def main():
hypos = numpy.linspace(0, 12, 201)
# start with a prior based on a pseudo observation
# chosen to yield the right prior mean
suite1 = Soccer(hypos, label='Germany')
suite1.Update(0.34)
suite2 = suite1.Copy(label='Argentina')
# update with the results of World Cup 2014 final
suite1.Update(1)
suite2.Update(0)
print('posterior mean Germany', suite1.Mean())
print('posterior mean Argentina', suite2.Mean())
# plot the posteriors
thinkplot.PrePlot(2)
thinkplot.Pdfs([suite1, suite2])
thinkplot.Show()
# TODO: compute posterior prob Germany is better than Argentina
# TODO: compute the Bayes factor of the evidence
# compute predictive distributions for goals scored in a rematch
pred1 = suite1.PredictiveDist(label='Germany')
pred2 = suite2.PredictiveDist(label='Argentina')
# plot the predictive distributions
thinkplot.PrePlot(2)
thinkplot.Pdfs([pred1, pred2])
thinkplot.Show()
def main():
"""
"""
user = User(label='user')
beta = thinkbayes2.Beta(2, 1)
for val, prob in beta.MakePmf().Items():
user.Set(val * 100, prob)
thinkplot.Pdf(user)
thinkplot.Show()
print(user.Mean(), user.CredibleInterval(90))
mean_r = user.Mean() / 100.0
link = Link(range(0, 101), label='link')
thinkplot.Pdf(link)
thinkplot.Show()
print(link.Mean(), link.CredibleInterval(90))
mean_q = link.Mean() / 100.0
user.Update(('up', mean_q))
thinkplot.Pdf(user)
thinkplot.Show()
print(user.Mean(), user.CredibleInterval(90))
link.Update(('up', mean_r))
thinkplot.Pdf(link)
thinkplot.Show()
print(link.Mean(), link.CredibleInterval(90))
return 0
def CH7_3(show = 1):
"""
计算后验分布
棕熊队 加人队
bruins canucks
0 1
2 3
8 1
4 0
"""
suite1 = Hockey('bruins')
suite2 = Hockey('canucks')
if show:
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(suite1)
thinkplot.Pmf(suite2)
thinkplot.Show(title='PRE', xlabel='Goals per game', ylabel='Probability')
suite1.UpdateSet([0, 2, 8, 4])
suite2.UpdateSet([1, 3, 1, 0])
if show:
# 观察最有可能lam的值, 每场比赛进球数的后验分布
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(suite1)
thinkplot.Pmf(suite2)
thinkplot.Show(title='POST', xlabel='Goals per game', ylabel='Probability')
return suite1, suite2
def CycleExtract(fw, data, pnum, trial, plane, marker, plot, plot2):
if fw == 'AFO':
choicedata = data[0]
elif fw == 'PPAFO':
choicedata = data[1]
elif fw == 'Shoes':
choicedata = data[2]
strike_charac, strike_loc = HeelStrike(fw, data, pnum, trial, marker, plot)
num_cycles = len(strike_charac)
dataframe = choicedata[pnum].GetTrial(trial).GetData(plane)
cycle_set = []
for i in range(num_cycles - 1):
start_rowindex = strike_charac[i][0] + 40
end_rowindex = strike_charac[i + 1][0] + 50
cycle = dataframe[start_rowindex:end_rowindex]
index = range(start_rowindex, end_rowindex, 1)
cycle_set.append((index, cycle))
if plot2 == True:
for j in range(len(cycle_set)):
index, cycle = cycle_set[j]
thinkplot.Plot(dataframe['R_HEEL'],
color='blue',
label='Right full set')
thinkplot.Plot(index,
cycle['R_HEEL'],
color='red',
label='Right cycle set')
thinkplot.Show(legend=True)
thinkplot.Plot(dataframe['L_HEEL'],
color='blue',
label='Left full set')
thinkplot.Plot(index,
cycle['L_HEEL'],
color='red',
label='Left cycle set')
thinkplot.Show(legend=True)
return cycle_set
def sin_spectrum():
wave = thinkdsp.make_note(69, 0.5, SinSignal)
spectrum = wave.spectrum()
spectrum.plot()
thinkplot.Show()
peaks = spectrum.peaks()
print peaks[0]
wave2 = spectrum.make_wave()
wave2.plot()
thinkplot.Show()
wave2.write()
def main():
filename = 'mystery0.dat'
data = read_file(filename)
cdf = thinkstats2.MakeCdfFromList(data)
thinkplot.SubPlot(2, 3, 1)
thinkplot.Cdf(cdf)
thinkplot.Config(title='linear')
thinkplot.SubPlot(2, 3, 2)
scale = thinkplot.Cdf(cdf, xscale='log')
thinkplot.Config(title='logx', **scale)
thinkplot.SubPlot(2, 3, 3)
scale = thinkplot.Cdf(cdf, transform='exponential')
thinkplot.Config(title='expo', **scale)
thinkplot.SubPlot(2, 3, 4)
xs, ys = thinkstats2.NormalProbability(data)
thinkplot.Plot(xs, ys)
thinkplot.Config(title='normal')
thinkplot.SubPlot(2, 3, 5)
scale = thinkplot.Cdf(cdf, transform='pareto')
thinkplot.Config(title='pareto', **scale)
thinkplot.SubPlot(2, 3, 6)
scale = thinkplot.Cdf(cdf, transform='weibull')
thinkplot.Config(title='weibull', **scale)
thinkplot.Show()
def main(script, filename='mystery0.dat'):
data = ReadFile(filename)
cdf = thinkstats2.Cdf(data)
thinkplot.PrePlot(num=6, rows=2, cols=3)
thinkplot.SubPlot(1)
thinkplot.Cdf(cdf, color='C0', label=filename)
thinkplot.Config(title='CDF on linear scale', ylabel='CDF')
thinkplot.SubPlot(2)
scale = thinkplot.Cdf(cdf, xscale='log', color='C0')
thinkplot.Config(title='CDF on log-x scale', ylabel='CDF', **scale)
thinkplot.SubPlot(3)
scale = thinkplot.Cdf(cdf, transform='exponential', color='C0')
thinkplot.Config(title='CCDF on log-y scale', ylabel='log CCDF', **scale)
thinkplot.SubPlot(4)
xs, ys = thinkstats2.NormalProbability(data)
thinkplot.Plot(xs, ys, color='C0')
thinkplot.Config(title='Normal probability plot',
xlabel='random normal',
ylabel='data')
thinkplot.SubPlot(5)
scale = thinkplot.Cdf(cdf, transform='pareto', color='C0')
thinkplot.Config(title='CCDF on log-log scale', ylabel='log CCDF', **scale)
thinkplot.SubPlot(6)
scale = thinkplot.Cdf(cdf, transform='weibull', color='C0')
thinkplot.Config(title='CCDF on loglog-y log-x scale',
ylabel='log log CCDF',
**scale)
thinkplot.Show(legend=False)
def ClassSizes():
# start with the actual distribution of class sizes from the book
d = {
7: 8,
12: 8,
17: 14,
22: 4,
27: 6,
32: 12,
37: 8,
42: 3,
47: 2,
}
# form the pmf
pmf = thinkstats2.MakePmfFromDict(d, 'actual')
print 'mean', pmf.Mean()
print 'var', pmf.Var()
# compute the biased pmf
biased_pmf = BiasPmf(pmf, 'observed')
print 'mean', biased_pmf.Mean()
print 'var', biased_pmf.Var()
# unbias the biased pmf
unbiased_pmf = UnbiasPmf(biased_pmf, 'unbiased')
print 'mean', unbiased_pmf.Mean()
print 'var', unbiased_pmf.Var()
# plot the Pmfs
thinkplot.Pmfs([pmf, biased_pmf])
thinkplot.Show(xlabel='Class size', ylabel='PMF')
def main():
k = 15
f = 0.1
# plot Detector suites for a range of hypothetical r
thinkplot.PrePlot(num=3)
for r in [100, 250, 400]:
suite = Detector(r, f, step=1)
suite.Update(k)
thinkplot.Pmf(suite)
print(suite.MaximumLikelihood())
thinkplot.Show(xlabel='Number of particles (n)', ylabel='PMF')
return
# plot the posterior distributions of r and n
hypos = range(1, 501, 5)
suite = Emitter2(hypos, f=f)
suite.Update(k)
thinkplot.PrePlot(num=2)
post_r = suite.DistOfR(name='posterior r')
post_n = suite.DistOfN(name='posterior n')
thinkplot.Pmf(post_r)
thinkplot.Pmf(post_n)
thinkplot.Save(root='jaynes2',
xlabel='Emission rate',
ylabel='PMF',
formats=FORMATS)
def scatter(x):
tot_crimes = df.Total_crimes
thinkplot.Scatter(df[x], tot_crimes, alpha=.5)
if x == 'month':
thinkplot.Show(title="Total Crimes vs Time",
xlabel="Year",
ylabel="Total Crimes")
else:
thinkplot.Show(title="Total Crimes vs " + x + " Crimes",
xlabel=x + " Crimes",
ylabel="Total Crimes")
print(x + " crime stats")
print("Spearman's correlation:",
thinkstats2.SpearmanCorr(tot_crimes, df[x]))
print("Covariance:", thinkstats2.Cov(tot_crimes, df[x]))
print()
def main():
probs = numpy.linspace(0, 1, 101)
hypos = []
for q in probs:
for r in probs:
hypos.append((q, r))
suite = Volunteer(hypos)
# update the Suite with the larger sample of students who
# signed up and reported
data = 140, 50
suite.Update(data)
# update again with the smaller sample of students who signed
# up, participated, and reported
data = 5, 3, 1
suite.Update(data)
#p_marginal = MarginalProduct(suite)
q_marginal = MarginalDistribution(suite, 0)
r_marginal = MarginalDistribution(suite, 1)
thinkplot.Pmf(q_marginal, label='q')
thinkplot.Pmf(r_marginal, label='r')
#thinkplot.Pmf(p_marginal)
thinkplot.Show()
def main():
suite = Version3()
print(suite.Mean())
thinkplot.Pdf(suite)
thinkplot.Show(legend=False)
def main():
suite = Version3()
print suite.Mean()
thinkplot.Pmf(suite)
thinkplot.Show()
def main():
df = hinc.ReadData()
log_sample = InterpolateSample(df, log_upper=6.0)
log_cdf = thinkstats2.Cdf(log_sample)
print("median", thinkstats2.Median(log_sample))
print("pearson's median skewness",
thinkstats2.PearsonMedianSkewness(log_sample))
print("skewness", thinkstats2.Skewness(log_sample))
print("mean", log_cdf.Mean())
print(
"the higher our log_upper, the more right-skewed (according to g_1) or at least less left-skewed (according to g_p) things get"
)
print("the mean moves to the right a bit, too.")
print("proportion of the population with income < mean",
log_cdf.Prob(log_cdf.Mean()))
print(
"the higher the upper bound, the greater the proprtion below the mean."
)
thinkplot.Cdf(log_cdf)
thinkplot.Show(xlabel='household income', ylabel='CDF')
def main():
suite = Euro(range(0, 101))
suite.Update('H')
thinkplot.Pdf(suite)
thinkplot.Show(xlabel='x', ylabel='Probability', legend=False)
def Specific_Character(House, Gender, Class, ksweep, lamsweep, Title=''):
"""Knits many function together to produce a prediction for a given house, gender and class
The house can be any key in hd, class can be 'Noble' or 'Small' or 'All' , and the gender can
be 'M' or 'F' or 'All'. This also needs to make a linspace for k and lambda, so ksweep and
lsweep are lists of the form [lower limit, upper limit, number of points]. You can also
choose what to title your graph."""
hd = PrepData() #Get the data
alive, dead = char_lists(hd, House, Gender,
Class) #Sort by alive/dead for given attributes
introductions, lifetimes = ages(alive, dead) #Get ages and lifespans
sf, haz = SurvivalHaz(introductions, lifetimes) #Use kaplan-meyer
lam = thinkbayes2.MakeUniformPmf(lamsweep[0], lamsweep[1],
lamsweep[2]) #Our uniform priors
k = thinkbayes2.MakeUniformPmf(ksweep[0], ksweep[1], ksweep[2])
k, lam = MakeDistr(introductions, lifetimes, k, lam) #Get our posterior
thinkplot.PrePlot(2)
thinkplot.Pdfs([k, lam])
plt.xlabel('Value')
plt.ylabel('Probability')
plt.title('Posterior Distributions')
print('If these distributions look chopped off, adjust kweep and lsweep')
thinkplot.Show()
mk = k.Mean()
ml = lam.Mean()
kl, kh = k.Percentile(5), k.Percentile(95)
ll, lh = lam.Percentile(5), lam.Percentile(95)
CredIntPlt(sf, kl, kh, ll, lh, House, mk, ml, Title)
plt.show()
def CH5_5():
"""
最大值操作:
转动3个6面的骰子, 计算它们的最大值 采用下面三种方式, 对比分布图.
模拟:
枚举:
指数计算:
"""
d6 = Die(6)
k = 3
# 模拟
N = 1000
dists = [d6] * k
pmf = SampleMax(dists, N)
pmf.name = 'sim'
thinkplot.Pmf(pmf)
# 枚举 km^2
pmf = PmfMax(d6, d6)
print("pmf1.Total() = %.3f" % pmf.Total())
pmf = PmfMax(pmf, d6)
print("pmf2.Total() = %.3f" % pmf.Total())
pmf.name = 'enum'
thinkplot.Pmf(pmf)
# CDF (指数max) TODO 不是很明白???
cdf = d6.Max(k)
cdf.name = "expo"
thinkplot.Cdf(cdf)
thinkplot.Show(xlabel='max([d6]*3)', ylabel='probablity')
def CH5_4():
"""
加法操作:
转动3个6面的骰子, 计算它们的和, 采用下面两种方式, 对比分布图.
模拟:
通过模拟随机样品, 累积和.
枚举:
枚举所有可能的数字对
"""
d6 = Die(6)
k = 3
print("mean(d6) = %.3f, sum(probs) = %.3f" % (d6.Mean(), d6.Total()))
# 模拟: 3个骰子分布, N越大越精确. 缺点: 耗时.
N = 1000
dists = [d6] * k
pmf = thinkbayes.SampleSum(dists, N)
pmf.name = 'sim'
thinkplot.Pmf(pmf)
print("mean([d6]*3) = %.3f, sum(*) = %.3f" % (pmf.Mean(), pmf.Total()))
# 枚举: x数值相加, y概率相乘
pmf = d6 + d6 + d6
pmf.name = 'enum'
thinkplot.Pmf(pmf)
thinkplot.Show(xlabel='sum([d6]*3)', ylabel='probablity')
print("mean([d6]*3) = %.3f, sum(*) = %.3f" % (pmf.Mean(), pmf.Total()))
def ProcessScoresTeamwise(pairs):
"""Average number of goals for each team.
pairs: map from (team1, team2) to (score1, score2)
"""
# map from team to list of goals scored
goals_scored = {}
for key, entries in pairs.iteritems():
t1, t2 = key
for entry in entries:
g1, g2 = entry
goals_scored.setdefault(t1, []).append(g1)
goals_scored.setdefault(t2, []).append(g2)
# make a list of average goals scored
lams = []
for key, goals in goals_scored.iteritems():
lam = thinkbayes2.Mean(goals)
lams.append(lam)
# make the distribution of average goals scored
cdf = thinkbayes2.MakeCdfFromList(lams)
thinkplot.Cdf(cdf)
thinkplot.Show()
mu, var = thinkbayes2.MeanVar(lams)
print('mu, sig', mu, math.sqrt(var))
def CH7_2():
"""
http://www.ruanyifeng.com/blog/2015/06/poisson-distribution.html
1. 一场比赛平均进球数为lam, 每场比赛进球分布: 泊松分布
(进球可以在任何时间点发生)
eg. 某医院平均每小时出生3个婴儿
重点是: 次数
2. 进球间隔的分布: 指数分布
eg. 某医院婴儿出生的时间间隔(20分钟一个(0.3h))
重点是: 间隔
泊松分布是单位时间内独立事件发生次数的概率分布
指数分布是独立事件的时间间隔的概率分布
"""
# 单位时间内出生1 - 10个婴儿的泊松分布
pmf = thinkbayes.MakePoissonPmf(3, 10, step=1)
thinkplot.Clf()
thinkplot.Pmf(pmf)
# thinkplot.Show();
# 婴儿出生时间间隔(20分钟)
pmf = thinkbayes.MakeExponentialPmf(0.3, 10, n=200)
thinkplot.Clf()
thinkplot.Pmf(pmf)
thinkplot.Show();
def print_num_albums_per_artist(all_genres):
num_albums_counts = {}
num_albums_list = []
for artist, albums in all_genres.items():
num_albums = len(albums)
num_albums_list.append(num_albums)
if num_albums in num_albums_counts:
num_albums_counts[num_albums] += 1
else:
num_albums_counts[num_albums] = 1
num_artists = len(all_genres)
num_albums = sum(num_albums_list)
print("In total,", num_artists, "artists, producing", num_albums,
"albums.")
print("An average of", "%.2f" % (num_albums / num_artists),
"albums per artist.")
num_albums_hist = ts2.Hist(num_albums_counts)
artists_more_than_6_albums = sum(
[v for k, v in num_albums_hist.Items() if k > 6])
print(artists_more_than_6_albums, 'artists with more than 6 albums.')
tp.Hist(num_albums_hist)
tp.Show(xlabel='Number of albums',
ylabel='Count of artists with this number of albums',
title='Histogram of the number of albums per artist')
def MakePlot(self):
"""Plot the CDFs."""
thinkplot.Cdf(self.pmf_y.MakeCdf())
thinkplot.Cdf(self.prior_zb.MakeCdf())
thinkplot.Cdf(self.post_zb.MakeCdf())
thinkplot.Cdf(self.pmf_mean_zb.MakeCdf())
thinkplot.Show()
def main():
df = hinc.ReadData()
log_sample = InterpolateSample(df, log_upper=6.0)
log_cdf = thinkstats2.Cdf(log_sample)
thinkplot.Cdf(log_cdf)
thinkplot.Show(xlabel='household income', ylabel='CDF')
def main():
filename = 'mystery0.dat'
data = read_file(filename)
pmf = thinkstats2.MakePmfFromList(data)
cdf = thinkstats2.MakeCdfFromList(data)
pdf = thinkstats2.EstimatedPdf(data)
low, high = min(data), max(data)
xs = numpy.linspace(low, high, 101)
kde_pmf = pdf.MakePmf(xs)
bin_data = BinData(data, low, high, 51)
bin_pmf = thinkstats2.MakePmfFromList(bin_data)
thinkplot.SubPlot(2, 2, 1)
thinkplot.Hist(pmf, width=0.1)
thinkplot.Config(title='Naive Pmf')
thinkplot.SubPlot(2, 2, 2)
thinkplot.Hist(bin_pmf)
thinkplot.Config(title='Binned Hist')
thinkplot.SubPlot(2, 2, 3)
thinkplot.Pmf(kde_pmf)
thinkplot.Config(title='KDE PDF')
thinkplot.SubPlot(2, 2, 4)
thinkplot.Cdf(cdf)
thinkplot.Config(title='CDF')
thinkplot.Show()
def main():
hypos = numpy.linspace(0, 12, 201)
suite = Soccer(hypos)
# the mean number of goals per game was 2.67
mean_rate = 2.67 / 2
mean_interarrival = 90 / mean_rate
# start with a prior based on the mean interarrival time
suite.Update(mean_interarrival)
thinkplot.Pdf(suite, label='prior')
print('prior mean', suite.Mean())
suite.Update(11)
thinkplot.Pdf(suite, label='posterior 1')
print('after one goal', suite.Mean())
suite.Update(12)
thinkplot.Pdf(suite, label='posterior 2')
print('after two goals', suite.Mean())
thinkplot.Show()
# plot the predictive distribution
suite.PredRemaining(90 - 23, 2)
def ProcessScoresPairwise(pairs):
"""Average number of goals for each team against each opponent.
pairs: map from (team1, team2) to (score1, score2)
"""
# map from (team1, team2) to list of goals scored
goals_scored = {}
for key, entries in pairs.iteritems():
t1, t2 = key
for entry in entries:
g1, g2 = entry
goals_scored.setdefault((t1, t2), []).append(g1)
goals_scored.setdefault((t2, t1), []).append(g2)
# make a list of average goals scored
lams = []
for key, goals in goals_scored.iteritems():
if len(goals) < 3:
continue
lam = thinkstats.Mean(goals)
lams.append(lam)
# make the distribution of average goals scored
cdf = thinkbayes.MakeCdfFromList(lams)
thinkplot.Cdf(cdf)
thinkplot.Show()
mu, var = thinkstats.MeanVar(lams)
print('mu, sig', mu, math.sqrt(var))
print('BOS v VAN', pairs['BOS', 'VAN'])
def main():
coords = numpy.linspace(-100, 100, 101)
joint = Gps(product(coords, coords))
joint.Update((51, -15))
joint.Update((48, 90))
pairs = [(11.903060613102866, 19.79168669735705),
(77.10743601503178, 39.87062906535289),
(80.16596823095534, -12.797927542984425),
(67.38157493119053, 83.52841028148538),
(89.43965206875271, 20.52141889230797),
(58.794021026248245, 30.23054016065644),
(2.5844401241265302, 51.012041625783766),
(45.58108994142448, 3.5718287379754585)]
joint.UpdateSet(pairs)
thinkplot.PrePlot(2)
pdfx = joint.Marginal(0)
pdfy = joint.Marginal(1)
thinkplot.Pdf(pdfx, label='posterior x')
thinkplot.Pdf(pdfy, label='posterior y')
thinkplot.Show()
print(pdfx.Mean(), pdfx.Std())
print(pdfy.Mean(), pdfy.Std())
def main():
fair = Euro()
fair.Set(50, 1)
bias = Euro()
for x in range(0, 51):
bias.Set(x, x)
for x in range(51, 101):
bias.Set(x, 100-x)
bias.Normalize()
thinkplot.Pmf(bias)
thinkplot.Show()
# notice that we've changed the representation of the data
data = 140, 110
like_bias = AverageLikelihood(bias, data)
print 'like_bias', like_bias
like_fair = AverageLikelihood(fair, data)
print 'like_fair', like_fair
ratio = like_bias / like_fair
print 'Bayes factor', ratio
def main(script, filename='mystery0.dat'):
data = ReadFile(filename)
cdf = thinkstats2.Cdf(data)
thinkplot.PrePlot(rows=2, cols=3)
thinkplot.SubPlot(1)
thinkplot.Cdf(cdf)
thinkplot.Config(title='linear')
thinkplot.SubPlot(2)
scale = thinkplot.Cdf(cdf, xscale='log')
thinkplot.Config(title='logx', **scale)
thinkplot.SubPlot(3)
scale = thinkplot.Cdf(cdf, transform='exponential')
thinkplot.Config(title='expo', **scale)
thinkplot.SubPlot(4)
xs, ys = thinkstats2.NormalProbability(data)
thinkplot.Plot(xs, ys)
thinkplot.Config(title='normal')
thinkplot.SubPlot(5)
scale = thinkplot.Cdf(cdf, transform='pareto')
thinkplot.Config(title='pareto', **scale)
thinkplot.SubPlot(6)
scale = thinkplot.Cdf(cdf, transform='weibull')
thinkplot.Config(title='weibull', **scale)
thinkplot.Show(legend=False)
def CH3_2():
"""
火车头问题(Train)
有一天看到一个编号60的火车头经过, 论共有多少个火车头?
假设 上限 N = 1000, 500, 2000
猜测结果对上限敏感
实际N个火车头, 假设看到了60号火车头
1 1/N 0
2 1/N 0
... ... ...
59 1/N 0
60 1/N 1/60
61 1/N 1/61
... ... ...
1000 1/N 1/1000
"""
# 假设有1 - 1000个编号的火车头
N = 1000
hypoes = range(1, N)
suite = Train(hypoes)
suite.Update(60)
thinkplot.PrePlot(num=1)
thinkplot.Pmf(suite)
thinkplot.Show(title='Train', xlabel='Number of trains', ylabel='Probability')
print(suite.Mean())
