def MakePosteriorPlot(suite):
"""Plots the posterior marginal distributions for alpha and beta.
suite: posterior joint distribution of location
"""
marginal_alpha = suite.Marginal(0)
marginal_alpha.name = 'alpha'
marginal_beta = suite.Marginal(1)
marginal_beta.name = 'beta'
print('alpha CI', marginal_alpha.CredibleInterval(50))
print('beta CI', marginal_beta.CredibleInterval(50))
thinkplot.PrePlot(num=2)
#thinkplot.Pmf(marginal_alpha)
#thinkplot.Pmf(marginal_beta)
thinkplot.Cdf(thinkbayes.MakeCdfFromPmf(marginal_alpha))
thinkplot.Cdf(thinkbayes.MakeCdfFromPmf(marginal_beta))
thinkplot.Save('paintball2',
xlabel='Distance',
ylabel='Prob',
loc=4,
formats=FORMATS)
def PlotCoefVariation(suites):
"""Plot the posterior distributions for CV.
suites: map from label to Pmf of CVs.
"""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
pmfs = {}
for label, suite in suites.iteritems():
pmf = CoefVariation(suite)
print('CV posterior mean', pmf.Mean())
cdf = thinkbayes.MakeCdfFromPmf(pmf, label)
thinkplot.Cdf(cdf)
pmfs[label] = pmf
thinkplot.Save(root='variability_cv',
xlabel='Coefficient of variation',
ylabel='Probability')
print('female bigger',
thinkbayes.PmfProbGreater(pmfs['female'], pmfs['male']))
print('male bigger', thinkbayes.PmfProbGreater(pmfs['male'],
pmfs['female']))
def PlotPosteriors(self, other):
"""Plots posterior distributions of efficacy.
self, other: Sat objects.
"""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
cdf1 = thinkbayes.MakeCdfFromPmf(self, 'posterior %d' % self.score)
cdf2 = thinkbayes.MakeCdfFromPmf(other, 'posterior %d' % other.score)
thinkplot.Cdfs([cdf1, cdf2])
thinkplot.Save(xlabel='efficacy',
ylabel='CDF',
axis=[0, 4.6, 0.0, 1.0],
root='sat_posteriors_eff',
formats=['pdf', 'eps'])
def CalibrateDifficulty(self):
"""Make a plot showing the model distribution of raw scores."""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
cdf = thinkbayes.MakeCdfFromPmf(self.raw, name='data')
thinkplot.Cdf(cdf)
efficacies = thinkbayes.MakeGaussianPmf(0, 1.5, 3)
pmf = self.MakeRawScoreDist(efficacies)
cdf = thinkbayes.MakeCdfFromPmf(pmf, name='model')
thinkplot.Cdf(cdf)
thinkplot.Save(root='sat_calibrate',
xlabel='raw score',
ylabel='CDF',
formats=['pdf', 'eps'])
def CH3_4():
"""
不同先验计算后验
Train: 先验概率为 均匀分布uniform
Train2: 先验概率为 指数分布power law
alpha = 1:
+-------------------------------------+
| 先验概率(未归一化) |
| 1 1/1 0 |
| 2 1/2 0 |
| ... ... ... |
| 59 1/59 0 |
| 60 1/60 1/60 |
| 61 1/61 1/61 |
| ... ... |
| 1000 1/1000 1/1000 |
+-------------------------------------+
"""
dataset = [60]
N = 1000
def _makePosterior(uppernum, constructor, dataset):
"""
根据构造器函数和数据集, 生成后验概率suite
"""
suite = constructor(range(1, uppernum))
for data in dataset:
suite.Update(data)
return suite
thinkplot.Clf()
thinkplot.PrePlot(num=2)
constructors = [Train, Train2]
labels = ['uniform', 'power law']
for constructor, label in zip(constructors, labels):
suite = _makePosterior(N, constructor, dataset)
suite.name = label
thinkplot.Pmf(suite)
thinkplot.Show(title='compare priors', xlabel='Number of trains', ylabel='prob')
dataset = [60, 30, 90]
for constructor, label in zip(constructors, labels):
for n in [500, 1000, 2000]:
suite = _makePosterior(n, constructor, dataset)
# 单点估计
print("%s: n = %d, mu = %.3f" % (label, n, suite.Mean()))
# 后验概率的置信区间5% - 95% (see CH3_5)
interval = thinkbayes.Percentile(suite, 5), thinkbayes.Percentile(suite, 95)
print(interval)
# CH3_6, 累计分布函数计算百分位数
if n == 2000:
cdf = thinkbayes.MakeCdfFromPmf(suite)
interval = cdf.Percentile(5), cdf.Percentile(95)
print("MakeCdfFromPmf:", interval)
def PlotMarginals(suite):
"""Plots marginal distributions from a joint distribution.
suite: joint distribution of mu and sigma.
"""
thinkplot.Clf()
pyplot.subplot(1, 2, 1)
pmf_m = suite.Marginal(0)
cdf_m = thinkbayes.MakeCdfFromPmf(pmf_m)
thinkplot.Cdf(cdf_m)
pyplot.subplot(1, 2, 2)
pmf_s = suite.Marginal(1)
cdf_s = thinkbayes.MakeCdfFromPmf(pmf_s)
thinkplot.Cdf(cdf_s)
thinkplot.Show()
def GenerateSampleGaps(self, n):
"""Generates a random sample of gaps seen by passengers.
n: sample size
Returns: sequence of values
"""
cdf_zb = thinkbayes.MakeCdfFromPmf(self.pmf_zb)
sample = cdf_zb.Sample(n)
return sample
def GenerateSampleWaitTimes(self, n):
"""Generates a random sample of wait times.
n: sample size
Returns: sequence of values
"""
cdf_y = thinkbayes.MakeCdfFromPmf(self.pmf_y)
sample = cdf_y.Sample(n)
return sample
def PlotPriorDist(pmf):
"""Plot the prior distribution of p_correct.
pmf: prior
"""
thinkplot.Clf()
thinkplot.PrePlot(num=1)
cdf1 = thinkbayes.MakeCdfFromPmf(pmf, 'prior')
thinkplot.Cdf(cdf1)
thinkplot.Save(root='sat_prior',
xlabel='p_correct',
ylabel='CDF',
formats=['pdf', 'eps'])
def main(script, *args):
#random.seed(22)
lam1 = 1
lam2 = 1.5
n = 300
t = MakeSeries(n, lam1, n, lam2)
series = Series(t)
low, high = 0.01, 5.01
for cons in [Split2, Split3]:
print cons.__name__
split = cons(series.n, low, high)
split.Update(series)
cdf = thinkbayes.MakeCdfFromPmf(split)
cdf.name = cons.__name__
myplot.Cdf(cdf)
myplot.Show()
def main():
ComparePriors()
dataset = [30, 60, 90]
thinkplot.Clf()
thinkplot.PrePlot(num=3)
for high in [500, 1000, 2000]:
suite = MakePosterior(high, dataset, Train2)
print(high, suite.Mean())
thinkplot.Save(root='train3',
xlabel='Number of trains',
ylabel='Probability')
interval = Percentile(suite, 5), Percentile(suite, 95)
print(interval)
cdf = thinkbayes.MakeCdfFromPmf(suite)
interval = cdf.Percentile(5), cdf.Percentile(95)
print(interval)
def addTeam( self, team, this_team, rest_of_league ):
this_x_cdf = tb.MakeCdfFromPmf( tb.MakePmfFromList( this_team.X ) )
this_y_cdf = tb.MakeCdfFromPmf( tb.MakePmfFromList( this_team.Y ) )
other_x_cdf = tb.MakeCdfFromPmf( tb.MakePmfFromList( rest_of_league.X ) )
other_y_cdf = tb.MakeCdfFromPmf( tb.MakePmfFromList( rest_of_league.Y ) )
self.addCDFs( team, this_x_cdf, this_y_cdf, other_x_cdf, other_y_cdf )