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 8. Observer Bias

The Red Line problem

In Massachusetts, the Red Line is a subway that connects Cambridge and Boston. When I was working in Cambridge I took the Red Line from Kendall Square to South Station and caught the commuter rail to Needham. During rush hour Red Line trains run every 7–8 minutes, on average.

When I arrived at the station, I could estimate the time until the next train based on the number of passengers on the platform. If there were only a few people, I inferred that I just missed a train and expected to wait about 7 minutes. If there were more passengers, I expected the train to arrive sooner. But if there were a large number of passengers, I suspected that trains were not running on schedule, so I would go back to the street level and get a taxi.

While I was waiting for trains, I thought about how Bayesian estimation could help predict my wait time and decide when I should give up and take a taxi. This chapter presents the analysis I came up with.

This chapter is based on a project by Brendan Ritter and Kai Austin, who took a class with me at Olin College. The code in this chapter is available from http://thinkbayes.com/redline.py. The code I used to collect data is in http://thinkbayes.com/redline_data.py. For more information see “Working with the code”.

The model

Before we get to the analysis, we have to make some modeling decisions. First, I will treat passenger arrivals as a Poisson process, which means I assume that passengers are equally likely to ...