def MakeFigures(firsts, others):
"""Plot Hists and Pmfs for the pregnancy length."""
# bar options is a list of option dictionaries to be passed to myplot.bar
bar_options = [dict(color='0.9'), dict(color='blue')]
# make the histogram
axis = [23, 46, 0, 2700]
Hists([firsts.hist, others.hist])
myplot.Save(root='nsfg_hist',
title='Histogram',
xlabel='weeks',
ylabel='frequency',
axis=axis)
# make the PMF
axis = [23, 46, 0, 0.6]
Hists([firsts.pmf, others.pmf])
myplot.Save(root='nsfg_pmf',
title='PMF',
xlabel='weeks',
ylabel='probability',
axis=axis)
def NormalProbPlot(samples):
"""Makes a normal probability plot for each sample in samples."""
pyplot.clf()
markers = dict(male='b', female='g')
for label, sample in samples.iteritems():
NormalPlot(sample, label, markers[label], jitter=0.0)
myplot.Save(
show=True,
#root='bayes_height_normal',
title='Normal probability plot',
xlabel='Standard normal',
ylabel='Reported height (cm)')
def PlotCdfs(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 = Cdf.MakeCdfFromList(outliers, label)
cdfs.append(cdf)
myplot.Clf()
myplot.Cdfs(cdfs)
myplot.Save(root='bayes_height_cdfs',
title='CDF of height',
xlabel='Reported height (cm)',
ylabel='CDF')
def PlotDiffs(filename='heri.0', root='heri1', flag=False):
pyplot.clf()
data = ReadData(filename)
xs, ys = zip(*data)
if flag:
RunFit(xs, ys)
pyplot.plot(xs, ys, 'b.:', markersize=15)
myplot.Save(root=root,
title='Yearly changes',
xlabel='',
ylabel='percentage points',
axis=[1972, 2013, -1.2, 2.1])
def MakeFigures():
pops = populations.ReadData()
print len(pops)
cdf = Cdf.MakeCdfFromList(pops, 'populations')
myplot.Clf()
myplot.Cdf(cdf)
myplot.Save(root='populations',
title='City/Town Populations',
xlabel='population',
ylabel='CDF',
legend=False)
myplot.Clf()
myplot.Cdf(cdf)
myplot.Save(root='populations_logx',
title='City/Town Populations',
xlabel='population',
ylabel='CDF',
xscale='log',
legend=False)
myplot.Clf()
myplot.Cdf(cdf, complement=True)
myplot.Save(root='populations_loglog',
title='City/Town Populations',
xlabel='population',
ylabel='Complementary CDF',
yscale='log',
xscale='log',
legend=False)
t = [math.log(x) for x in pops]
t.sort()
rankit.MakeNormalPlot(t, 'populations_rankit')
def PlotProbs(filename='p.heri.31'):
pyplot.clf()
for x in [1975.5, 1984.5, 1998.5, 2006.5]:
xs = [x, x]
ys = [0, 1]
pyplot.plot(xs, ys, color='0.8', linewidth=10)
data = ReadData(filename)
xs, ys = zip(*data)
pyplot.plot(xs, ys, 'bo-', color='blue', linewidth=2, markersize=6)
myplot.Save(root='heri2',
title='Location of changepoints',
xlabel='',
ylabel='cumulative probability',
axis=[1972, 2010, 0, 1])
def PlotOneSimulation(xscale='linear'):
pyplot.clf()
PlotSimulation(100000)
if xscale == 'linear':
pyplot.axis([-0.1, 1.1, 0.0, 0.7])
pyplot.xticks([0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
else:
pyplot.subplots_adjust(bottom=0.15)
pyplot.xscale(xscale)
myplot.Save(root='world_record_sim_%s' % xscale,
title='Simulated world record progression',
xlabel='Fraction of population tested',
ylabel='Max potential seen')
def main():
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
pmf = Pmf.MakePmfFromList(speeds, 'speeds')
pmf = BiasPmf(7,pmf)
myplot.Hist(pmf)
#myplot.Show(title='PMF of observed speed',
# xlabel='speed (mph)',
# ylabel='probability')
myplot.Save(
formats=['png'],
root='runner',
title='PMF of observed speed',
xlabel='speed (mph)',
ylabel='probability')
def CheckCdf():
"""Compare chi2 values from simulation with chi2 distributions.
"""
for df in [1, 2, 3]:
xs, ys = Chi2Cdf(df=df, high=15)
pyplot.plot(xs, ys, label=df)
t = [SimulateChi2() for i in range(1000)]
cdf = Cdf.MakeCdfFromList(t)
myplot.Cdf(cdf)
myplot.Save(root='khan3',
xlabel='chi2 value',
ylabel="CDF",
formats=['png'])
def MakeNormalPlot(ys, root=None, line_options={}, **options):
"""Makes a normal probability plot.
Args:
ys: sequence of values
line_options: dictionary of options for pyplot.plot
options: dictionary of options for myplot.Save
"""
# TODO: when n is small, generate a larger sample and desample
n = len(ys)
xs = [random.normalvariate(0.0, 1.0) for i in range(n)]
pyplot.clf()
pyplot.plot(sorted(xs), sorted(ys), 'b.', markersize=3, **line_options)
myplot.Save(root, xlabel='Standard normal values', legend=False, **options)
def MakeFigures(pmf, biased_pmf):
"""Makes figures showing the CDF of the biased and unbiased PMFs"""
cdf = Cdf.MakeCdfFromPmf(pmf, 'unbiased')
print('unbiased median', cdf.Percentile(50))
print('percent < 100', cdf.Prob(100))
print('percent < 1000', cdf.Prob(1000))
biased_cdf = Cdf.MakeCdfFromPmf(biased_pmf, 'biased')
print('biased median', biased_cdf.Percentile(50))
myplot.Clf()
myplot.Cdfs([cdf, biased_cdf])
myplot.Save(root='slashdot.logx',
xlabel='Number of friends/foes',
ylabel='CDF',
xscale='log')
def main():
weeks = range(35, 46)
pyplot.clf()
p = {'first': [], 'others': []}
for week in weeks:
firstBabies, otherBabies = BornAtButNotBefore(week)
p['first'].append(firstBabies.Prob(week))
p['others'].append(otherBabies.Prob(week))
pyplot.plot(weeks, p['first'], label="First babies")
pyplot.plot(weeks, p['others'], label="Others babies")
myplot.Save(root='first_conditional_pmf',
title='My conditional',
xlabel='weeks',
ylabel='probability')
def Main(script):
# read 'em and sort 'em
birthdays = ReadBirthdays()
birthdays.sort()
# compute the intervals in days
deltas = Diff(birthdays)
days = [inter.days for inter in deltas]
# make and plot the CCDF on a log scale.
cdf = Cdf.MakeCdfFromList(days, name='intervals')
scale = myplot.Cdf(cdf, transform='exponential')
myplot.Save(root='intervals',
xlabel='days',
ylabel='ccdf',
**scale)
def MakePercentiles(shelf, n=50):
pairs = ReadShelf(shelf)
pairs.sort()
for x, y in pairs:
print x, y
return
xs = []
plists = []
for i in range(0, len(pairs), n):
subset = pairs[i:i + n]
print i, len(subset)
halfs, fulls = zip(*subset)
cdf = Cdf.MakeCdfFromList(fulls)
ys = [cdf.Percentile(x) for x in [5, 25, 50, 75, 95]]
x = thinkstats.Mean(halfs)
print x, ys
xs.append(x)
plists.append(ys)
# drop the last point
xs.pop()
plists.pop()
ylists = zip(*plists)
plot_options = [
dict(color='red', label='5%ile', linestyle='dotted'),
dict(color='orange', label='25%ile', linestyle='dashed'),
dict(color='yellow', label='50%ile', linestyle='solid'),
dict(color='green', label='75%ile', linestyle='dashed'),
dict(color='cyan', label='95%ile', linestyle='dotted'),
]
pyplot.plot([94, 94], [100, 350])
for ys, d in zip(ylists, plot_options):
pyplot.plot(xs, ys, linewidth=3, **d)
myplot.Save(root='race_predictor4',
xlabel='Half marathon (min)',
ylabel='Marathon (min)',
show=True)
def MakeDiffFigure(firsts, others):
"""Plot the difference between the PMFs."""
weeks = range(35, 46)
diffs = []
for week in weeks:
p1 = firsts.pmf.Prob(week)
p2 = others.pmf.Prob(week)
diff = 100 * (p1 - p2)
diffs.append(diff)
pyplot.clf()
pyplot.bar(weeks, diffs, align='center')
myplot.Save(root='nsfg_diffs',
title='Difference in PMFs',
xlabel='weeks',
ylabel='100 (PMF$_{first}$ - PMF$_{other}$)',
legend=False)
def plot_data(self, root='caws.accident'):
"""Plots a time series of monthly accidents.
root: string prefix of the output files.
"""
pyplot.clf()
for name, av_dict in self.subsets.iteritems():
hist = self.count_accidents(av_dict)
print name, 'Total accidents', hist.Total()
years, counts = zip(*sorted(hist.Items()))
pyplot.plot(years, counts, label=name)
myplot.Save(root=root,
title='Monthly Accident Counts',
xlabel='Year',
ylabel='Number of accidents',
axis=[1991.5, 2002.5, 0, 40])
def MakeParetoCdf():
"""Generates a plot of the CDF of height in Pareto World."""
n = 50
max = 1000.0
xs = [max * i / n for i in range(n)]
xmin = 100
alpha = 1.7
ps = [ParetoCdf(x, alpha, xmin) for x in xs]
print 'Median', ParetoMedian(xmin, alpha)
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
myplot.Save('pareto_world1',
title='Pareto CDF',
xlabel='height (cm)',
ylabel='CDF',
legend=False)
def MakeParetoCdf():
"""Generates a plot of the Pareto CDF."""
n = 50
max = 10.0
xs = [max * i / n for i in range(n)]
xmin = 0.5
alpha = 1.0
ps = [ParetoCdf(x, alpha, xmin) for x in xs]
print('Fraction <= 10', ParetoCdf(xmin, alpha, 10))
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
myplot.Save('pareto_cdf',
title='Pareto CDF',
xlabel='x',
ylabel='CDF',
legend=False)
def PlotReligiousSubset(years, cols, labels, i, j):
"""Helper function that factors out common plotting code.
years: sequence of years
cols: list of columns to plot
labels: list of labels (corresponding to cols)
i,j: slice indices of the columns to plot
"""
pyplot.clf()
options = dict(linewidth=3, markersize=0, alpha=0.7)
for col, label in zip(cols[i:j], labels[i:j]):
pyplot.plot(years, col, label=label, **options)
root = 'heri.religious.%d.%d' % (i, j)
myplot.Save(root=root,
formats=FORMATS,
xlabel='Year',
ylabel='% None',
title='Religious preference')
def MakeExpoCdf():
"""Generates a plot of the exponential CDF."""
n = 40
max = 2.5
xs = [max * i / n for i in range(n)]
lam = 2.0
ps = [ExpoCdf(x, lam) for x in xs]
percentile = -math.log(0.05) / lam
print('Fraction <= ', percentile, ExpoCdf(lam, percentile))
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
myplot.Save('expo_cdf',
title='Exponential CDF',
xlabel='x',
ylabel='CDF',
legend=False)
def PlotCurves(curves, root=None, clf=False):
"""Plots a set of curves.
curves is a list of curves; each curve is a list of (x, y) pairs.
"""
if root:
pyplot.clf()
n = len(curves)
for i, curve in enumerate(curves):
curve = OffsetCurve(curve, i, n)
xs, ys = zip(*curve)
pyplot.plot(xs, ys, color='blue', alpha=0.2)
myplot.Save(root=root,
clf=clf,
xlabel='# samples',
ylabel='# taxa',
legend=False)
def plot_data(self, root='caws.traffic'):
"""Makes a plot of AADT for each location."""
pyplot.clf()
series = {}
for loc, name in self.locs.iteritems():
for year in self.years:
adt = self.lookup(year, loc) / 1000
series.setdefault(name, []).append(adt)
# TODO: fix the year labels
for name, adts in series.iteritems():
pyplot.plot(self.years, adts, label=name)
myplot.Save(root=root,
title='Traffic volume',
xlabel='Year',
ylabel='AADT',
axis=[1991.5, 2002.5, 0, 160])
def main():
print 'pae', 0.3 / (0.3 + 3.0 / 13)
doorA = MakeUniformSuite(0.0, 1.0, 101, name='Door A')
evidence = 3, 2
Update(doorA, evidence)
doorC = MakeUniformSuite(0.0, 1.0, 101, name='Door C')
evidence = 3, 10
Update(doorC, evidence)
print TotalProbability(doorA, doorC, ProbWinning)
# plot the posterior distributions
myplot.Pmfs([doorA, doorC])
myplot.Save(root='blinky',
formats=['pdf', 'png'],
title='Probability of blinking',
xlabel='P(blink)',
ylabel='Posterior probability')
def PlotMarginals(suite):
"""Plot the marginal distributions for a 2-D joint distribution."""
pmf_m, pmf_s = ComputeMarginals(suite)
pyplot.clf()
pyplot.figure(1, figsize=(7, 4))
pyplot.subplot(1, 2, 1)
cdf_m = Cdf.MakeCdfFromPmf(pmf_m, 'mu')
myplot.Cdf(cdf_m)
pyplot.xlabel('Mean height (cm)')
pyplot.ylabel('CDF')
pyplot.subplot(1, 2, 2)
cdf_s = Cdf.MakeCdfFromPmf(pmf_s, 'sigma')
myplot.Cdf(cdf_s)
pyplot.xlabel('Std Dev height (cm)')
pyplot.ylabel('CDF')
myplot.Save(root='bayes_height_marginals_%s' % suite.name)
def MakeDiffFigure(firsts, others):
'''
绘制两个 PMF 的不同之处
'''
weeks = range(35, 46) # 只绘制这个范围的，我们关注这个范围
diffs = []
for week in weeks:
p1 = firsts.pmf.Prob(week)
p2 = others.pmf.Prob(week)
diff = 100 * (p1 - p2) #计算两种概率的差异
diffs.append(diff)
# 要开始绘图了
pyplot.clf()
# 数值序列，概率差异序列，对其方式
pyplot.bar(weeks, diffs, align='center')
myplot.Save(root='nsfg_diffs',
title='Difference in PMFs',
xlabel='weeks',
ylabel='100 (PMF$_{first}$ - PMF$_{other}$)',
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 PlotSimulations():
pyplot.rc('figure', figsize=(4, 4.5))
pyplot.rc('font', size=9.0)
pyplot.rc('xtick.major', size=0)
pyplot.rc('ytick.major', size=0)
pyplot.subplots_adjust(wspace=0.4,
hspace=0.4,
right=0.95,
left=0.1,
top=0.95,
bottom=0.05)
pyplot.title('Simulated world records')
for i in range(1, 5):
pyplot.subplot(2, 2, i)
pyplot.xscale('log')
PlotSimulation(100000)
myplot.Save(root='world_record_sim2')
pyplot.rcdefaults()
def PlotPosterior(xs, ys, suite, pcolor=False, contour=True):
"""Makes a contour plot.
xs: sequence of values
ys: sequence of values
suite: Pmf that maps (x, y) to z
"""
X, Y = numpy.meshgrid(xs, ys)
func = lambda x, y: suite.Prob((x, y))
prob = numpy.vectorize(func)
Z = prob(X, Y)
pyplot.clf()
if pcolor:
pyplot.pcolor(X, Y, Z)
if contour:
pyplot.contour(X, Y, Z)
myplot.Save(root='bayes_height_posterior_%s' % suite.name,
title='Posterior joint distribution',
xlabel='Mean height (cm)',
ylabel='Stddev (cm)')
def PlotCoefVariation(suites):
"""Plot the posterior distributions for CV.
suites: map from label to Pmf of CVs.
"""
pyplot.clf()
pmfs = {}
for label, suite in suites.iteritems():
pmf = ComputeCoefVariation(suite)
cdf = Cdf.MakeCdfFromPmf(pmf, label)
myplot.Cdf(cdf)
pmfs[label] = pmf
myplot.Save(root='bayes_height_cv',
title='Coefficient of variation',
xlabel='cv',
ylabel='CDF')
print 'female bigger', ProbBigger(pmfs['female'], pmfs['male'])
print 'male bigger', ProbBigger(pmfs['male'], pmfs['female'])
def MakeNormalModel(values):
"""Plot the CDF of birthweights with a normal model."""
# estimate parameters: trimming outliers yields a better fit
mu, var = thinkstats.TrimmedMeanVar(values, p=0.01)
print 'Mean, Var', mu, var
# plot the model
sigma = math.sqrt(var)
print 'Sigma', sigma
xs, ps = RenderNormalCdf(mu, sigma, 200)
pyplot.clf()
pyplot.plot(xs, ps, label='model', linewidth=4, color='0.8')
# plot the data
cdf = Cdf.MakeCdfFromList(values)
xs, ps = cdf.Render()
pyplot.plot(xs, ps, label='data', linewidth=2, color='red')
myplot.Save(show=True,
ylabel = 'CDF')
