def RunLoop(gap_times, nums, lam=0.0333):
"""Runs the basic analysis for a range of num_passengers.
gap_times: sequence of float
nums: sequence of values for num_passengers
lam: arrival rate in passengers per second
Returns: WaitMixtureEstimator
"""
global UPPER_BOUND
UPPER_BOUND = 4000
thinkplot.Clf()
RandomSeed(18)
# resample gap_times
n = 220
cdf_z = thinkbayes.MakeCdfFromList(gap_times)
sample_z = cdf_z.Sample(n)
pmf_z = thinkbayes.MakePmfFromList(sample_z)
# compute the biased pmf and add some long delays
cdf_zp = BiasPmf(pmf_z).MakeCdf()
sample_zb = cdf_zp.Sample(n) + [1800, 2400, 3000]
# smooth the distribution of zb
pdf_zb = thinkbayes.EstimatedPdf(sample_zb)
xs = MakeRange(low=60)
pmf_zb = pdf_zb.MakePmf(xs)
# unbias the distribution of zb and make wtc
pmf_z = UnbiasPmf(pmf_zb)
wtc = WaitTimeCalculator(pmf_z)
probs = []
for num_passengers in nums:
ete = ElapsedTimeEstimator(wtc, lam, num_passengers)
# compute the posterior prob of waiting more than 15 minutes
cdf_y = ete.pmf_y.MakeCdf()
prob = 1 - cdf_y.Prob(900)
probs.append(prob)
# thinkplot.Cdf(ete.pmf_y.MakeCdf(name=str(num_passengers)))
thinkplot.Plot(nums, probs)
thinkplot.Save(
root='redline5',
xlabel='Num passengers',
ylabel='P(y > 15 min)',
formats=FORMATS,
)
def PlotPosterior(suite, pcolor=False, contour=True):
"""Makes a contour plot.
suite: Suite that maps (mu, sigma) to probability
"""
thinkplot.Clf()
thinkplot.Contour(suite.GetDict(), pcolor=pcolor, contour=contour)
thinkplot.Save(root='variability_posterior_%s' % suite.name,
title='Posterior joint distribution',
xlabel='Mean height (cm)',
ylabel='Stddev (cm)')
def MakePlots(player1, player2):
"""Generates two plots.
price1 shows the priors for the two players
price2 shows the distribution of diff for the two players
"""
# plot the prior distribution of price for both players
thinkplot.Clf()
thinkplot.PrePlot(num=2)
pmf1 = player1.PmfPrice()
pmf1.name = 'showcase 1'
pmf2 = player2.PmfPrice()
pmf2.name = 'showcase 2'
thinkplot.Pmfs([pmf1, pmf2])
thinkplot.Save(root='price1',
xlabel='price ($)',
ylabel='PDF',
formats=FORMATS)
# plot the historical distribution of underness for both players
thinkplot.Clf()
thinkplot.PrePlot(num=2)
cdf1 = player1.CdfDiff()
cdf1.name = 'player 1'
cdf2 = player2.CdfDiff()
cdf2.name = 'player 2'
print 'Player median', cdf1.Percentile(50)
print 'Player median', cdf2.Percentile(50)
print 'Player 1 overbids', player1.ProbOverbid()
print 'Player 2 overbids', player2.ProbOverbid()
thinkplot.Cdfs([cdf1, cdf2])
thinkplot.Save(root='price2',
xlabel='diff ($)',
ylabel='CDF',
formats=FORMATS)
def PlotJointDist(self):
"""Makes a pcolor plot of the age-size joint distribution."""
thinkplot.Clf()
joint = self.cache.GetDistAgeSize()
thinkplot.Contour(joint, contour=False, pcolor=True)
thinkplot.Save(root='kidney8',
formats=FORMATS,
axis=[0, 41, -0.7, 1.31],
yticks=MakeLogTicks([0.2, 0.5, 1, 2, 5, 10, 20]),
xlabel='ages',
ylabel='diameter (cm, log scale)')
def PlotSuites(suites, root):
"""Plots two suites.
suite1, suite2: Suite objects
root: string filename to write
"""
thinkplot.Clf()
thinkplot.PrePlot(len(suites))
thinkplot.Pmfs(suites)
thinkplot.Save(root=root,
xlabel='x',
ylabel='Probability',
formats=['pdf', 'eps'])
def _test1(show=0):
# 已知r, 求n的分布 即泊松分布
r = 150
# MakePoissonPmf: 存在一个上限(无极限), 需要归一化
pmf = thinkbayes2.MakePoissonPmf(r, 2 * r, 1)
if show:
thinkplot.Clf()
thinkplot.Pmf(pmf)
thinkplot.Show(title="test1",
xlabel='Event Count',
ylabel='Probality')
print("Total: ", pmf.Total())
return pmf
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 _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 PlotPmfs(self, root='redline0'):
"""Plots the computed Pmfs.
root: string
"""
pmfs = ScaleDists([self.pmf_z, self.pmf_zb], 1.0 / 60)
thinkplot.Clf()
thinkplot.PrePlot(2)
thinkplot.Pmfs(pmfs)
thinkplot.Save(root=root,
xlabel='Time (min)',
ylabel='CDF',
formats=FORMATS)
def CH6_5(diff1, diff2):
"""
两组展品的出价差的CDF累计分布
"""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
diff1_cdf = thinkbayes.MakeCdfFromList(diff1, name='diff1')
diff2_cdf = thinkbayes.MakeCdfFromList(diff2, name='diff2')
thinkplot.Cdfs([diff1_cdf, diff2_cdf])
thinkplot.Show(xlabel='diff $', ylabel="CDF")
# 计算CDF(diff <= 0), 判断选手是否偏向低估商品
print(diff1_cdf.Prob(0), diff2_cdf.Prob(0))
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 PlotOutliers(samples):
"""Make CDFs showing the distribution of outliers."""
cdfs = []
for label, sample in samples.iteritems():
outliers = [x for x in sample if x < 150]
cdf = thinkbayes.MakeCdfFromList(outliers, label)
cdfs.append(cdf)
thinkplot.Clf()
thinkplot.Cdfs(cdfs)
thinkplot.Save(root='variability_cdfs',
title='CDF of height',
xlabel='Reported height (cm)',
ylabel='CDF')
def PlotSuites(suites, root):
"""Plots two suites.
suite1, suite2: Suite objects
root: string filename to write
"""
formats = ['pdf', 'png']
thinkplot.Clf()
thinkplot.PrePlot(len(suites))
thinkplot.Pmfs(suites)
thinkplot.Save(root=root,
xlabel='Percentage of Active Female Users',
ylabel='Probability',
formats=formats,
legend=True)
def sim_pearson(perfs, p1, p2):
"""
皮尔逊相关系数(Pearson correlation coefficient)
cov(X, Y) / sigmaX*sigmaY
协方差(X,Y) / X的标准方差*Y的标准方差
"""
shared_items = {}
for item in perfs[p1]:
if item in perfs[p2]:
shared_items[item] = 1
n = len(shared_items)
if n == 0: return 0
# p1, p2共同的影评数据
data_p1 = [perfs[p1][it] for it in shared_items]
data_p2 = [perfs[p2][it] for it in shared_items]
# 计算影评均值
mu_p1 = sum(data_p1) / n
mu_p2 = sum(data_p2) / n
# print(mu_p1, mu_p2)
# 计算标准方差
var_p1 = sum([pow(it-mu_p1, 2) for it in data_p1]) / n
var_p2 = sum([pow(it-mu_p2, 2) for it in data_p2]) / n
# print(var_p1, var_p2)
if var_p1 == 0 or var_p2 == 0: return 0
# 计算协方差
cov = sum([(x-mu_p1)*(y-mu_p2) for x, y in zip(data_p1, data_p2)]) / n
# print(cov)
# 计算皮尔逊相关系数
r = cov / sqrt(var_p1*var_p2)
# ============ thinkstat 方法 ===============
if show:
rr = correlation.Corr(data_p1, data_p2)
print(r, rr)
thinkplot.Clf()
thinkplot.Scatter(data_p1, data_p2)
thinkplot.Show()
return r
def PlotCdfs(d, labels):
"""Plot CDFs for each sequence in a dictionary.
Jitters the data and subtracts away the mean.
d: map from key to sequence of values
labels: map from key to string label
"""
thinkplot.Clf()
for key, xs in d.iteritems():
mu = thinkstats.Mean(xs)
xs = thinkstats.Jitter(xs, 1.3)
xs = [x - mu for x in xs]
cdf = thinkbayes.MakeCdfFromList(xs)
thinkplot.Cdf(cdf, label=labels[key])
thinkplot.Show()
def main():
h1 = Hockey()
h2 = Hockey()
h1.UpdateSet([0, 2, 8, 4])
h2.UpdateSet([0, 1, 2, 3])
h1 = MakeGoalPmf(h1)
h2 = MakeGoalPmf(h2)
thinkplot.Clf()
thinkplot.preplot(num=2)
thinkplot.Pmf(h1)
thinkplot.Pmf(h2)
thinkplot.Save(root='hockey_self5_MakeGoalPmf',
xlabel='',
ylabel='Probability',
formats=['pdf'])
def CalibrateDifficulty(self):
"""Make a plot showing the model distribution of raw scores."""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
cdf = thinkbayes2.Cdf(self.raw, label='data')
thinkplot.Cdf(cdf)
efficacies = thinkbayes2.MakeNormalPmf(0, 1.5, 3)
pmf = self.MakeRawScoreDist(efficacies)
cdf = thinkbayes2.Cdf(pmf, label='model')
thinkplot.Cdf(cdf)
thinkplot.Save(root='sat_calibrate',
xlabel='raw score',
ylabel='CDF',
formats=['pdf', 'eps'])
def PlotPosteriors(self, other):
"""Plots posterior distributions of efficacy.
self, other: Sat objects.
"""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
cdf1 = thinkbayes2.Cdf(self, label='posterior %d' % self.score)
cdf2 = thinkbayes2.Cdf(other, label='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 PlotBuckets(self):
"""Plots the set of sequences that ended in a given bucket."""
# 2.01, 4.95 cm, 9.97 cm
buckets = [7.0, 16.0, 23.0]
buckets = [23.0]
colors = ['blue', 'green', 'red', 'cyan']
thinkplot.Clf()
for bucket, color in zip(buckets, colors):
self.PlotBucket(bucket, color)
thinkplot.Save(root='kidney5',
formats=FORMATS,
title='History of simulated tumors',
axis=[-40, 1, MINSIZE, 12],
xlabel='years',
ylabel='diameter (cm, log scale)',
yscale='log')
def QQPlot(cdf, fit):
"""Makes a QQPlot of the values from actual and fitted distributions.
cdf: actual Cdf of RDT
fit: model
"""
xs = [-1.5, 5.5]
thinkplot.Clf()
thinkplot.Plot(xs, xs, 'b-')
xs, ps = cdf.xs, cdf.ps
fs = [fit.Value(p) for p in ps]
thinkplot.Plot(xs, fs, 'gs')
thinkplot.Save(root='kidney3',
formats=FORMATS,
xlabel='Actual',
ylabel='Model')
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 MakePlot(self, root='redline1'):
"""Plot the prior and posterior CDF of passengers arrival rate.
root: string
"""
thinkplot.Clf()
thinkplot.PrePlot(2)
# convert units to passengers per minute
prior = self.prior_lam.MakeCdf().Scale(60)
post = self.post_lam.MakeCdf().Scale(60)
thinkplot.Cdfs([prior, post])
thinkplot.Save(root=root,
xlabel='Arrival rate (passengers / min)',
ylabel='CDF',
formats=FORMATS)
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 MakePlot(self, root='redline3'):
"""Plot the CDFs.
root: string
"""
# observed gaps
cdf_prior_x = self.prior_x.MakeCdf()
cdf_post_x = self.post_x.MakeCdf()
cdf_y = self.pmf_y.MakeCdf()
cdfs = ScaleDists([cdf_prior_x, cdf_post_x, cdf_y], 1.0 / 60)
thinkplot.Clf()
thinkplot.PrePlot(3)
thinkplot.Cdfs(cdfs)
thinkplot.Save(root=root,
xlabel='Time (min)',
ylabel='CDF',
formats=FORMATS)
def PlotConditionalCdfs(self):
"""Plots the cdf of ages for each bucket."""
buckets = [7.0, 16.0, 23.0, 27.0]
# 2.01, 4.95 cm, 9.97 cm, 14.879 cm
names = ['2 cm', '5 cm', '10 cm', '15 cm']
cdfs = []
for bucket, name in zip(buckets, names):
cdf = self.cache.ConditionalCdf(bucket, name)
cdfs.append(cdf)
thinkplot.Clf()
thinkplot.PrePlot(num=len(cdfs))
thinkplot.Cdfs(cdfs)
thinkplot.Save(root='kidney6',
title='Distribution of age for several diameters',
formats=FORMATS,
xlabel='tumor age (years)',
ylabel='CDF',
loc=4)
def PlotExpectedGains(guess1=20000, guess2=40000, path='.', save=True):
"""Plots expected gains as a function of bid.
guess1: player1's estimate of the price of showcase 1
guess2: player2's estimate of the price of showcase 2
"""
player1, player2 = MakePlayers(path)
MakePlots(player1, player2)
player1.MakeBeliefs(guess1)
player2.MakeBeliefs(guess2)
print('Player 1 prior mle', player1.prior.MaximumLikelihood())
print('Player 2 prior mle', player2.prior.MaximumLikelihood())
print('Player 1 mean', player1.posterior.Mean())
print('Player 2 mean', player2.posterior.Mean())
print('Player 1 mle', player1.posterior.MaximumLikelihood())
print('Player 2 mle', player2.posterior.MaximumLikelihood())
player1.PlotBeliefs('price3')
player2.PlotBeliefs('price4')
calc1 = GainCalculator(player1, player2)
calc2 = GainCalculator(player2, player1)
thinkplot.Clf()
thinkplot.PrePlot(num=2)
bids, gains = calc1.ExpectedGains()
thinkplot.Plot(bids, gains, label='Player 1')
print('Player 1 optimal bid', max(zip(gains, bids)))
bids, gains = calc2.ExpectedGains()
thinkplot.Plot(bids, gains, label='Player 2')
print('Player 2 optimal bid', max(zip(gains, bids)))
if save:
thinkplot.Save(root='price5',
xlabel='bid ($)',
ylabel='expected gain ($)',
formats=FORMATS)
def MakePlot(self, root='redline2'):
"""Plots the computed CDFs.
root: string
"""
print('Mean z', self.pmf_z.Mean() / 60)
print('Mean zb', self.pmf_zb.Mean() / 60)
print('Mean y', self.pmf_y.Mean() / 60)
cdf_z = self.pmf_z.MakeCdf()
cdf_zb = self.pmf_zb.MakeCdf()
cdf_y = self.pmf_y.MakeCdf()
cdfs = ScaleDists([cdf_z, cdf_zb, cdf_y], 1.0 / 60)
thinkplot.Clf()
thinkplot.PrePlot(3)
thinkplot.Cdfs(cdfs)
thinkplot.Save(root=root,
xlabel='Time (min)',
ylabel='CDF',
formats=FORMATS)
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 CH6_2(price1, price2):
"""
两组展览品的价格分布
"""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
# 因为price变量值没有重复的, 所以PMF绘图是看不出什么的.
# price1_pmf = thinkbayes.MakePmfFromList(price1, name='showcase1')
# price2_pmf = thinkbayes.MakePmfFromList(price2, name='showcase2')
price1_max = max(price1)
price2_max = max(price2)
price_max = max(price1_max, price2_max)
xs = numpy.linspace(0, price_max + 100, num=150)
price1_pdf = thinkbayes.EstimatedPdf(price1)
price2_pdf = thinkbayes.EstimatedPdf(price2)
price1_pmf = price1_pdf.MakePmf(xs, name='showcase1')
price2_pmf = price2_pdf.MakePmf(xs, name='showcase2')
thinkplot.Pmfs([price1_pmf, price2_pmf])
thinkplot.Show(xlabel='price $', ylabel='PMF')
def MakePlot(self, root='redline4'):
"""Makes a plot showing the mixture."""
thinkplot.Clf()
# plot the MetaPmf
# for pmf, prob in sorted(self.metapmf.Items()):
for pmf, prob in self.metapmf.Items():
cdf = pmf.MakeCdf().Scale(1.0/60)
width = 2/math.log(-math.log(prob))
thinkplot.Plot(cdf.xs, cdf.ps,
alpha=0.2, linewidth=width, color='blue',
label='')
# plot the mixture and the distribution based on a point estimate
thinkplot.PrePlot(2)
#thinkplot.Cdf(self.point.MakeCdf(name='point').Scale(1.0/60))
thinkplot.Cdf(self.mixture.MakeCdf(name='mix').Scale(1.0/60))
thinkplot.Save(root=root,
xlabel='Wait time (min)',
ylabel='CDF',
formats=FORMATS,
axis=[0,10,0,1])
