Flexible Bayesian Regression Modelling PDF
Preview Flexible Bayesian Regression Modelling
AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UnitedKingdom 525BStreet,Suite1650,SanDiego,CA92101,UnitedStates 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom Copyright©2020ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans, electronicormechanical,includingphotocopying,recording,oranyinformationstorageand retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek permission,furtherinformationaboutthePublisher’spermissionspoliciesandourarrangements withorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency, canbefoundatourwebsite:www.elsevier.com/permissions. Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythe Publisher(otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperience broadenourunderstanding,changesinresearchmethods,professionalpractices,ormedical treatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribedherein.In usingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyof others,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors, assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproducts liability,negligenceorotherwise,orfromanyuseoroperationofanymethods,products, instructions,orideascontainedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-815862-3 ForinformationonallAcademicPresspublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:CandiceJanco AcquisitionEditor:CandiceJanco EditorialProjectManager:SusanIkeda ProductionProjectManager:OmerMukthar Designer:ChristianBilbow TypesetbyVTeX Contents Contributors ix Preface xiii 1. BayesianquantileregressionwiththeasymmetricLaplace distribution 1 J.-L.Dortet-Bernadet,Y.Fan,T.Rodrigues 1.1. Introduction 1 1.2. TheasymmetricLaplacedistributionforquantileregression 3 1.3. Oncoverageprobabilities 16 1.4. Postprocessingformultiplefittings 18 1.5. Finalremarksandconclusion 22 References 23 2. Avignetteonmodel-basedquantileregression:analysingexcess zeroresponse 27 ErikaCunningham,SuryaT.Tokdar,JamesS.Clark 2.1. Introduction 28 2.2. Excesszeroregressionanalysis 30 2.3. Casestudydataandobjective 31 2.4. Fittingsinglecovariatebasalareamodels 32 2.5. Interpretingquantileregressions 37 2.6. Assessingmodelassumptionsandmakingimprovements 41 2.7. Predictionandinterpretingpredictedresponses 47 2.8. Fittingmultipleregressionbasalareamodels 50 2.9. Conclusionsandfinalremarks 62 Acknowledgement 63 References 63 3. Bayesiannonparametricdensityregressionforordinalresponses 65 MariaDeYoreo,AthanasiosKottas 3.1. Introduction 65 3.2. Bayesiannonparametricdensityregression 68 3.3. Mixturemodellingforordinalresponses 73 3.4. Summary 86 Acknowledgements 87 References 87 v vi Contents 4. Bayesian nonparametric methods for financial and macroeconomictimeseriesanalysis 91 MariaKalli 4.1. Introduction 91 4.2. Bayesiannonparametricmethodsfortheinnovationdistributionin volatilitymodels 93 4.3. Bayesiannonparametricmethodsforlong-rangedependenceinSV models 98 4.4. Bayesiannonparametricmethodsfortheanalysisofmacroeconomic timeseries 105 4.5. Conclusion 114 References 115 5. Bayesianmixedbinary-continuouscopularegressionwithan applicationtochildhoodundernutrition 121 NadjaKlein,ThomasKneib,GiampieroMarra,RosalbaRadice 5.1. Introduction 121 5.2. Bivariatecopulamodelswithmixedbinary-continuousmarginals 125 5.3. Bayesianinference 132 5.4. Modelselectionandmodelevaluation 138 5.5. Results 142 5.6. Summaryanddiscussion 147 Acknowledgements 149 References 149 6. NonstandardflexibleregressionviavariationalBayes 153 JohnT.Ormerod 6.1. Introduction 154 6.2. Preparatorymodellingcomponents 156 6.3. Astandardsemiparametricregressionmodel 163 6.4. Robustnonparametricregression 165 6.5. Generalisedadditivemodelwithheteroscedasticvariance 170 6.6. Generalisedadditivenegativebinomialmodel 173 6.7. Logisticregressionwithmissingcovariates 177 6.8. Conclusion 182 Acknowledgements 183 References 183 7. ScalableBayesianvariableselectionregressionmodelsforcount data 187 YinsenMiao,JeongHwanKook,YadongLu,MicheleGuindani, MarinaVannucci Contents vii 7.1. Introduction 188 7.2. Bayesianvariableselectionviaspike-and-slabpriors 189 7.3. Negativebinomialregressionmodels 190 7.4. Dirichlet-multinomialregressionmodels 200 7.5. Simulationstudy 206 7.6. Benchmarkapplications 212 7.7. Conclusion 215 References 216 8. Bayesianspectralanalysisregression 221 TaeryonChoi,PeterJ.Lenk 8.1. Introduction 221 8.2. Smoothoperators 223 8.3. Bayesianspectralanalysisregression 227 8.4. Shapeconstraints 234 8.5. Nonnormaldistributions 237 8.6. RlibrarybsamGP 238 8.7. Conclusion 245 Acknowledgements 246 References 246 9. Flexibleregressionmodellingundershapeconstraints 251 AndrewA.Manderson,KevinMurray,BerwinA.Turlach 9.1. Introduction 252 9.2. Orthonormaldesignmatrices 253 9.3. Monotonicpolynomialmodel 254 9.4. Covariateselection 261 9.5. Conclusion 278 References 278 Index 281 Contributors TaeryonChoi KoreaUniversity,DepartmentofStatistics,Seoul,RepublicofKorea JamesS.Clark DukeUniversity,Durham,NC,UnitedStates ErikaCunningham DukeUniversity,Durham,NC,UnitedStates MariaDeYoreo TheRANDCorporation,1776MainSt.,SantaMonica,CA90401,UnitedStates J.-L.Dortet-Bernadet InstitutdeRechercheMathématiqueAvancée,UMR7501CNRS,Universitéde Strasbourg,Strasbourg,France Y.Fan SchoolofMathematicsandStatistics,UniversityofNewSouthWales,Sydney, NSW,Australia MicheleGuindani UniversityofCalifornia,Irvine,DepartmentofStatistics,BrentHall2241,Irvine,CA 92697,UnitedStates MariaKalli UniversityofKent,SchoolofMathematics,Statistics&ActuarialScience,Sibson Building,ParkwoodRoad,Canterbury,CT27FS,UnitedKingdom NadjaKlein HumboldtUniversitätzuBerlin,SchoolofBusinessandEconomics,Unterden Linden6,10099Berlin,Germany ThomasKneib Georg-August-UniversitätGöttingen,FacultyofBusinessandEconomicSciences, Humboldtallee3,37073Göttingen,Germany JeongHwanKook RiceUniversity,DepartmentofStatistics,6100MainSt,Houston,TX77005, UnitedStates ix x Contributors AthanasiosKottas UniversityofCalifornia,SantaCruz,DepartmentofStatistics,1156HighStreet, SantaCruz,CA95064,UnitedStates PeterJ.Lenk UniversityofMichigan,StephenM.RossSchoolofBusiness,AnnArbor,MI, UnitedStates YadongLu UniversityofCalifornia,Irvine,DepartmentofStatistics,BrentHall2241,Irvine,CA 92697,UnitedStates AndrewA.Manderson TheUniversityofWesternAustralia,DepartmentofMathematicsandStatistics, 35StirlingHighway,Crawley,WA6009,Australia GiampieroMarra UniversityCollegeLondon,DepartmentofStatisticalScience,GowerStreet, LondonWC1E6BT,UnitedKingdom YinsenMiao RiceUniversity,DepartmentofStatistics,6100MainSt,Houston,TX77005, UnitedStates KevinMurray TheUniversityofWesternAustralia,SchoolofPopulationandGlobalHealth,35 StirlingHighway,Crawley,WA6009,Australia JohnT.Ormerod SchoolofMathematicsandStatistics,UniversityofSydney,Sydney,NSW2006, Australia ARCCentreofExcellenceforMathematical&StatisticalFrontiers,Universityof Melbourne,Parkville,VIC3010,Australia RosalbaRadice CassBusinessSchool,CityUniversityofLondon,FacultyofActuarialScienceand Insurance,106BunhillRow,LondonEC1Y8TZ,UnitedKingdom T.Rodrigues DepartamentodeEstatistica,UniversidadedeBrasilia,Brasília,Brazil Contributors xi SuryaT.Tokdar DukeUniversity,Durham,NC,UnitedStates BerwinA.Turlach TheUniversityofWesternAustralia,DepartmentofMathematicsandStatistics, 35StirlingHighway,Crawley,WA6009,Australia MarinaVannucci RiceUniversity,DepartmentofStatistics,6100MainSt,Houston,TX77005, UnitedStates Preface The2000sand2010shaveseenhugegrowthinBayesianmodelling,which nowfindsapplicationinfieldsasdiverseasengineering,law,medicine,psy- chology, astronomy, climate science and philosophy. Much of the increase in popularity is due to advances in Bayesian computation, most notably Markov chain Monte Carlo methods. The availability of general and easily applicable simulation-based computational algorithms has made it easier to build more realistic models, involving greater complexity and high dimen- sionality. Introductory textbook accounts of Bayesian regression inference often focus on rather inflexible parametric models. When planning this book, we wanted to bring together, in a single volume, a discussion of Bayesian regression methods allowing three types of flexibility: flexibility in the re- sponselocation,flexibilityintheresponse-covariaterelationship,andflexi- bilityintheerrordistributions.Theaimistoproduceacollectionofworks accessibletopractitioners,whileatthesametimedetailedenoughforinter- estedresearchersinBayesianmethods.Softwareimplementingthemethods in the book is also available. Chapters 1 and 2 cover quantile regression. These are methods where inferential interest may lie away from the mean, in noncentral parts of the distribution. Quantile methods do not specify an error model, and are therefore challenging to implement in the Bayesian setting. Chapters 3 and 4 cover regression using Dirichlet process (DP) mixtures to flexibly capture the unknown error distribution. In Chapter 3, DP mixtures are consideredin anordinal regressionsetting,wheretherelationship between the covariates and response is modelled flexibly via density regression. In Chapter 4, DP mixtures are used for time series. Chapter 5 extends to regression with multivariate response, using the copula approach to han- dle mixed binary-continuous responses. Chapters 6 and 7 cover scalable BayesianmodellingusingvariationalBayesianinference:inChapter6,vari- ational inference is described in detail for various spline-based models to flexibly model the covariate-response relationship in the mean. Chapter 7 developsavariationalalgorithmforcountresponsedata,inthepresenceof variableselection.Finally,Chapters8and9showcasesomeoftheflexibility of the Bayesian methods when models incorporate shape constraints. The chapters of the book often deal with quite specialised and complex models xiii xiv Preface and data types, but some general themes emerge from the discussion. The reader will obtain an understanding of the basic modelling and computa- tionalbuildingblockswhicharefundamentaltosuccessfulnewapplications of modern and flexible Bayesian regression methods. Each of the chapters is written in an easy to follow, tutorial style, with the aim to encourage practitioners to take advantage of powerful Bayesian regression methodology. Computer codes are available for each chapter at the website https://www.elsevier.com/books/ flexible-bayesian-regression-modelling/fan/978-0-12-815862-3 Wherever appropriate, the chapters contain instructions on how to use the codes. We are proud to be able to bring together a book containing the lat- est developments in flexible Bayesian methods. We warmly thank all the contributors to this project. Yanan Fan David Nott Michael S. Smith Jean-Luc Dortet-Bernadet
The list of books you might like
