 0.0005] thinkplot.PrePlot(2, cols =2) thinkplot.Hist(flfindistdfpmf, align = 'right', width = width) thinkplot.Hist(vfindistdfpmf, align = 'left', width = width) thinkplot.Config(xlabel = 'Total Revenue', ylabel = 'PMF') # In[54]: thinkplot.Pmf(flfindistdfpmf) thinkplot.Pmf(vfindistdfpmf) # In[55]: thinkplot.PrePlot(2) thinkplot.subplot(2) #axis = [0, 800, 0, 0.0005] thinkplot.Pmfs([flfindistdfpmf,vfindistdfpmf ]) thinkplot.Show(xlabel = 'Total Revenue', ylabel = 'PMF') # # Lets plot PMF of log transformed columns
df = brfss.ReadBrfss(nrows=None)
female = df[df.sex == 2]
female_heights = female.htm3.dropna()
## female height statistics
mean, std = female_heights.mean(), female_heights.std()
print('mean:\n', mean)
print('std:\n', std)
## make pdf representing female distribution
pdf = thinkstats2.NormalPdf(mean, std)
pmf = pdf.MakePmf()
thinkplot.PrePlot(2)
thinkplot.Pdf(pdf, label='normal pdf')
thinkplot.Pmf(pmf, label='normal pmf')
thinkplot.Show(xlabel='x', xlim=[140, 186])
## KDE of normal pdf
i = 6
thinkplot.PrePlot(i + 1)
thinkplot.Pdf(pdf, label='normal')
for _ in range(i):
sample = np.random.normal(mean, std, 500)
sample_pdf = thinkstats2.EstimatedPdf(sample, label='sample')
thinkplot.Pdf(sample_pdf, label='sample KDE')
thinkplot.Show(xlabel='x', ylabel='PDF', xlim=[140, 186])
## calculate moments
def main():
#ReadHockeyData()
#return
formats = ['pdf', 'eps']
suite1 = Hockey('bruins')
suite2 = Hockey('canucks')
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(suite1)
thinkplot.Pmf(suite2)
thinkplot.Save(root='hockey0',
xlabel='Goals per game',
ylabel='Probability',
formats=formats)
suite1.UpdateSet([0, 2, 8, 4])
suite2.UpdateSet([1, 3, 1, 0])
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(suite1)
thinkplot.Pmf(suite2)
thinkplot.Save(root='hockey1',
xlabel='Goals per game',
ylabel='Probability',
formats=formats)
goal_dist1 = MakeGoalPmf(suite1)
goal_dist2 = MakeGoalPmf(suite2)
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(goal_dist1)
thinkplot.Pmf(goal_dist2)
thinkplot.Save(root='hockey2',
xlabel='Goals',
ylabel='Probability',
formats=formats)
time_dist1 = MakeGoalTimePmf(suite1)
time_dist2 = MakeGoalTimePmf(suite2)
print('MLE bruins', suite1.MaximumLikelihood())
print('MLE canucks', suite2.MaximumLikelihood())
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(time_dist1)
thinkplot.Pmf(time_dist2)
thinkplot.Save(root='hockey3',
xlabel='Games until goal',
ylabel='Probability',
formats=formats)
diff = goal_dist1 - goal_dist2
p_win = diff.ProbGreater(0)
p_loss = diff.ProbLess(0)
p_tie = diff.prob(0)
print(p_win, p_loss, p_tie)
p_overtime = thinkbayes2.PmfProbLess(time_dist1, time_dist2)
p_adjust = thinkbayes2.PmfProbEqual(time_dist1, time_dist2)
p_overtime += p_adjust / 2
print('p_overtime', p_overtime)
print(p_overtime * p_tie)
p_win += p_overtime * p_tie
print('p_win', p_win)
# win the next two
p_series = p_win**2
# split the next two, win the third
p_series += 2 * p_win * (1-p_win) * p_win
print('p_series', p_series)
#--- Chapter2 Ex4
wgt_live = live.totalwgt_lb.dropna()
wgt_first = firsts.totalwgt_lb.dropna()
wgt_other = others.totalwgt_lb.dropna()
mean_diff = 100 * (wgt_first.mean() - wgt_other.mean()) / wgt_live.mean()
wgt_cohend = thinkstats2.CohenEffectSize(wgt_first, wgt_other)
plen_cohend = thinkstats2.CohenEffectSize(firsts.prglngth, others.prglngth)
print('Difference in relative mean:', mean_diff)
print('Cohen\'s d for total weight in lbs:', wgt_cohend)
print('Cohen\'s d for pregnancy length in weeks:', plen_cohend)
#--- Chapter3 Ex1
actual_pmf = thinkstats2.Pmf(resp.numkdhh, label='actual')
biased_pmf = BiasPmf(actual_pmf, label='biased')
thinkplot.PrePlot(2)
actual_hist = thinkplot.Pmf(actual_pmf)
biased_hist = thinkplot.Pmf(biased_pmf)
thinkplot.Show(xlabel='#kids in household', ylabel='PMF')
print('Actual Mean:', actual_pmf.Mean())
print('Biased Mean:', biased_pmf.Mean())
#--- Chapter4 Ex2
my_seq = np.random.random(1000)
my_pmf = thinkstats2.Pmf(my_seq)
my_cdf = thinkstats2.Cdf(my_seq)
thinkplot.Pmf(my_pmf, linewidth=0.1)
thinkplot.Show(xlabel='Random variable', ylabel='PMF')
thinkplot.Cdf(my_cdf)
thinkplot.Show(xlabel='Random variable', ylabel='CDF')
#--- Chapter5 Ex1
