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 plotJointDist(pmf1, pmf2, thresh=0.8):
"""Plot the joint distribution of p_correct.
pmf1, pmf2: posterior distributions
thresh: lower bound of the range to be plotted
"""
def clean(pmf):
"""Removes values below thresh."""
vals = [val for val in pmf.keys() if val < thresh]
[pmf.remove(val) for val in vals]
clean(pmf1)
clean(pmf2)
pmf = thinkbayes.makeJoint(pmf1, pmf2)
thinkplot.figure(figsize=(6, 6))
thinkplot.contour(pmf, contour=False, pcolor=True)
thinkplot.plot([thresh, 1.0], [thresh, 1.0],
color='gray',
alpha=0.2,
linewidth=4)
thinkplot.save(root='sat_4_joint',
xlabel='p_correct Alice',
ylabel='p_correct Bob',
axis=[thresh, 1.0, thresh, 1.0],
formats=['pdf'])
def MakeNormalPlot(weights):
"""Generates a normal probability plot of birth weights.
weights: sequence
"""
mean, var = thinkbayes2.TrimmedMeanVar(weights, p=0.01)
std = math.sqrt(var)
xs = [-5, 5]
xs, ys = thinkbayes2.FitLine(xs, mean, std)
thinkplot.plot(xs, ys, color='0.8', label='model')
xs, ys = thinkbayes2.NormalProbability(weights)
thinkplot.plot(xs, ys, label='weights')
def MakeNormalModel(weights):
"""Plots a CDF with a Normal model.
weights: sequence
"""
cdf = thinkbayes2.Cdf(weights, label='weights')
mean, var = thinkbayes2.TrimmedMeanVar(weights)
std = math.sqrt(var)
print('n, mean, std', len(weights), mean, std)
xmin = mean - 4 * std
xmax = mean + 4 * std
xs, ps = thinkbayes2.RenderNormalCdf(mean, std, xmin, xmax)
thinkplot.plot(xs, ps, label='model', linewidth=4, color='0.8')
thinkplot.cdf(cdf)
def plotExpectedGains(guess1=20000, guess2=40000):
"""Plots expected gains as a function of bid.
guess1: player1's estimate of the price of showcase 1
guess2: player2's estimate of the price of showcase 2
"""
player1, player2 = makePlayers()
makePlots(player1, player2)
player1.makeBeliefs(guess1)
player2.makeBeliefs(guess2)
print('\n\nPlayer 1 prior mle', player1.prior.maximumLikelihood())
print('Player 2 prior mle', player2.prior.maximumLikelihood())
print('\nPlayer 1 mean', player1.posterior.mean())
print('Player 2 mean', player2.posterior.mean())
print('\nPlayer 1 mle', player1.posterior.maximumLikelihood())
print('Player 2 mle', player2.posterior.maximumLikelihood())
player1.plotBeliefs('price3_prior,posterior_player1') # was price3
player2.plotBeliefs('price4_prior,posterior_player2') # was price4
calc1 = GainCalculator(player1, player2)
calc2 = GainCalculator(player2, player1)
thinkplot.clf()
thinkplot.prePlot(num=2)
# NOTE: player 1 optimal bid = 21,000, expgain = 16,700, best guesss = 20,000
bids, gains = calc1.expectedGains()
thinkplot.plot(bids, gains, label='Player 1')
print('\nPlayer 1 optimal bid', max(zip(gains, bids)))
# NOTE: player 2 optimal bid = 31,500, expgain = 19,400, best guess = 40,000
bids, gains = calc2.expectedGains()
thinkplot.plot(bids, gains, label='Player 2')
print('Player 2 optimal bid', max(zip(gains, bids)))
thinkplot.save(root='price5_expectedGainsFromBids_player1,2',
xlabel='bid ($)',
ylabel='expected gain ($)',
formats=FORMATS)
def plotOptimalBid():
"""Plots optimal bid vs estimated price.
"""
player1, player2 = makePlayers()
guesses = numpy.linspace(15000, 60000, 21) # note we don't know the guesses so we make some up.
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_mean_bid_gains',
xlabel='guessed price ($)',
formats=FORMATS)
def runLoop(gap_times, nums, lmbda=0.0333):
"""Runs the basic analysis for a range of num_passengers.
gap_times: sequence of float
nums: sequence of values for num_passengers
lam: arrival rate in passengers per second
Returns: WaitMixtureEstimator
"""
global UPPER_BOUND
UPPER_BOUND = 4000
thinkplot.clf()
randomSeed(18)
# resample gap_times
n = 220
cdf_z = thinkbayes.makeCdfFromList(gap_times)
sample_z = cdf_z.sample(n)
pmf_z = thinkbayes.makePmfFromList(sample_z)
# compute the biased pmf and add some long delays
cdf_zp = biasPmf(pmf_z).makeCdf()
sample_zb = cdf_zp.sample(n) + [1800, 2400, 3000]
# smooth the distribution of zb
pdf_zb = thinkbayes.EstimatedPDF(sample_zb)
xs = makeRange(low=60)
pmf_zb = pdf_zb.makePmf(xs)
# unbias the distribution of zb and make wtc
pmf_z = unbiasPmf(pmf_zb)
wtc = WaitTimeCalculator(pmf_z)
# NOTE: THis is the prob of long wait part on page 89
# Given number of passengers on platform, problongwait makes an
# * elapsedtimeestimator
# * extracts dist of wait time (y)
# * compute probability that wait time exceeds minutes (15 here)
# RESULT PLOT: when passgrs num < 20, system isoperating normally so prob of long delay is small
# But if greater than 30 pssgrs, then it has been 15 mins since last train, which is longer than
# normal delay so need to take taxi.
probs = []
for num_passengers in nums:
ete = ElapsedTimeEstimator(wtc, lmbda, num_passengers)
# compute the posterior prob of waiting more than 15 minutes
cdf_y = ete.pmf_y.makeCdf()
prob = 1 - cdf_y.prob(900)
probs.append(prob)
# thinkplot.Cdf(ete.pmf_y.MakeCdf(name=str(num_passengers)))
thinkplot.plot(nums, probs)
thinkplot.save(
root='redline5',
xlabel='Num passengers',
ylabel='P(y > 15 min)',
formats=FORMATS,
)