book

Think Bayes

by Allen B. Downey

September 2013

Beginner

210 pages

4h 38m

English

O'Reilly Media, Inc.

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My theory, which is mineModeling and approximationWorking with the codeCode stylePrerequisitesConventions Used in This BookSafari® Books OnlineHow to Contact UsContributor List
Conditional probabilityConjoint probabilityThe cookie problemBayes’s theoremThe diachronic interpretationThe M&M problemThe Monty Hall problemDiscussion
DistributionsThe cookie problemThe Bayesian frameworkThe Monty Hall problemEncapsulating the frameworkThe M&M problemDiscussionExercises
The dice problemThe locomotive problemWhat about that prior?An alternative priorCredible intervalsCumulative distribution functionsThe German tank problemDiscussionExercises
The Euro problemSummarizing the posteriorSwamping the priorsOptimizationThe beta distributionDiscussionExercises
OddsThe odds form of Bayes’s theoremOliver’s bloodAddendsMaximaMixturesDiscussion
The Price is Right problemThe priorProbability density functionsRepresenting PDFsModeling the contestantsLikelihoodUpdateOptimal biddingDiscussion
The Boston Bruins problemPoisson processesThe posteriorsThe distribution of goalsThe probability of winningSudden deathDiscussionExercises
The Red Line problemThe modelWait timesPredicting wait timesEstimating the arrival rateIncorporating uncertaintyDecision analysisDiscussionExercises
PaintballThe suiteTrigonometryLikelihoodJoint distributionsConditional distributionsCredible intervalsDiscussionExercises

The Variability HypothesisMean and standard deviationUpdateThe posterior distribution of CVUnderflowLog-likelihoodA little optimizationABCRobust estimationWho is more variable?DiscussionExercises
Back to the Euro problemMaking a fair comparisonThe triangle priorDiscussionExercises
Interpreting SAT scoresThe scaleThe priorPosteriorA better modelCalibrationPosterior distribution of efficacyPredictive distributionDiscussion
The Kidney Tumor problemA simple modelA more general modelImplementationCaching the joint distributionConditional distributionsSerial CorrelationDiscussion
The Geiger counter problemStart simpleMake it hierarchicalA little optimizationExtracting the posteriorsDiscussionExercises
Belly button bacteriaLions and tigers and bearsThe hierarchical versionRandom samplingOptimizationCollapsing the hierarchyOne more problemWe’re not done yetThe belly button dataPredictive distributionsJoint posteriorCoverageDiscussion

Content preview from Think Bayes

Chapter 7. Prediction

The Boston Bruins problem

In the 2010-11 National Hockey League (NHL) Finals, my beloved Boston Bruins played a best-of-seven championship series against the despised Vancouver Canucks. Boston lost the first two games 0-1 and 2-3, then won the next two games 8-1 and 4-0. At this point in the series, what is the probability that Boston will win the next game, and what is their probability of winning the championship?

As always, to answer a question like this, we need to make some assumptions. First, it is reasonable to believe that goal scoring in hockey is at least approximately a Poisson process, which means that it is equally likely for a goal to be scored at any time during a game. Second, we can assume that against a particular opponent, each team has some long-term average goals per game, denoted λ.

Given these assumptions, my strategy for answering this question is

Use statistics from previous games to choose a prior distribution for λ.
Use the score from the first four games to estimate λ for each team.
Use the posterior distributions of λ to compute distribution of goals for each team, the distribution of the goal differential, and the probability that each team wins the next game.
Compute the probability that each team wins the series.

To choose a prior distribution, I got some statistics from http://www.nhl.com, specifically the average goals per game for each team in the 2010-11 season. The distribution is roughly Gaussian with mean 2.8 and standard deviation ...