def _scatter_plot(root, heights, weights, alpha=1.0):
pyplot.scatter(heights, weights, alpha=alpha, edgecolors='none')
_05_myplot._save(root=root,
xlabel='Height (cm)',
ylabel='Weight (kg)',
axis=[140, 210, 20, 200],
legend=False)
def _hex_bin(root, heights, weights, cmap=matplotlib.cm.Blues):
pyplot.hexbin(heights, weights, cmap=cmap)
_05_myplot._save(root=root,
xlabel='Height (cm)',
ylabel='Weight (kg)',
axis=[140, 210, 20, 200],
legend=False)
def main():
# make a uniform prior
param = 1.2
prior = _make_uniform_suite(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 = _estimate_parameter(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 = _estimate_parameter(prior, sample, name)
t.append(posterior)
# plot the posterior distributions
for i, posterior in enumerate(t):
pyplot.subplot(2, 2, i + 1)
_05_myplot._pmf(posterior)
pyplot.xlabel('lambda')
pyplot.ylabel('Posterior probability')
pyplot.legend()
_05_myplot._save(root='posteriors')
def _make_figures(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])
_05_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])
_05_myplot._save(root='nsfg_pmf',
title='PMF',
xlabel='weeks',
ylabel='probability',
axis=axis)
def _make_figure(firsts, others):
"""Makes a figure showing..."""
weeks = range(35, 46)
# probs is a map from table name to list of conditional probabilities
probs = {}
for table in [firsts, others]:
name = table.pmf.name
probs[name] = []
for week in weeks:
cond = _condition_on_weeks(table.pmf, week)
prob = cond._prob(week)
print(week, prob, table.pmf.name)
probs[name].append(prob)
# make a plot with one line for each table
pyplot.clf()
# for name, ps in probs.iteritems():
for name, ps in probs.items():
pyplot.plot(weeks, ps, label=name)
print(name, ps)
_05_myplot._save(
root="conditional",
xlabel="weeks",
ylabel=r"Prob{x $=$ weeks | x $\geq$ weeks}",
title="Conditional Probability",
)
def _make_normal_model(self,
weights,
root,
xmax=175,
xlabel='adult weight (kg)',
axis=None):
cdf = _13_Cdf._make_cdf_from_list(weights)
pyplot.clf()
t = weights[:]
t.sort()
mu, var = _03_thinkstats._trimmed_mean_var(t)
print('n, Mean, Var', len(weights), mu, var)
sigma = math.sqrt(var)
print('Sigma', sigma)
xs, ps = continuous._render_normal_cdf(mu, sigma, xmax)
pyplot.plot(xs, ps, label='model', linewidth=4, color='0.7')
xs, ps = cdf._render()
pyplot.plot(xs, ps, label='data', linewidth=2, color='blue')
_05_myplot._save(root,
title='Adult weight',
xlabel=xlabel,
ylabel='CDF',
axis=axis or [0, xmax, 0, 1])
def main():
results = _10_relay._read_results()
speeds = _10_relay._get_speeds(results)
# plot the distribution of actual speeds
pmf = _04_Pmf._make_pmf_from_list(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 = _bias_pmf(pmf, 7.5, name='observed speeds')
_05_myplot._clf()
_05_myplot._hist(biased)
_05_myplot._save(root='observed_speeds',
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='probability')
cdf = _13_Cdf._make_cdf_from_pmf(biased)
_05_myplot._clf()
_05_myplot._cdf(cdf)
_05_myplot._save(root='observed_speeds_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='cumulative probability')
def _make_spaghetti(iters=1000, lines=100, n=300, thresh=0.05, index=2):
"""
Makes a spaghetti plot of random-walk lines.
Args:
iters: number of simulations to run
lines: number of lines to plot
n: number of trials to simulate
thresh: threshold p-value
"""
pyplot.clf()
if thresh is not None:
pyplot.plot([1, n], [thresh, thresh], color='red', alpha=1, linewidth=2)
count = 0.0
for i in range(iters):
lists = _simulate(0.5, 0.5, n)
pairs = lists[index]
xs, ys = zip(*pairs)
if _crosses(ys, thresh):
count += 1
if i < lines:
pyplot.plot(xs, ys, alpha=0.2)
print(iters, count / iters)
labels = ['Difference in success rate', 'chi-squared stat', 'p-value']
_05_myplot._save(root='khan%d' % index,
xlabel='Number of trials',
ylabel=labels[index],
title='A-B test random walk',
formats=['png'])
def _resample(cdf, n=10000):
sample = cdf._sample(n)
new_cdf = _13_Cdf._make_cdf_from_list(sample, 'resampled')
_05_myplot._clf()
_05_myplot._cdfs([cdf, new_cdf])
_05_myplot._save(root='resample_cdf',
title='CDF',
xlabel='weight in oz',
ylabel='CDF(x)')
def _make_normal_cdf():
"""Generates a plot of the normal CDF."""
xs, ps = _render_normal_cdf(2.0, 0.5, 4.0)
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
_05_myplot._save('normal_cdf',
title='Normal CDF',
xlabel='x',
ylabel='CDF',
legend=False)
def _log_cdf_time_interval():
timeInterval = _calc_time_interval()
pmf = _04_Pmf._make_pmf_from_list(timeInterval, "baby birth interval")
cdf = _13_Cdf._make_cdf_from_pmf(pmf, "baby birth interval")
_05_myplot._clf()
_05_myplot._cdf(cdf, complement=True, xscale="linear", yscale="log")
_05_myplot._save(
root="baby_birth_interval_logccdf",
title="LogCCDF of baby birth interval",
xlabel="interval(minutes)",
ylabel="LogCCdf",
)
def _make_example():
"""Make a simple example CDF."""
t = [2, 1, 3, 2, 5]
cdf = _13_Cdf._make_cdf_from_list(t)
_05_myplot._clf()
_05_myplot._cdf(cdf)
_05_myplot._save(root='example_cdf',
title='CDF',
xlabel='x',
ylabel='CDF(x)',
axis=[0, 6, 0, 1],
legend=False)
def main():
results = _10_relay._read_results()
speeds = _10_relay._get_speeds(results)
# plot the distribution of actual speeds
cdf = _13_Cdf._make_cdf_from_list(speeds, 'speeds')
_05_myplot._cdf(cdf)
_05_myplot._save(root='relay_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='probability')
def _make_line_plot(age_bins):
xs = []
ys = []
for bin, weights in sorted(age_bins.iteritems()):
xs.append(bin)
ys.append(_03_thinkstats._mean(weights))
_05_myplot._plot(xs, ys, 'bs-')
_05_myplot._save(root='agemodel_line',
xlabel="Mother's age (years)",
ylabel='Mean birthweight (oz)',
legend=False)
def _check_cdf():
"""Compare chi2 values from simulation with chi2 distributions."""
for df in [1, 2, 3]:
xs, ys = _chi2_cdf(df=df, high=15)
pyplot.plot(xs, ys, label=df)
t = [_simulate_chi2() for i in range(1000)]
cdf = _13_Cdf._make_cdf_from_list(t)
_05_myplot._cdf(cdf)
_05_myplot._save(root='khan3',
xlabel='chi2 value',
ylabel="CDF",
formats=['png'])
def _normal_prob_plot(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():
_normal_plot(sample, label, markers[label], jitter=0.0)
_05_myplot._save(show=True,
# root='bayes_height_normal',
title='Normal probability plot',
xlabel='Standard normal',
ylabel='Reported height (cm)')
def _plot_cdfs(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 = _13_Cdf._make_cdf_from_list(outliers, label)
cdfs.append(cdf)
_05_myplot._clf()
_05_myplot._cdfs(cdfs)
_05_myplot._save(root='bayes_height_cdfs',
title='CDF of height',
xlabel='Reported height (cm)',
ylabel='CDF')
def _make_figures(pmf, biased_pmf):
"""Makes figures showing the CDF of the biased and unbiased PMFs"""
cdf = _13_Cdf._make_cdf_from_pmf(pmf, 'unbiased')
print('unbiased median', cdf._percentile(50))
print('percent < 100', cdf._prob(100))
print('percent < 1000', cdf._prob(1000))
biased_cdf = _13_Cdf._make_cdf_from_pmf(biased_pmf, 'biased')
print('biased median', biased_cdf._percentile(50))
_05_myplot._clf()
_05_myplot._cdfs([cdf, biased_cdf])
_05_myplot._save(root='slashdot.logx',
xlabel='Number of friends/foes',
ylabel='CDF',
xscale='log')
def main(script):
# read 'em and sort 'em
birthdays = _read_birthdays()
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 = _13_Cdf._make_cdf_from_list(days, name='intervals')
scale = _05_myplot._cdf(cdf, transform='exponential')
_05_myplot._save(root='intervals',
xlabel='days',
ylabel='ccdf',
**scale)
def _make_cdfs(lens):
cdf = _13_Cdf._make_cdf_from_list(lens, 'slashdot')
_05_myplot._clf()
_05_myplot._cdf(cdf)
_05_myplot._save(root='slashdot.logx',
xlabel='Number of friends/foes',
ylabel='CDF',
xscale='log')
_05_myplot._clf()
_05_myplot._cdf(cdf, complement=True)
_05_myplot._save(root='slashdot.loglog',
xlabel='Number of friends/foes',
ylabel='CDF',
xscale='log',
yscale='log')
def _make_figures(pool, firsts, others):
"""Creates several figures for the book."""
# CDF of all ages
_05_myplot._clf()
_05_myplot._cdf(pool.age_cdf)
_05_myplot._save(root='agemodel_age_cdf',
title="Distribution of mother's age",
xlabel='age (years)',
ylabel='CDF',
legend=False)
# CDF of all weights
_05_myplot._clf()
_05_myplot._cdf(pool.weight_cdf)
_05_myplot._save(root='agemodel_weight_cdf',
title="Distribution of birth weight",
xlabel='birth weight (oz)',
ylabel='CDF',
legend=False)
# plot CDFs of birth ages for first babies and others
_05_myplot._clf()
_05_myplot._cdfs([firsts.age_cdf, others.age_cdf])
_05_myplot._save(root='agemodel_age_cdfs',
title="Distribution of mother's age",
xlabel='age (years)',
ylabel='CDF')
_05_myplot._clf()
_05_myplot._cdfs([firsts.weight_cdf, others.weight_cdf])
_05_myplot._save(root='agemodel_weight_cdfs',
title="Distribution of birth weight",
xlabel='birth weight (oz)',
ylabel='CDF')
# make a scatterplot of ages and weights
ages, weights = _get_age_weight(pool)
pyplot.clf()
# pyplot.scatter(ages, weights, alpha=0.2)
pyplot.hexbin(ages, weights, cmap=matplotlib.cm.gray_r)
_05_myplot._save(root='agemodel_scatter',
xlabel='Age (years)',
ylabel='Birth weight (oz)',
legend=False)
def _make_diff_figure(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')
_05_myplot._save(root='nsfg_diffs',
title='Difference in PMFs',
xlabel='weeks',
ylabel='100 (PMF$_{first}$ - PMF$_{other}$)',
legend=False)
def _make_pareto_cdf():
"""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 = [_pareto_cdf(x, alpha, xmin) for x in xs]
print('Median', _pareto_median(xmin, alpha))
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
_05_myplot._save('pareto_world1',
title='Pareto CDF',
xlabel='height (cm)',
ylabel='CDF',
legend=False)
def _make_pareto_cdf():
"""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 = [_pareto_cdf(x, alpha, xmin) for x in xs]
print('Fraction <= 10', _pareto_cdf(xmin, alpha, 10))
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
_05_myplot._save('pareto_cdf',
title='Pareto CDF',
xlabel='x',
ylabel='CDF',
legend=False)
def _make_expo_cdf():
"""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 = [_expo_cdf(x, lam) for x in xs]
percentile = -math.log(0.05) / lam
print('Fraction <= ', percentile, _expo_cdf(lam, percentile))
pyplot.clf()
pyplot.plot(xs, ps, linewidth=2)
_05_myplot._save('expo_cdf',
title='Exponential CDF',
xlabel='x',
ylabel='CDF',
legend=False)
def _plot_marginals(suite):
"""Plot the marginal distributions for a 2-D joint distribution."""
pmf_m, pmf_s = _compute_marginals(suite)
pyplot.clf()
pyplot.figure(1, figsize=(7, 4))
pyplot.subplot(1, 2, 1)
cdf_m = _13_Cdf._make_cdf_from_pmf(pmf_m, 'mu')
_05_myplot._cdf(cdf_m)
pyplot.xlabel('Mean height (cm)')
pyplot.ylabel('CDF')
pyplot.subplot(1, 2, 2)
cdf_s = _13_Cdf._make_cdf_from_pmf(pmf_s, 'sigma')
_05_myplot._cdf(cdf_s)
pyplot.xlabel('Std Dev height (cm)')
pyplot.ylabel('CDF')
_05_myplot._save(root='bayes_height_marginals_%s' % suite.name)
def main():
print('pae', 0.3 / (0.3 + 3.0 / 13))
doorA = _make_uniform_suite(0.0, 1.0, 101, name='Door A')
evidence = 3, 2
_update(doorA, evidence)
doorC = _make_uniform_suite(0.0, 1.0, 101, name='Door C')
evidence = 3, 10
_update(doorC, evidence)
print(_total_probability(doorA, doorC, _prob_winning))
# plot the posterior distributions
_05_myplot._pmfs([doorA, doorC])
_05_myplot._save(root='blinky',
formats=['pdf', 'png'],
title='Probability of blinking',
xlabel='P(blink)',
ylabel='Posterior probability')
def _make_normal_plot(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)
_05_myplot._save(root,
xlabel='Standard normal values',
legend=False,
**options)
def _make_figures(pool, firsts, others):
"""Creates several figures for the book."""
# plot PMFs of birth weights for first babies and others
_05_myplot._clf()
_05_myplot._hist(firsts.weight_pmf, linewidth=0, color='blue')
_05_myplot._hist(others.weight_pmf, linewidth=0, color='orange')
_05_myplot._save(root='nsfg_birthwgt_pmf',
title='Birth weight PMF',
xlabel='weight (ounces)',
ylabel='probability')
# plot CDFs of birth weights for first babies and others
_05_myplot._clf()
_05_myplot._cdf(firsts.weight_cdf, linewidth=2, color='blue')
_05_myplot._cdf(others.weight_cdf, linewidth=2, color='orange')
_05_myplot._save(root='nsfg_birthwgt_cdf',
title='Birth weight CDF',
xlabel='weight (ounces)',
ylabel='probability',
axis=[0, 200, 0, 1])
def main():
upper_bound = 200
prior = _make_uniform_suite(1, upper_bound, upper_bound)
prior.name = 'prior'
evidence = 60
posterior = prior._copy()
_update(posterior, evidence)
posterior.name = 'posterior'
print(_credible_interval(posterior, 90))
# plot the posterior distribution
pyplot.subplots_adjust(wspace=0.4, left=0.15)
plot_options = dict(linewidth=2)
_05_myplot._pmf(posterior, **plot_options)
_05_myplot._save(root='locomotive',
title='Locomotive problem',
xlabel='Number of trains',
ylabel='Posterior probability')