printingsandremainstobeakeyreferenceonappliedstatisticalmodellingutilizing generalizedlinearmodels. Ludwigalsohadgreatin?uenceonthecreationofthe StatisticalModellingSociety,andiscurrentlyontheadvisoryboardofthecor- spondingjournalon"StatisticalModelling. "Boththesocietyandjournalemerged outoftheearlyGLIMworkshopsandproceedings. v vi Foreword Ofcourse,Ludwig'sworkisde?nitelynotrestrictedtogeneralizedlinearmodels but-onthecontrary-spansawiderangeofmodernStatistics. Heco-authoredor co-editedseveralmonographs,e. g. onMultivariateStatistics,StochasticProcesses, MeasurementofCreditRisks,aswellaspopulartextbooksonRegressionandan IntroductiontoStatistics. Hisrecentresearchcontributionsaremostlyconcentrated insemiparametricregressionandspatialstatisticswithinaBayesianframework. When?rstcirculatingtheideaofaFestschriftforthecelebrationofLudwig's 65thbirthday,allpotentialcontributorswereextremelypositive,manyimmediately agreeingtocontribute. ThesereactionsatesttoLudwig'shighpersonalandp- fessionalappreciationinthestatisticalcommunity. Thefarreachingandvarietyof subjectscoveredwithinthesecontributionsalsorepresentsLudwig'sbroadinterest andimpactinmanybranchesofmodernStatistics. BotheditorsofthisFestschriftwereluckyenoughtoworkwithLudwigatseveral occasionsandinparticularearlyintheircareersasPhDstudentsandPostDocs. His personalandprofessionalmentorshipandhisstrongcommitmentmadehimaperfect supervisorandhispatient,con?dentandencouragingworkingstylewillalwaysbe rememberedbyallofhisstudentsandcolleagues. Ludwigalwaysprovidedafriendly workingenvironmentthatmadeitapleasureandanhonortobeapartofhisworking group. WeareproudtobeabletosaythatLudwigismuchmorethanacolleague butturnedintoafriendforbothofus. OldenburgandMunich,January2010 ThomasKneib,GerhardTutz Acknowledgements Theeditorswouldliketoexpresstheirgratitudeto . allauthorsofthisvolumefortheiragreementtocontributeandtheireasyco- erationatseveralstagesofputtingtogetherthe?nalversionoftheFestschrift. . JohannaBrandt,JanGertheiss,AndreasGroll,FelixHeinzl,SebastianPetry,Jan UlbrichtandStephanieRubenbauerfortheirinvaluablecontributionsinproof- A readingandcorrectionofthepapers,aswellasinsolvingseveralLTX-related E problems. . theSpringerVerlagforagreeingtopublishthisFestschriftandinparticularNils- PeterThomas,AliceBlanck and FrankHolzwarthfor the smooth collabo- tion in preparing th emanuscript. vii Contents ListofContributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix TheSmoothComplexLogarithmandQuasi-PeriodicModels . . . . . . . . . . 1 PaulH. C. Eilers 1 Foreword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 DataandModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. 1 TheBasicModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. 2 SplinesandPenalties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. 3 StartingValues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3. 4 SimpleTrendCorrectionandPriorTransformation. . . . . 8 3. 5 AComplexSignal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. 6 Non-normalDataandCascadedLinks. . . . . . . . . . . . . . . . 10 3. 7 AddingHarmonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4 MoretoExplore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 P-splineVaryingCoef?cientModelsforComplexData. . . . . . . . . . . . . . . . 19 BrianD. Marx 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 "LargeScale"VCM,withoutBack?tting. . . . . . . . . . . . . . . . . . . . . . 22 3 NotationandSnapshotofaSmoothingTool:B-splines. . . . . . . . . . 24 3. 1 GeneralKnotPlacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3. 2 SmoothingtheKTBData. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4 UsingB-splinesforVaryingCoef?cientModels. . . . . . . . . . . . . . . . 26 5 P-splineSnapshot:Equally-SpacedKnots&Penalization. . . . . . . . 28 5. 1 P-splinesforAdditiveVCMs. . . . . . . . . . . . . . . . . . . . . . . . 30 5. 2 StandardErrorBands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6 OptimallyTuningP-splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7 MoreKTBResults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8 ExtendingP-VCMintotheGeneralizedLinearModel. . . . . . . . . . 33 9 Two-dimensionalVaryingCoef?cientModels. . . . . . . . . . . . . . . . . 36 ix x Contents 9. 1 Mechanicsof2D-VCMthroughExample . . . . . . . . . . . . . 37 9. 2 VCMsandPenaltiesasArrays. . . . . . . . . . . . . . . . . . . . . . . 39 9. 3 Ef?cientComputationUsingArrayRegression. . . . . . . . . 40 10 DiscussionTowardMoreComplexVCMs. . . . . . . . . . . . . . . . . . . . . 41 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 PenalizedSplines,MixedModelsandBayesianIdeas. . . . . . . . . . . . . . . . . . 45 ¿ GoranKauermann 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2 NotationandPenalizedSplinesasLinearMixedModels. . . . . . . . 46 3 Classi?cationwithMixedModels. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4 VariableSelectionwithSimplePriors. . . . . . . . . . . . . . . . . . . . . . . . 50 4. 1 MarginalAkaikeInformationCriterion. . . . . . . . . . . . . . . 50 4. 2 ComparisoninLinearModels. . . . . . . . . . . . . . . . . . . . . . .

The Smooth Complex Logarithm and Quasi-Periodic Models.- P-spline Varying Coefficient Models for Complex Data.- Penalized Splines, Mixed Models and Bayesian Ideas.- Bayesian Linear Regression #x2014; Different Conjugate Models and Their (In)Sensitivity to Prior-Data Conflict.- An Efficient Model Averaging Procedure for Logistic Regression Models Using a Bayesian Estimator with Laplace Prior.- Posterior and Cross-validatory Predictive Checks: A Comparison of MCMC and INLA.- Data Augmentation and MCMC for Binary and Multinomial Logit Models.- Generalized Semiparametric Regression with Covariates Measured with Error.- Determinants of the Socioeconomic and Spatial Pattern of Undernutrition by Sex in India: A Geoadditive Semi-parametric Regression Approach.- Boosting for Estimating Spatially Structured Additive Models.- Generalized Linear Mixed Models Based on Boosting.- Measurement and Predictors of a Negative Attitude towards Statistics among LMU Students.- Graphical Chain Models and their Application.- Indirect Comparison of Interaction Graphs.- Modelling, Estimation and Visualization of Multivariate Dependence for High-frequency Data.- Ordinal- and Continuous-Response Stochastic Volatility Models for Price Changes: An Empirical Comparison.- Copula Choice with Factor Credit Portfolio Models.- Penalized Estimation for Integer Autoregressive Models.- Bayesian Inference for a Periodic Stochastic Volatility Model of Intraday Electricity Prices.- Online Change-Point Detection in Categorical Time Series.- Multiple Linear Panel Regression with Multiplicative Random Noise.- A Note on Using Multiple Singular Value Decompositions to Cluster Complex Intracellular Calcium Ion Signals.- On the self-regularization property of the EM algorithm for Poisson inverse problems.- SequentialDesign of Computer Experiments for Constrained Optimization.