def QUpdatePlot(pmf, data, thresh, label=None):
if (type(data) is int or type(data) is float):
pmf.Update(data)
thinkplot.Pdf(pmf.generateQ(thresh), label=label)
else:
pmf.UpdateSet(data)
thinkplot.Pdf(pmf.generateQ(thresh), label=label)
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():
hypos = range(0, 101)
suite = Electorate(hypos)
thinkplot.PrePlot(3)
thinkplot.Pdf(suite, label='prior')
data = 1.1, 3.7, 53
suite.Update(data)
thinkplot.Pdf(suite, label='posterior1')
thinkplot.Save(root='electorate1',
xlabel='percentage of electorate',
ylabel='PMF',
formats=['png'],
clf=False)
print(suite.Mean())
print(suite.Std())
print(suite.ProbLess(50))
data = -2.3, 4.1, 49
suite.Update(data)
thinkplot.Pdf(suite, label='posterior2')
thinkplot.Save(root='electorate2',
xlabel='percentage of electorate',
ylabel='PMF',
formats=['png'])
print(suite.Mean())
print(suite.Std())
print(suite.ProbLess(50))
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 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 main():
hypos = numpy.linspace(0, 100, 101)
suite = Electorate(hypos)
thinkplot.Pdf(suite, label='prior')
data = 1.1, 3.7, 53
suite.Update(data)
thinkplot.Pdf(suite, label='posterior')
thinkplot.Show()
def MakePdfs(greq, less):
greqpdf = thinkstats2.EstimatedPdf(greq.totalwgt_lb.dropna())
lesspdf = thinkstats2.EstimatedPdf(less.totalwgt_lb.dropna())
thinkplot.PrePlot(rows=1, cols=2)
thinkplot.SubPlot(1)
thinkplot.Pdf(greqpdf, label='greater/equal to 30')
thinkplot.Config(xlabel='Birth weight (lbs)', ylabel='PDF')
thinkplot.SubPlot(2)
thinkplot.Pdf(lesspdf, label='less than 30')
thinkplot.Config(xlabel='Birth weight (lbs)', ylabel='PDF')
thinkplot.Show()
def main():
hypos = numpy.linspace(0, 12, 201)
suite = Soccer(hypos)
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())
thinkplot.Show()
def main():
hypos = range(1, 1000)
suite = Hyrax(hypos)
suite2 = Hyrax2(hypos)
data = 10, 10, 2
suite.Update(data)
suite2.Update(data)
thinkplot.Pdf(suite, label='binomial')
thinkplot.Pdf(suite, label='hypergeom')
thinkplot.Show()
def main(): maleRates = [0.52, 0.38, 0.39, 1.01, 2.63] femaleRates = [50, 20.5] pdfMale = thinkbayes2.EstimatedPdf(maleRates) pdfFemale = thinkbayes2.EstimatedPdf(femaleRates) low, high = 0, 100 n = 1001 xs = numpy.linspace(low, high, n) pmfMale = pdfMale.MakePmf(steps=xs) pmfFemale = pdfFemale.MakePmf(steps=xs) thinkplot.Pdf(pdfMale, label='Male Prior') thinkplot.Pdf(pdfFemale, label='Female Prior') thinkplot.show()
def main():
hypos = numpy.linspace(0, 100, 101)
suite = Electorate(hypos)
thinkplot.Pdf(suite, label='prior')
data = 1.1, 3.7, 53
suite.Update(data)
thinkplot.Pdf(suite, label='posterior')
thinkplot.Show()
print(suite.Std())
print(suit.Mean())
print(suite.ProbLess(50))
def main():
suite = Version3()
print(suite.Mean())
thinkplot.Pdf(suite)
thinkplot.Show(legend=False)
def main():
suite = Euro(range(0, 101))
suite.Update('H')
thinkplot.Pdf(suite)
thinkplot.Show(xlabel='x', ylabel='Probability', legend=False)
def main(): maleRates = [0.52, 0.38, 0.39, 1.01, 2.63, 30] femaleRates = [50, 20.5, 40, 30, 45] pdfMale = thinkbayes2.EstimatedPdf(maleRates) pdfFemale = thinkbayes2.EstimatedPdf(femaleRates) low, high = 0, 100 n = 1001 xs = numpy.linspace(low, high, n) pmfMale = MakePmfTest(pdfMale,steps=xs) pmfFemale = MakePmfTest(pdfFemale,steps=xs) pmfMale.Normalize() pmfFemale.Normalize() thinkplot.Pdf(pmfMale, label='Male Prior') thinkplot.Pdf(pmfFemale, label='Female Prior') thinkplot.show()
def main():
hypos = range(1, 1000)
suite = Hyrax(hypos)
data = 10, 10, 2
suite.Update(data)
thinkplot.Pdf(suite, label='posterior')
thinkplot.Show()
def main():
hypos = numpy.linspace(0, 100, 101)
suite = Electorate(hypos)
thinkplot.Pdf(suite, label='prior')
data = 1.1, 3.7, 53 #mean prior error, std, measurement
suite.Update(data)
PrintSuiteInfo(suite)
thinkplot.Pdf(suite, label='before poll')
newpolldata = -2.3, 4.1, 49
suite.Update(newpolldata)
PrintSuiteInfo(suite)
thinkplot.Pdf(suite, label='after poll')
thinkplot.Show()
def PriorPost(pmf, data):
thinkplot.Pdf(pmf, label='Prior')
pmf.UpdateSet(data)
thinkplot.Pdf(pmf, label='Posterior')
# thinkplot.Show(xlabel='Lambda',
# ylabel='Probability',
# legend=True,
# title='Arrival Rate Distribution')
formats = ['png']
root = 'PriorAndPosterior'
thinkplot.Save(root=root,
xlabel='Lambda',
ylabel='Probability',
legend=True,
formats=formats,
title='Arrival Rate Distribution')
def generate_pmf(fb, hk):
pmf_fb = Pmf(degrees(fb))
pmf_hk = Pmf(degrees(hk))
thinkplot.preplot(cols=2)
thinkplot.plot([30, 2000], [5e-2, 2e-4], color='gray', linestyle='dashed')
thinkplot.Pdf(pmf_fb, style='.', label='Facebook')
thinkplot.config(xscale='log', yscale='log', xlabel='degree', ylabel='PMF')
thinkplot.subplot(2)
thinkplot.plot([55, 500], [5e-2, 2e-4], color='gray', linestyle='dashed')
thinkplot.Pdf(pmf_hk, style='.', label='HK graph')
thinkplot.config(xscale='log', yscale='log', xlabel='degree', ylabel='PMF')
plt.savefig('PMFGraphs_Original.png')
def generate_pmf(fb, hk):
pmf_fb = Pmf(degrees(fb))
pmf_hk = Pmf(degrees(hk))
thinkplot.plot([6, 150], [5e-1, 2e-4], color='gray', linestyle='dashed')
thinkplot.Pdf(pmf_hk, style='.', label='RPA')
thinkplot.config(xscale='log', yscale='log', xlabel='degree', ylabel='PMF')
plt.savefig('PMFGraphs_Modified.png')
def MakePdfExample():
# mean and var of women's heights in cm, from the BRFSS
mean, var = 163, 52.8
std = math.sqrt(var)
# make a PDF and compute a density, FWIW
pdf = thinkstats2.GaussianPdf(mean, std)
print(pdf.Density(mean + std))
# make a PMF and plot it
thinkplot.PrePlot(2)
thinkplot.Pdf(pdf, label='Gaussian')
# make a sample, make an estimated PDF, and plot it
sample = [random.gauss(mean, std) for i in range(100)]
sample_pdf = thinkstats2.EstimatedPdf(sample)
thinkplot.Pdf(sample_pdf, label='sample KDE')
thinkplot.Save(root='pdf_example', xlabel='Height (cm)', ylabel='Density')
def main():
suite = Euro(range(0, 101))
obs = 'H' * 140 + 'T' * 110
for o in obs:
suite.Update(o)
thinkplot.Pdf(suite)
thinkplot.Show(xlabel='x', ylabel='Probability', legend=False)
print(suite.Mean(), suite.MaximumLikelihood(), suite.CredibleInterval(90))
def ComputeSkewnesses():
"""Plots KDE of birthweight and adult weight.
"""
def VertLine(x, y):
thinkplot.Plot([x, x], [0, y], color='0.6', linewidth=1)
live, firsts, others = first.MakeFrames()
data = live.totalwgt_lb.dropna()
print('Birth weight')
mean, median = Summarize(data)
y = 0.35
VertLine(mean, y)
thinkplot.Text(mean - 0.15, 0.1 * y, 'mean', horizontalalignment='right')
VertLine(median, y)
thinkplot.Text(median + 0.1, 0.1 * y, 'median', horizontalalignment='left')
pdf = thinkstats2.EstimatedPdf(data)
thinkplot.Pdf(pdf, label='birth weight')
thinkplot.Save(root='density_totalwgt_kde', xlabel='lbs', ylabel='PDF')
df = brfss.ReadBrfss(nrows=None)
data = df.wtkg2.dropna()
print('Adult weight')
mean, median = Summarize(data)
y = 0.02499
VertLine(mean, y)
thinkplot.Text(mean + 1, 0.1 * y, 'mean', horizontalalignment='left')
VertLine(median, y)
thinkplot.Text(median - 1.5,
0.1 * y,
'median',
horizontalalignment='right')
pdf = thinkstats2.EstimatedPdf(data)
thinkplot.Pdf(pdf, label='adult weight')
thinkplot.Save(root='density_wtkg2_kde',
xlabel='kg',
ylabel='PDF',
xlim=[0, 200])
def main():
data = 20, 15, 3
probs = numpy.linspace(0, 1, 31)
hypos = []
for n in range(32, 350):
for p1 in probs:
for p2 in probs:
hypos.append((n, p1, p2))
suite = Lincoln(hypos)
suite.Update(data)
n_marginal = suite.Marginal(0)
thinkplot.Pmf(n_marginal, label='n')
thinkplot.Save(root='lincoln1',
xlabel='number of bugs',
ylabel='PMF',
formats=['pdf', 'png'])
print('post mean n', n_marginal.Mean())
print('MAP n', n_marginal.MaximumLikelihood())
p1_marginal = suite.Marginal(1, label='p1')
p2_marginal = suite.Marginal(2, label='p2')
thinkplot.Pdf(p1_marginal)
thinkplot.Pdf(p2_marginal)
thinkplot.Show()
print('post mean p1', p1_marginal.Mean())
print('MAP p1', p1_marginal.MaximumLikelihood())
print('post mean p2', p2_marginal.Mean())
print('MAP p2', p2_marginal.MaximumLikelihood())
print('p1 > p2', p1_marginal > p2_marginal)
print('p1 < p2', p1_marginal < p2_marginal)
def MakePdfExample(n=500):
"""Plots a normal density function and a KDE estimate.
n: sample size
"""
# mean and var of women's heights in cm, from the BRFSS
mean, var = 163, 52.8
std = math.sqrt(var)
# make a PDF and compute a density, FWIW
pdf = thinkstats2.NormalPdf(mean, std)
print(pdf.Density(mean + std))
# make a PMF and plot it
thinkplot.PrePlot(2)
thinkplot.Pdf(pdf, label='normal')
# make a sample, make an estimated PDF, and plot it
sample = [random.gauss(mean, std) for _ in range(n)]
sample_pdf = thinkstats2.EstimatedPdf(sample)
thinkplot.Pdf(sample_pdf, label='sample KDE')
thinkplot.Save(root='pdf_example', xlabel='Height (cm)', ylabel='Density')
def MakePmfPlot(alpha = 10):
"""Plots Pmf of location for a range of betas."""
locations = range(0, 31)
betas = [10, 20, 40]
thinkplot.PrePlot(num=len(betas))
for beta in betas:
pmf = MakeLocationPmf(alpha, beta, locations)
pmf.name = 'beta = %d' % beta
thinkplot.Pdf(pmf)
thinkplot.Save('paintball1',
xlabel='Distance',
ylabel='Prob',
formats=FORMATS)
def main():
ps = numpy.linspace(0, 1, 101)
bill = Billiards(ps)
bill.Update((5, 3))
thinkplot.Pdf(bill)
thinkplot.Save(root='billiards1',
xlabel='probability of win',
ylabel='PDF',
formats=['png'])
bayes_result = ProbWinMatch(bill)
print(thinkbayes.Odds(1-bayes_result))
mle = 5 / 8
freq_result = (1-mle)**3
print(thinkbayes.Odds(1-freq_result))
def MakeConditionalPlot(suite):
"""Plots marginal CDFs for alpha conditioned on beta.
suite: posterior joint distribution of location
"""
betas = [10, 20, 40]
thinkplot.PrePlot(num=len(betas))
for beta in betas:
cond = suite.Conditional(0, 1, beta)
cond.name = 'beta = %d' % beta
thinkplot.Pdf(cond)
thinkplot.Save('paintball3',
xlabel='Distance',
ylabel='Prob',
formats=FORMATS)
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')
sample = np.power(10, log_sample)
mean, median = density.Summarize(sample)
cdf = thinkstats2.Cdf(sample)
print('cdf[mean]', cdf[mean])
pdf = thinkstats2.EstimatedPdf(sample)
thinkplot.Pdf(pdf)
thinkplot.Show(xlabel='household income', ylabel='PDF')
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')
sample = np.power(10, log_sample)
mean = np.mean(sample)
cdf = thinkstats2.Cdf(sample)
print "Median:", np.median(sample)
print "Mean:", mean
print "Skewness:", thinkstats2.Skewness(sample)
print "Pearson's Skewness:", thinkstats2.PearsonMedianSkewness(sample)
print "Percent of people with incomes <= mean:", cdf[mean]
pdf = thinkstats2.EstimatedPdf(sample)
thinkplot.Pdf(pdf)
#
# - probability dencity function
#
# $PDF_{normal}(x) = \frac{1}{\sigma \sqrt{2\pi}}\exp[-\frac{1}{2}(\frac{x-\mu}{\sigma})^2]$
#%%
import thinkstats2
import math
mean, var = 163, 52.8
std = math.sqrt(var)
pdf = thinkstats2.NormalPdf(mean, std)
pdf.Density(mean + std)
#%%
import thinkplot
thinkplot.Pdf(pdf, label='normal')
thinkplot.Show(xlabel='height (cm)', ylabel='dencity')
#%%
pmf = pdf.MakePmf()
#%% [markdown]
# ## 6.2 KDE
#
# - Kernel density estimation
#%%
import random
sample = [random.gauss(mean, std) for _ in range(500)]
sample_pdf = thinkstats2.EstimatedPdf(sample)
thinkplot.Pdf(sample_pdf, label='sample KDE')
