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We will adopt a pragmatic approach to Bayesian statistics and we will not care too much about other statistical paradigms and their relationship to Bayesian statistics. The aim of this book is to learn about Bayesian data analysis with the help of Python.
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BayesianAnalysiswithPython
TableofContents
BayesianAnalysiswithPython
Credits
AbouttheAuthor
AbouttheReviewer
www.PacktPub.com
eBooks,discountoffers,andmore
Whysubscribe?
Preface
Whatthisbookcovers
Whatyouneedforthisbook
Whothisbookisfor
Conventions
Readerfeedback
Customersupport
Downloadingtheexamplecode
Downloadingthecolorimagesofthisbook
Errata
Piracy
Questions
1.ThinkingProbabilistically-ABayesianInferencePrimer
Statisticsasaformofmodeling
Exploratorydataanalysis
Inferentialstatistics
Probabilitiesanduncertainty
Probabilitydistributions
Bayes'theoremandstatisticalinference
Singleparameterinference
Thecoin-flippingproblem
Thegeneralmodel
Choosingthelikelihood
Choosingtheprior
Gettingtheposterior
Computingandplottingtheposterior
Influenceofthepriorandhowtochooseone
CommunicatingaBayesiananalysis
Modelnotationandvisualization
Summarizingtheposterior
Highestposteriordensity
Posteriorpredictivechecks
InstallingthenecessaryPythonpackages
Summary
Exercises
2.ProgrammingProbabilistically–APyMC3Primer
Probabilisticprogramming
Inferenceengines
Non-Markovianmethods
Gridcomputing
Quadraticmethod
Variationalmethods
Markovianmethods
MonteCarlo
Markovchain
Metropolis-Hastings
HamiltonianMonteCarlo/NUTS
OtherMCMCmethods
PyMC3introduction
Coin-flipping,thecomputationalapproach
Modelspecification
Pushingtheinferencebutton
Diagnosingthesamplingprocess
Convergence
Autocorrelation
Effectivesize
Summarizingtheposterior
Posterior-baseddecisions
ROPE
Lossfunctions
Summary
Keepreading
Exercises
3.JugglingwithMulti-ParametricandHierarchicalModels
Nuisanceparametersandmarginalizeddistributions
Gaussians,Gaussians,Gaussianseverywhere
Gaussianinferences
Robustinferences
Student'st-distribution
Comparinggroups
Thetipsdataset
Cohen'sd
Probabilityofsuperiority
Hierarchicalmodels
Shrinkage
Summary
Keepreading
Exercises
4.UnderstandingandPredictingDatawithLinearRegressionModels
Simplelinearregression
Themachinelearningconnection
Thecoreoflinearregressionmodels
Linearmodelsandhighautocorrelation
Modifyingthedatabeforerunning
Changingthesamplingmethod
Interpretingandvisualizingtheposterior
Pearsoncorrelationcoefficient
PearsoncoefficientfromamultivariateGaussian
Robustlinearregression
Hierarchicallinearregression
Correlation,causation,andthemessinessoflife
Polynomialregression
Interpretingtheparametersofapolynomialregression
Polynomialregression–theultimatemodel?
Multiplelinearregression
Confoundingvariablesandredundantvariables
Multicollinearityorwhenthecorrelationistoohigh
Maskingeffectvariables
Addinginteractions
TheGLMmodule
Summary
Keepreading
Exercises
5.ClassifyingOutcomeswithLogisticRegression
Logisticregression
Thelogisticmodel
Theirisdataset
Thelogisticmodelappliedtotheirisdataset
Makingpredictions
Multiplelogisticregression
Theboundarydecision
Implementingthemodel
Dealingwithcorrelatedvariables
Dealingwithunbalancedclasses
Howdowesolvethisproblem?
Interpretingthecoefficientsofalogisticregression
Generalizedlinearmodels
Softmaxregressionormultinomiallogisticregression
Discriminativeandgenerativemodels
Summary
Keepreading
Exercises
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