def Main():
# make a redditor with some trustworthiness (mean_t = 0.67)
founder = Redditor(name='redditor')
beta = thinkbayes.Beta(2, 1)
for val, prob in beta.MakePmf().Items():
founder.Set(val * 100, prob)
# make a new item with unknown quality (mean_q = 0.5)
item = Item(range(0, 101), name='item')
# compute the means
mean_t = founder.Mean() / 100.0
mean_q = item.Mean() / 100.0
print mean_t
print mean_q
# perform simultaneous updates
founder.Update(('up', mean_q))
item.Update(('up', mean_t))
Summarize(item)
# display the posterior distributions
myplot.Pmf(founder)
myplot.Pmf(item)
myplot.Show()
def ExpoErlangDemo():
num = 10
lam1 = 1
lam2 = 2
t = MakeSeries(num, lam1, num, lam2)
series = Series(t)
n, s1, m, s2 = series.Split(num)
print n, s1, m, s2
low, high = 0.01, 5.01
lams = numpy.linspace(low, high, 101)
expo = Expo(lams)
expo.name = 'expo'
expo.Update((n, s1))
erlang = Erlang(lams)
erlang.name = 'erlang'
erlang.Update((n, s1))
myplot.Pmf(expo)
myplot.Pmf(erlang)
myplot.Show()
def main():
resp = brfss.Respondents()
resp.ReadRecords(data_dir='res')
d = resp.SummarizeHeight()
man_d = d[1]
lady_d = d[2]
# 男性的mu, var, sigma, 变异系数CV
man_mu, man_var = thinkstats.TrimmedMeanVar(man_d)
man_sigma = math.sqrt(man_var)
man_cv = man_sigma/man_mu
print("man: mu = %.3f, var = %.3f, sigma = %.3f, cv = %.3f" % (man_mu, man_var, man_sigma, man_cv))
# 女性的mu, var, sigma, 变异系数CV
lady_mu, lady_var = thinkstats.TrimmedMeanVar(lady_d)
lady_sigma = math.sqrt(lady_var)
lady_cv = lady_sigma/lady_mu
print("lady: mu = %.3f, var = %.3f, sigma = %.3f, cv = %.3f" % (lady_mu, lady_var, lady_sigma, lady_cv))
# 男性, 女性Hist分布
man_hist = Pmf.MakeHistFromList(man_d, name='man hist')
myplot.Hist(man_hist)
myplot.Show()
myplot.Clf()
lady_hist = Pmf.MakeHistFromList(lady_d, name='lady hist')
myplot.Hist(lady_hist)
myplot.Show()
myplot.Clf()
# 男性, 女性Pmf分布
man_pmf = Pmf.MakePmfFromHist(man_hist, name='man pmf')
myplot.Pmf(man_pmf)
myplot.Show()
myplot.Clf()
lady_pmf = Pmf.MakePmfFromHist(lady_hist, name='lady pmf')
myplot.Pmf(lady_pmf)
myplot.Show()
myplot.Clf()
# 男性/女性Cdf累积分布
man_cdf = Cdf.MakeCdfFromPmf(man_pmf, name='man cdf')
lady_cdf = Cdf.MakeCdfFromPmf(lady_pmf, name='lady cdf')
myplot.Cdfs((man_cdf, lady_cdf), complement=False, transform=None)
myplot.Show()
def main():
# make a uniform prior
param = 1.2
prior = MakeUniformSuite(0.5, 1.5, 1000)
# try out the sample in the book
t = []
sample = [2.675, 0.198, 1.152, 0.787, 2.717, 4.269]
name = 'post%d' % len(sample)
posterior = EstimateParameter(prior, sample, name)
t.append(posterior)
# try out a range of sample sizes
for n in [10, 20, 40]:
# generate a sample
sample = [random.expovariate(param) for _ in range(n)]
name = 'post%d' % n
# compute the posterior
posterior = EstimateParameter(prior, sample, name)
t.append(posterior)
# plot the posterior distributions
for i, posterior in enumerate(t):
pyplot.subplot(2, 2, i+1)
myplot.Pmf(posterior)
pyplot.xlabel('lambda')
pyplot.ylabel('Posterior probability')
pyplot.legend()
myplot.Save(root='posteriors')
def process(data):
# Hist 分布图
hist = Pmf.MakeHistFromList(data, name='hist')
myplot.Hist(hist, color='blue')
myplot.Show()
# Pmf 分布图
pmf = Pmf.MakePmfFromHist(hist, name='pmf')
myplot.Pmf(pmf, color='yellow')
myplot.Show()
myplot.Clf()
# 实际数据的CDF分布图
cdf = Cdf.MakeCdfFromList(data, name='loafs')
myplot.Cdf(cdf)
mu, var = thinkstats.MeanVar(data)
sigma = math.sqrt(var)
print("mu = %.3f, sigma = %.3f" % (mu, sigma))
# 正态分布
xs = normal_sample(len(data), mu, sigma) # xs = data
ys = [erf.NormalCdf(x, mu=mu, sigma=sigma) for x in xs]
myplot.Scatter(xs, ys, color='red', label='sample')
myplot.Show()
def main():
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
# plot the distribution of actual speeds
pmf = Pmf.MakePmfFromList(speeds, 'actual speeds')
# myplot.Clf()
# myplot.Hist(pmf)
# myplot.Save(root='observed_speeds',
# title='PMF of running speed',
# xlabel='speed (mph)',
# ylabel='probability')
# plot the biased distribution seen by the observer
biased = BiasPmf(pmf, 7.5, name='observed speeds')
myplot.Pmf(biased)
myplot.Show(title='soln. PMF of running speed',
xlabel='speed (mph)',
ylabel='probability')
myplot.Clf()
myplot.Hist(biased)
myplot.Save(root='observed_speeds',
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='probability')
cdf = Cdf.MakeCdfFromPmf(biased)
myplot.Clf()
myplot.Cdf(cdf)
myplot.Save(root='observed_speeds_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='cumulative probability')
def observe_data(l, name=None, show=False):
cdf = pmf = None
if isinstance(l, list):
cdf = Cdf.MakeCdfFromList(l,name+' cdf')
pmf = Pmf.MakePmfFromList(l, name+' pmf')
elif isinstance(l, Pmf.Pmf):
pmf = l
cdf = Cdf.MakeCdfFromPmf(l)
if name is None: name = pmf.name
elif isinstance(l, Cdf.Cdf):
cdf = l
if name is None: name = cdf.name
else:
raise Exception('input parameter type is wrong')
v_25, median, v_75 = cdf.Percentile(25), cdf.Percentile(50), cdf.Percentile(75)
mean = cdf.Mean()
print('%s: 1/4:%4.2f(%4.2f), 1/2:%4.2f(mean-median:%4.2f), mean:%4.2f, 3/4:%4.2f(%4.2f)' % \
(name, v_25, median-v_25, median, mean-median, mean, v_75,v_75-median))
if show:
if pmf is not None:
myplot.Pmf(pmf)
myplot.Show()
myplot.Cdf(cdf)
myplot.Show()
def PlotPmf(results):
speeds = GetSpeeds(results)
pmf = Pmf.MakePmfFromList(speeds, 'speeds')
myplot.Pmf(pmf,
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='probability',
show=True)
def main():
results = ReadResults()
speeds = GetSpeeds(results)
pmf = Pmf.MakePmfFromList(speeds, 'speeds')
myplot.Pmf(pmf)
myplot.Show(title='PMF of running speed',
xlabel='speed (mph)',
ylabel='probability')
def main():
hypos = xrange(100, 1001)
suite = Train(hypos)
suite.Update(321)
print suite.Mean()
myplot.Pmf(suite)
myplot.Show()
def main():
list = [100 * random.random() for i in range(1000)]
pmf = Pmf.MakePmfFromList(list, name='pfm')
cdf = Cdf.MakeCdfFromList(list, name='cdf')
myplot.Pmf(pmf)
myplot.Show()
myplot.Clf()
myplot.Cdf(cdf)
myplot.Show()
def PlotSurvivalCurve(ts, lams, ss):
# scale lams
denom = max(lams.Probs())
lams.Normalize(denom)
myplot.Pmf(lams,
line_options=dict(linewidth=2, linestyle='dashed', color='0.7'))
pyplot.plot(ts, ss, linewidth=2, color='blue', label='survival')
myplot.Save(root='seer1',
title='',
xlabel='Survival time (years)',
ylabel='Probability')
def main():
suite = Euro(range(0, 101))
#myplot.Pmf(suite)
#myplot.Show()
for i in range(140):
suite.Update('H')
for i in range(110):
suite.Update('T')
myplot.Pmf(suite)
myplot.Show()
def MakeFigures(exam, alice, bob):
formats = ['png']
myplot.Pmf(exam.prior, label='prior')
myplot.Save(root='sat_prior', formats=formats, xlabel='p', ylabel='PMF')
myplot.Clf()
myplot.Pmfs([alice, bob])
myplot.Save(root='sat_posterior',
formats=formats,
xlabel='p',
ylabel='PMF')
def Main():
suite = Liar(y=0.1)
dataset = 'H'
for data in dataset:
suite.Update(data)
Summarize(suite)
myplot.Pmf(suite)
myplot.Show()
def main():
suite = MakeUniformSuite(0.0, 1.0, 1001)
evidence = 140, 110
Update(suite, evidence)
suite.name = 'posterior'
# plot the posterior distributions
myplot.Pmf(suite)
myplot.Show(title='Biased coin',
xlabel='P(heads)',
ylabel='Posterior probability')
def main(script):
# make an exam object with data from the 2010 SAT
exam = Exam()
# look up Alice's raw score
alice = 780
alice_correct = exam.GetRawScore(alice)
print 'Alice raw score', alice_correct
# display the distribution of raw scores for the population
prior = exam.GetPrior()
myplot.Pmf(prior, show=True)
def ExpoDemo():
num = 10
lam1 = 1
lam2 = 2
t = MakeSeries(num, lam1, num, lam2)
series = Series(t)
n, s1, m, s2 = series.Split(num)
print n, s1, m, s2
low, high = 0.01, 5.01
lams = numpy.linspace(low, high, 101)
expo = Expo(lams)
expo.Update((n, s1))
expo2 = Expo(lams)
expo2.Update((m, s2))
myplot.Pmf(expo)
myplot.Pmf(expo2)
myplot.Show()
def PlotPosteriorSigma(posterior):
ci = CredibleInterval(posterior, 90)
print 'CI:', ci
pyplot.clf()
PlotCredibleInterval(posterior, ci)
myplot.Pmf(posterior,
root='sigma',
clf=False,
title='Posterior PMF',
xlabel='sigma',
ylabel='probability',
show=True)
def main():
suite = MakeUniformSuite(0.001, 1.5, 1000)
evidence = [1.5, 2, 3, 4, 5, 12]
Update(suite, evidence)
suite.name = 'posterior'
# plot the posterior distributions
myplot.Pmf(suite)
myplot.Show(title='Decay parameter',
xlabel='Parameter (inverse cm)',
ylabel='Posterior probability')
print 'Naive parameter estimate:', 1.0 / thinkstats.Mean(evidence)
print 'Mean of the posterior distribution:', suite.Mean()
def main():
# Exercise 3.1
d = {
7: 8,
12: 8,
17: 14,
22: 4,
27: 6,
32: 12,
37: 8,
42: 3,
47: 2
}
classSizeDean = Pmf.MakePmfFromDict(d, name='Actual')
print(classSizeDean.Mean())
classSizeStudent = classSizeDean.Copy(name='Student Perspective')
for x, _ in classSizeStudent.Items():
classSizeStudent.Mult(x, x)
classSizeStudent.Normalize()
print(classSizeStudent.Mean())
classSizeUnbaised = UnbiasPmf(classSizeStudent, 'Student Unbiased')
print(classSizeUnbaised.Mean())
getValue = itemgetter(0)
deanPlot = sorted(classSizeDean.Items(), key=getValue)
studentPlot = sorted(classSizeStudent.Items(), key=getValue)
plt.plot(zip(*deanPlot)[0], zip(*deanPlot)[1], 'g-', label='Actual')
plt.plot(zip(*studentPlot)[0], zip(*studentPlot)[1], 'r-', label='Student Perspective')
plt.legend(loc=4)
plt.xlabel('Class Size')
plt.ylabel('Probability')
plt.show()
#Exercise 3.2
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
unbaisedSpeedsPmf = Pmf.MakePmfFromList(speeds, 'speeds')
biasedSpeedsPmf = BiasPmf(unbaisedSpeedsPmf, 7.5, '7.5 mph biased speeds')
biasedPlot = sorted(biasedSpeedsPmf.Items(), key=getValue)
myplot.Pmf(biasedSpeedsPmf)
myplot.Show(title='7.5mph biased speeds',
xlabel='speeds (mph)',
ylabel='probability')
def main():
ran = generate_random_sample(1000)
pmf = Pmf.MakePmfFromList(ran)
cdf = Cdf.MakeCdfFromPmf(pmf)
myplot.Cdf(cdf)
myplot.show()
myplot.scatter(*cdf.Render())
myplot.show()
myplot.Hist(pmf)
myplot.show()
myplot.Pmf(pmf)
myplot.show()
def main(script, *args):
pmf = UniformOdds()
cdf = Cdf.MakeCdfFromPmf(pmf)
myplot.Cdf(cdf, show=True)
return
beta = Beta(1, 0)
pmf = beta.Pmf()
myplot.Pmf(pmf,
show=True,
xlabel='Probability of sunrise: p',
ylabel='Probability density',
title='Beta distribution')
cdf = beta.Cdf()
print cdf.Percentile(5)
print cdf.Percentile(95)
print cdf.Prob(0.5)
def PlotPosteriorPmf(self, root=None, clf=False):
if root: clf = True
if clf: pyplot.clf()
posterior = self.Pmf()
cdf = self.Cdf()
low, high = cdf.Percentile(5), cdf.Percentile(95)
xs = [x for x in posterior.Values() if low <= x <= high]
ys = [posterior.Prob(x) for x in xs]
pyplot.fill_between(xs, ys, y2=0.0001, color='blue', alpha=0.2)
myplot.Pmf(posterior,
root=root,
clf=False,
xlabel='# of taxa',
ylabel='prob',
legend=False)
def main():
upper_bound = 200
prior = MakeUniformSuite(1, upper_bound, upper_bound)
prior.name = 'prior'
evidence = 60
posterior = prior.Copy()
Update(posterior, evidence)
posterior.name = 'posterior'
print CredibleInterval(posterior, 90)
# plot the posterior distribution
pyplot.subplots_adjust(wspace=0.4, left=0.15)
plot_options = dict(linewidth=2)
myplot.Pmf(posterior, **plot_options)
myplot.Save(root='locomotive',
title='Locomotive problem',
xlabel='Number of trains',
ylabel='Posterior probability')
def main():
# Exercise 3.9
table = survey.Pregnancies()
table.ReadRecords()
unfilteredLiveBirthWeights = [(p.birthwgt_lb, p.birthwgt_oz)
for p in table.records if p.outcome == 1]
liveBirthWeights = [
lbs * 16 + oz for lbs, oz in unfilteredLiveBirthWeights
if type(lbs) == int and type(oz) == int and lbs * 16 + oz <= 200
]
liveBirthWeightsCdf = Cdf.MakeCdfFromList(liveBirthWeights,
name="live birth weights")
samepleListLiveBirthWeights = sample(liveBirthWeightsCdf, 1000)
myplot.Cdf(Cdf.MakeCdfFromList(samepleListLiveBirthWeights))
myplot.show(title="CDF of live births resampled")
# Exercise 3.10
randomList = [random.random() for x in range(1000)]
myplot.Pmf(Pmf.MakePmfFromList(randomList))
myplot.show(title="random pmf")
myplot.Cdf(Cdf.MakeCdfFromList(randomList))
myplot.Show(title="random cdf")
def main():
p = optparse.OptionParser()
p.add_option('--infile', '-i')
p.add_option('--outfile', '-o')
options, arguments = p.parse_args()
ifile = sys.stdin
ofile = sys.stdout
if options.infile is not None:
ifile = open(options.infile, 'r')
if options.outfile is not None:
ofile = open(options.outfile, 'w')
word_count_dict = scan_file(ifile)
cdf = Cdf.MakeCdfFromList(word_count_dict.values())
pmf = Pmf.MakePmfFromList(word_count_dict.values())
#myplot.Cdf(cdf, transform='pareto')
#myplot.Show(title="KJV Biblical word frequency", complement=True, xscale='log', yscale='log')
myplot.Pmf(pmf)
myplot.Show(title='KJV Biblical word frequency',
xscale='log',
yscale='log')
import Cdf import populations import math import myplot import numpy import Pmf pops = populations.ReadData() bucketed_pops = map(lambda(x):50*math.floor(x/50.0),pops) pmf = Pmf.MakePmfFromList(bucketed_pops) cdf = Cdf.MakeCdfFromPmf(pmf) myplot.Pmf(pmf) myplot.Show(title="Pmf of populations", xscale='log') myplot.Cdf(cdf) myplot.Show(title="Cdf of populations", inverse=True, xscale='log') xs = sorted(numpy.random.normal(0, 1, len(pops))) ys = sorted(bucketed_pops) myplot.Plot(xs, ys) myplot.Show(title="Normal plot for populations") ys2 = sorted(map(lambda(y):math.log10(y+1),bucketed_pops)) myplot.Plot(xs, ys2) myplot.Show(title="LogNormal plot for populations") #it looks more like a lognormal, but with a hard lower bound (as expected)
def MakePmf(table):
lengths = [record.prglength for record in table.records]
pmf = Pmf.MakePmfFromList(lengths, name='pregnancy length')
myplot.Pmf(pmf, show=True, xlabel='weeks', ylabel='probability')
# Example 3-10
import random, Pmf, Cdf, myplot
size = 10000
lst = [random.random() for i in range(size)]
lst_pmf = Pmf.MakePmfFromList(lst)
lst_cdf = Cdf.MakeCdfFromList(lst)
myplot.Clf()
myplot.Pmf(lst_pmf)
myplot.Show(title='PMF of {0} randoms'.format(size))
myplot.Clf()
myplot.Cdf(lst_cdf)
myplot.Show(title='CDF of {0} randoms'.format(size))
# yes, the distribution is uniform
