def comparePriors():
"""Runs the analysis with two different priors and compares them."""
dataset = [60]
high = 1000
thinkplot.clf()
thinkplot.prePlot(num=2)
constructors = [Train, Train2]
labels = ['uniform', 'power law']
# NOTE: the uniform prior means we assign probability 1/1000 to each hypotheses from 1 ... 1000
# note then we normalize it and update by multiplying by likelihood then normalize again (why?)
# NOTE: the power law prior means we assign 1/hypo to each hypothesis from 1 ... 1000
# note: then normalize by summing total and dividing then update by likelihood and normalize again (why?)
for constructor, label in zip(constructors, labels):
suite = makePosterior(high, dataset, constructor)
suite.name = label
thinkplot.pmf(suite)
thinkplot.save(root='train4',
xlabel='Number of trains',
ylabel='Probability')
def makePosterior(high, dataset):
hypos = range(1, high + 1)
suite = Train(hypos)
suite.name = str(high)
for data in dataset:
suite.update(data)
thinkplot.pmf(suite)
return suite
def main():
# note: METHOD 1: assume that f = 0.1 is known! ------------------------
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.save(root='jaynes1',
xlabel='Number of particles (n)',
ylabel='PMF',
formats=FORMATS)
# note: METHOD 2: k is unknown. ---------------------------------------
# plot the posterior distributions of r and n
hypos = range(1, 501, 5)
suite = Emitter(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)
# note: BUILDING ON 2: optimization in Emitter's likelihood.
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='jaynes3',
xlabel='Emission rate',
ylabel='PMF',
formats=FORMATS)
def main():
suite = version2()
print(suite.mean())
thinkplot.pmf(suite)
thinkplot.show()
suite = version3()
print(suite.mean())
thinkplot.pmf(suite)
thinkplot.show()
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 = 'PMF(alpha = 10, beta = %d)' % beta
thinkplot.pmf(pmf)
thinkplot.save('paintball1_pmfOfLocationForRangeOfBetas',
xlabel='Distance',
ylabel='Prob',
formats=FORMATS)
def main():
# Step 1: Prior P(N) = 1/1000
hypos = range(
1, 1001
) # assume there are 1 - 1000 locomotives in the train, given we saw the number 60
suite = Train(hypos)
suite.update(60)
print(suite.mean())
thinkplot.prePlot(1)
thinkplot.pmf(suite)
thinkplot.save(root='train1',
xlabel='Number of trains',
ylabel='Probability',
formats=['pdf', 'eps'])
thinkplot.show()
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) # i=0 (variable we want), j=1 (variable cond), val=beta (value that jth variable must have)
cond.name = 'PMF(alpha | beta = %d)' % beta
thinkplot.pmf(cond)
# THe posterior conditional marginal distributions
thinkplot.save('paintball3_marginalCDFS_for_alpha|beta',
xlabel='Distance',
ylabel='Prob',
formats=FORMATS)
def plotPmfs(self):
"""Plot the PMFs."""
print('Mean y', self.pmf_y.mean())
print('Mean z', self.post_z.mean())
print('Mean zb', self.post_zb.mean())
thinkplot.pmf(self.pmf_y)
thinkplot.pmf(self.post_z)
thinkplot.pmf(self.post_zb)
def main():
pmfDice = thinkbayes.PMF()
pmfDice.set(Die(4), 5)
pmfDice.set(Die(6), 4)
pmfDice.set(Die(8), 3)
pmfDice.set(Die(12), 2)
pmfDice.set(Die(20), 1)
pmfDice.normalize()
#@fix: was unhashable error here:
# http://stackoverflow.com/questions/10994229/how-to-make-an-object-properly-hashable
# http://stackoverflow.com/questions/2909106/python-whats-a-correct-and-good-way-to-implement-hash
mix = thinkbayes.PMF()
for die, weight in pmfDice.items():
for outcome, prob in die.items():
mix.incr(outcome, weight * prob)
mix = thinkbayes.makeMixture(pmfDice)
colors = thinkplot.Brewer.getColors()
thinkplot.hist(mix, width=0.9, color=colors[4])
thinkplot.save(root='dungeons3',
xlabel='Outcome',
ylabel='Probability',
formats=FORMATS)
random.seed(17)
d6 = Die(6, 'd6')
# finding distribution of rolled-dice sum by SIMULATION
dice = [d6] * 3
three = thinkbayes.sampleSum(dice, 1000)
three.name = 'sample'
print("\n\nSAMPLING: ")
three.printSuite()
# finding distribution of rolled-dice sum by ENUMERATION
threeExact = d6 + d6 + d6
threeExact.name = 'exact'
print("\n\nENUMERATION:")
threeExact.printSuite()
thinkplot.prePlot(num=2)
thinkplot.pmf(three)
thinkplot.pmf(threeExact, linestyle='dashed')
thinkplot.save(root='dungeons1',
xlabel='Sum of three d6',
ylabel='Probability',
axis=[2, 19, 0, 0.15],
formats=FORMATS)
thinkplot.clf()
thinkplot.prePlot(num=1)
# Note: pmf of max (best) attribute:
bestAttribute2 = pmfMax(threeExact, threeExact)
bestAttribute4 = pmfMax(bestAttribute2, bestAttribute2)
bestAttribute6 = pmfMax(bestAttribute4, bestAttribute2)
thinkplot.pmf(bestAttribute6)
# Note: finding pmf max using efficient Cdf method:
bestAttributeCdf = threeExact.max(6) #@ Max() in class Cdf
bestAttributeCdf.name = ''
bestAttributePmf = thinkbayes.makePmfFromCdf(bestAttributeCdf)
bestAttributePmf.printSuite()
thinkplot.pmf(bestAttributePmf)
thinkplot.save(root='dungeons2',
xlabel='Sum of three d6',
ylabel='Probability',
axis=[2, 19, 0, 0.23],
formats=FORMATS)