def main():
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
speeds = relay.BinData(speeds, 3, 12, 100)
# plot the distribution of actual speeds
pmf = thinkstats2.Pmf(speeds, 'actual speeds')
# plot the biased distribution seen by the observer
biased = ObservedPmf(pmf, 7.5, label='observed speeds')
thinkplot.Pmf(biased)
thinkplot.Save(root='observed_speeds',
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='PMF')
cdf = thinkstats2.Cdf(pmf)
cdf_biased = thinkstats2.Cdf(biased)
thinkplot.PrePlot(2)
thinkplot.Cdfs([cdf, cdf_biased])
thinkplot.Save(root='observed_speeds_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='CDF')
def ComparePriors(constructors, labels, \
dataset = [60], largest_size = 1000):
"""Runs the likelihood of a train with number specified by
dataset given a arbitrary number of priors.
constructors = a list of anything that inherits from the Dice class
labels = labels for these prior distributions
dataset = the number of the train spotted
largest_size = the assumed size of the largest train company out there
"""
thinkplot.Clf()
thinkplot.PrePlot(num=2)
for constructor, label in zip(constructors, labels):
suite = MakePosterior(largest_size, dataset, constructor)
suite.name = label
print "Expected Value for {}".format(suite.name)
print "\t {}: {}".format(largest_size, suite.Mean())
print("\t 90 percent Credibility Interval")
interval = Percentile(suite, 5), Percentile(suite, 95)
print '\t', interval
thinkplot.Pmf(suite)
thinkplot.Save(root='one_many_firm_comparison',
xlabel='Number of trains',
ylabel='Probability')
def MakePlot(self, root='redline4'):
"""Makes a plot showing the mixture."""
thinkplot.Clf()
# plot the MetaPmf
for pmf, prob in sorted(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])
def PlotSurvivalFunctions(sf_map, predict_flag=False, colormap=None):
"""Plot estimated survival functions.
sf_map: map from group name to sequence of survival functions
predict_flag: whether the lines are predicted or actual
colormap: map from group name to color
"""
thinkplot.PrePlot(num=len(sf_map))
for name, sf_seq in sorted(sf_map.items(), reverse=True):
if len(sf_seq) == 0:
continue
sf = sf_seq[0]
if len(sf) == 0:
continue
ts, rows = MakeSurvivalCI(sf_seq, [10, 50, 90])
thinkplot.FillBetween(ts, rows[0], rows[2], color='gray', alpha=0.2)
if not predict_flag:
if colormap:
color = colormap[name]
thinkplot.Plot(ts, rows[1], label='%ds' % name, color=color)
else:
thinkplot.Plot(ts, rows[1], label='%ds' % name)
def main():
print("Single Die:")
d6 = Die(6)
print(d6)
#use thinkbayes to simulate
dice = [d6] * 3
three = SampleSum(dice, 5000)
print("##################################")
print("Three Die:")
print(three)
#use thinkbayes to enumerate
three_exact = d6 + d6 + d6
print("##################################")
print("Exact Three Die:")
print(three_exact)
# Use Allen Downey's thinkplot module to create a graph
thinkplot.PrePlot(1)
thinkplot.Plot(three)
thinkplot.Plot(three_exact)
thinkplot.Save(root='DD1',
xlabel='Sum of 3 d6',
ylabel='Probability',
formats=['pdf'])
print("Program Complete")
def MakeNormalModel(arrivalDelays):
"""Plot the CDF of arrival delays with a normal model.
This is a modified copy from analytic.py
"""
# estimate parameters: trimming outliers yields a better fit
mu, var = thinkstats2.TrimmedMeanVar(arrivalDelays, p=0.01)
print('Mean, Var', mu, var)
# plot the model
sigma = math.sqrt(var)
print('Sigma', sigma)
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=12.5)
thinkplot.Plot(xs, ps, label='model', color='0.8')
# plot the data
cdf = thinkstats2.Cdf(arrivalDelays, label='data')
thinkplot.PrePlot(1)
thinkplot.Cdf(cdf)
thinkplot.Save(root='NormalModel_arrivaldelay_model',
title='Arrival Delays',
xlabel='arrival delays (min)',
ylabel='CDF')
def MakeArrivalDepartureDelayScatterPlots(flights):
"""Make scatterplots.
"""
sample = thinkstats2.SampleRows(flights, 10000)
# simple scatter plot
thinkplot.PrePlot(cols=2)
# departureDelays, arrivalDelays = GetArrivalDepartureDelay(sample)
# airports = sample.AIRLINE
# arrivalDelays = sample.ARRIVAL_DELAY
# ScatterPlot(airports, arrivalDelays)
# scatter plot with jitter
# thinkplot.SubPlot(2)
departureDelays, arrivalDelays = GetArrivalDepartureDelay(sample,
hjitter=1.3,
wjitter=0.5)
thinkplot.Scatter(arrivalDelays, departureDelays, alpha=1)
thinkplot.Config(
xlabel='arrival delay (min)',
ylabel='departure delay (min)',
# axis=[-20, 20, 20, 200],
legend=False)
thinkplot.Save(root='ArrivalDepartureDelayScatterplot')
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(thinkbayes2.MakeCdfFromPmf(marginal_alpha))
thinkplot.Cdf(thinkbayes2.MakeCdfFromPmf(marginal_beta))
thinkplot.Save('paintball2',
xlabel='Distance',
ylabel='Prob',
loc=4,
formats=FORMATS)
def PlotCdf(cdf):
"""Plots the actual and fitted distributions.
cdf: CDF object
"""
xs, ps = cdf.xs, cdf.ps
cps = [1-p for p in ps]
# CCDF on logy scale: shows exponential behavior
thinkplot.Clf()
thinkplot.Plot(xs, cps, 'bo-')
thinkplot.Save(root='kidney1',
formats=FORMATS,
xlabel='RDT',
ylabel='CCDF (log scale)',
yscale='log')
# CDF, model and data
thinkplot.Clf()
thinkplot.PrePlot(num=2)
mxs, mys = ModelCdf()
thinkplot.Plot(mxs, mys, label='model', linestyle='dashed')
thinkplot.Plot(xs, ps, 'gs', label='data')
thinkplot.Save(root='kidney2',
formats=FORMATS,
xlabel='RDT (volume doublings per year)',
ylabel='CDF',
title='Distribution of RDT',
axis=[-2, 7, 0, 1],
loc=4)
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.items():
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 PlotSurvivalFunctions(sf_map, predict_flag=False):
"""Plot estimated survival functions.
sf_map: map from group name to sequence of survival functions
predict_flag: whether the lines are predicted or actual
"""
thinkplot.PrePlot(len(sf_map))
for name, sf_seq in sorted(sf_map.items(), reverse=True):
if len(sf_seq) == 0:
continue
sf = sf_seq[0]
if len(sf) == 0:
continue
ts, rows = MakeSurvivalCI(sf_seq, [10, 50, 90])
thinkplot.FillBetween(ts, rows[0], rows[2], color='gray')
if not predict_flag:
thinkplot.Plot(ts, rows[1], label='19%d'%name)
thinkplot.Config(xlabel='age (years)', ylabel='prob unmarried',
xlim=[14, 45], ylim=[0, 1],
legend=True, loc='upper right')
def PlotRemainingLifetime(sf1, sf2):
"""Plots remaining lifetimes for pregnancy and age at first marriage.
sf1: SurvivalFunction for pregnancy length
sf2: SurvivalFunction for age at first marriage
"""
thinkplot.PrePlot(cols=2)
rem_life1 = sf1.RemainingLifetime()
thinkplot.Plot(rem_life1)
thinkplot.Config(title='remaining pregnancy length',
xlabel='weeks',
ylabel='mean remaining weeks')
thinkplot.SubPlot(2)
func = lambda pmf: pmf.Percentile(50)
rem_life2 = sf2.RemainingLifetime(filler=np.inf, func=func)
thinkplot.Plot(rem_life2)
thinkplot.Config(title='years until first marriage',
ylim=[0, 15],
xlim=[11, 31],
xlabel='age (years)',
ylabel='median remaining years')
thinkplot.Save(root='survival6',
formats=FORMATS)
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
MakePrice1(player1, player2)
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 main():
euro = Euro(range(101))
euro.label = "Uniform prior"
euro_triangleprior = Euro(range(101), triangle_prior=True)
euro_triangleprior.label = "Triangle prior"
for data in range(140):
euro.Update('H')
euro_triangleprior.Update('H')
for data in range(110):
euro.Update('T')
euro_triangleprior.Update('T')
print("Summary for uniform prior: ")
summarize_posterior(euro)
print("Summary for triangle prior: ")
summarize_posterior(euro_triangleprior)
# Use Allen Downey's thinkplot module to create a graph
thinkplot.PrePlot(1)
thinkplot.Plot(euro)
thinkplot.Plot(euro_triangleprior)
thinkplot.Save(root='euro2',
xlabel='Bias of heads vs. tails',
ylabel='Probability',
formats=['pdf'])
def main():
# d6 = Die(6)
# d8 = Die(8)
d6 = Pmf()
print type(d6)
d6.Set(Die(6), 2)
print type(d6)
d8 = Pmf()
d8.Set(Die(8), 3)
d12 = Pmf()
d12.Set(Die(12), 1)
d20 = Pmf()
d20.Set(Die(20), 1)
mix = Pmf()
for dice in [d6, d8, d12, d20]:
# print type(dice)
for die, weight in dice.Items():
# print type(die)
for outcome, prob in die.Items():
mix.Incr(outcome, weight * prob)
mix.Normalize()
thinkplot.PrePlot(1)
thinkplot.Pmf(mix)
thinkplot.Save(root='dice_Mix_self2',
xlabel='',
ylabel='Probability',
formats=['pdf'])
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())
def PlotOptimalBid():
"""Plots optimal bid vs estimated price.
"""
player1, player2 = MakePlayers()
guesses = numpy.linspace(15000, 60000, 21)
res = []
for guess in guesses:
player1.MakeBeliefs(guess)
mean = player1.posterior.Mean()
mle = player1.posterior.MaximumLikelihood()
calc = GainCalculator(player1, player2)
bids, gains = calc.ExpectedGains()
gain, bid = max(zip(gains, bids))
res.append((guess, mean, mle, gain, bid))
guesses, means, _mles, gains, bids = zip(*res)
thinkplot.PrePlot(num=3)
pyplot.plot([15000, 60000], [15000, 60000], color='gray')
thinkplot.Plot(guesses, means, label='mean')
#thinkplot.Plot(guesses, mles, label='MLE')
thinkplot.Plot(guesses, bids, label='bid')
thinkplot.Plot(guesses, gains, label='gain')
thinkplot.Save(root='price6', xlabel='guessed price ($)', formats=FORMATS)
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 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 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 class_sizes():
"""Generate PMFs of observed and actual class size.
"""
# 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.Pmf(d, label='actual')
print('mean', pmf.Mean())
print('var', pmf.Var())
# compute the biased pmf
biased_pmf = bias_pmf(pmf, label='observed')
print('mean', biased_pmf.Mean())
print('var', biased_pmf.Var())
# unbias the biased pmf
unbiased_pmf = unbias_pmf(biased_pmf, label='unbiased')
print('mean', unbiased_pmf.Mean())
print('var', unbiased_pmf.Var())
# plot the Pmfs
thinkplot.PrePlot(2)
thinkplot.Pmfs([pmf, biased_pmf])
thinkplot.Save(root='class_size1',
xlabel='class size',
ylabel='PMF',
axis=[0, 52, 0, 0.27])
def PlotResiduals(live):
"""Plots percentiles of the residuals.
live: DataFrame
"""
ages = live.agepreg
weights = live.totalwgt_lb
inter, slope = thinkstats2.LeastSquares(ages, weights)
live['residual'] = thinkstats2.Residuals(ages, weights, inter, slope)
bins = np.arange(10, 48, 3)
indices = np.digitize(live.agepreg, bins)
groups = live.groupby(indices)
ages = [group.agepreg.mean() for _, group in groups][1:-1]
cdfs = [thinkstats2.Cdf(group.residual) for _, group in groups][1:-1]
thinkplot.PrePlot(3)
for percent in [75, 50, 25]:
weights = [cdf.Percentile(percent) for cdf in cdfs]
label = '%dth' % percent
thinkplot.Plot(ages, weights, label=label)
thinkplot.Save(root='linear2',
xlabel='age (years)',
ylabel='residual (lbs)',
xlim=[10, 45])
def PlotPercentileLines(x_means, cdfs, **options):
thinkplot.PrePlot(3)
for percent in [75, 50, 25]:
y_percentiles = [cdf.Percentile(percent) for cdf in cdfs]
label = '%dth' % percent
thinkplot.Plot(x_means, y_percentiles, label=label)
thinkplot.Show(**options)
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 EstimateMarriageSurvivalByDecade(groups, **options):
"""Groups respondents by decade and plots survival curves.
groups: GroupBy object
"""
thinkplot.PrePlot(len(groups))
for _, group in groups:
_, sf = EstimateMarriageSurvival(group)
thinkplot.Plot(sf, **options)
def AddLabelsByDecade(groups, **options):
"""Draws fake points in order to add labels to the legend.
groups: GroupBy object
"""
thinkplot.PrePlot(len(groups))
for name, _ in groups:
label = '%d0s' % name
thinkplot.Plot([15], [1], label=label, **options)
def MakeCdfs(male, female):
malecdf = thinkstats2.Cdf(male.totalwgt_lb, label='Male')
femalecdf = thinkstats2.Cdf(female.totalwgt_lb, label='Female')
thinkplot.PrePlot(2)
thinkplot.Cdfs([malecdf, femalecdf])
thinkplot.Config(xlabel='Baby Weight (Lbs)',
ylabel='CDF',
title='Baby Weights')
thinkplot.Show()
def MakePrice1(player1, player2):
""" 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])
def MakeCdfs(male, female):
malecdf = thinkstats2.Cdf(male.alcwknd, label='Male')
femalecdf = thinkstats2.Cdf(female.alcwknd, label='Female')
thinkplot.PrePlot(2)
thinkplot.Cdfs([malecdf, femalecdf])
thinkplot.Config(xlabel='Alcohol Consumed (grams)',
ylabel='CDF',
title='Weekend Alcohol Consumption')
thinkplot.Show()
def main():
hypos = range(1, 1001)
suite = Train(hypos)
suite.Update(60)
print(suite.Mean())
thinkplot.PrePlot(1)
thinkplot.Pmf(suite)
