Take me out to (analyze) the ballgame: visualization and analysis techniques for big spatial data

145 Pages·2017·27.8 MB·English

AN ABSTRACT OF THE DISSERTATION OF
ChrisComiskeyforthedegreeofDoctorofPhilosophyinStatisticspresentedon
September1,2017.
Title: TakeMeOutto(Analyze)theBallgame: VisualizationandAnalysisTechniques
forBigSpatialData
Abstractapproved:
AlixI.Gitelman CharlotteWickham
For spatial data visualization, we approach two problems and provide solutions:
heat map resolution selection, and heat map confidence interval presentation. Analysts
often present spatial data in gridded heat maps, at some chosen resolution. However,
manydatatypesvaryindensityacrossthedomain. Wedevelopvariable-resolutionheat
maps to visually accommodate this changing density, and an R package, varyres, to
implementit. Further,heatmapconfidenceintervalstypicallyconsistoftwoheatmaps,
one for each confidence interval bound. We develop an interactive heat map confidence
interval that changes dynamically as a user moves through the interval surfaces; and an
Rpackage,mapapp,toimplementit.
For spatial data analysis, Bayesian hierarchical models work well for accommodat-
ingcomplexspatialcorrelationstructures. However,withbigspatialdatawefaceacom-
putationalbottleneckontheorderofn3. Wedelineate,use,andassessthreeapproaches
to addressing the "big N" problem with our spatial baseball strike zone data. Hamil-
tonian Monte Carlo implemented with Stan proved too slow despite computational op-
timization. Predictive Process Models, a dimension reduction technique implemented
withspBayes,weremuchfasterbutMarkovchainsfailedtoconverge. IntegratedNested
LaplaceApproximationwastheonlysuccessfulmethod.
(cid:13)c CopyrightbyChrisComiskey
September1,2017
AllRightsReserved
Take Me Out to (Analyze) the Ballgame: Visualization and Analysis
Techniques for Big Spatial Data
by
ChrisComiskey
ADISSERTATION
submittedto
OregonStateUniversity
inpartialfulfillmentof
therequirementsforthe
degreeof
DoctorofPhilosophy
PresentedSeptember1,2017
CommencementJune2018
DoctorofPhilosophydissertationofChrisComiskeypresentedonSeptember1,2017.
APPROVED:
MajorProfessor,representingStatistics
ChairoftheDepartmentofStatistics
DeanoftheGraduateSchool
Iunderstandthatmydissertationwillbecomepartofthepermanentcollectionof
OregonStateUniversitylibraries. Mysignaturebelowauthorizesreleaseofmy
dissertationtoanyreaderuponrequest.
ChrisComiskey,Author
ACKNOWLEDGEMENTS
Thanks Betsy! You’re my everything, my sunshine, my MVP; you keep me happy
and sane. Thanks Alix Jane and Ewan! You inspire, amaze, and fulfill me. You are
my proudest achievements. Thanks to my advisers Alix and Charlotte—you rock. My
skills, professionalism, and direction increased tenfold under your tutelage. Charlotte,
thanks for teaching me the Way of RStudio and ggplot2. Alix, thanks for teaching me
the Way of Bayes. Thanks Mom and Dad for your unfailing support (and for funding
my undergraduate education!); without you I would not have made it to Dr. Chris.
ThanksCourt,foryourconstantloveandencouragement. Lili,Blake,Elysia—youguys
are amazing, aim for the stars! Thank you baseball, my lifelong companion, comfort,
teacher,inspiration. IfollowtheWayofBaseball.
TABLE OF CONTENTS
Page
1 Introduction 1
1.1 “GetaGoodBalltoHit” . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 PITCHf/x(cid:13)R Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 BaseballContextandMotivation . . . . . . . . . . . . . . . . . . . . . . 6
1.4 StatisticalContextandContributions . . . . . . . . . . . . . . . . . . . . 8
1.5 Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Variable-ResolutionHeatMaps 14
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 “Apictureisworthathousandwords.” . . . . . . . . . . . . . . 14
2.1.2 HeatMapHistory . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 BernoulliSwings . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.4 EmpiricalHittingZoneHeatMaps . . . . . . . . . . . . . . . . 17
2.2 TraditionalHeatMaps . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 ResolutionSelection . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Variable-ResolutionHeatMaps . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 TheVaryingResolutionSolution . . . . . . . . . . . . . . . . . 25
2.3.2 Variable-ResolutionAlgorithm . . . . . . . . . . . . . . . . . . 28
2.3.3 DataDensityInformation . . . . . . . . . . . . . . . . . . . . . 31
2.3.4 Example: AlternateStoppingRule . . . . . . . . . . . . . . . . 32
2.3.5 Interpretation: Hittervs. Pitcher . . . . . . . . . . . . . . . . . 36
2.4 Example: TornadoIntensity . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.2 Variable-ResolutionMap . . . . . . . . . . . . . . . . . . . . . 40
2.5 FutureResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7 varyres: AnRPackage . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 DynamicHeatMapConfidenceIntervalswithShiny 49
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 AGeneralizedLinearModelforHitterSuccessProbabilities . . . . . . . 49
3.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
TABLE OF CONTENTS (Continued)
Page
3.2.2 RotationalBiomechanics . . . . . . . . . . . . . . . . . . . . . 52
3.2.3 BiomechanicalCovariates . . . . . . . . . . . . . . . . . . . . 54
3.2.4 GeneralizedLinearModel . . . . . . . . . . . . . . . . . . . . 55
3.2.5 Hosmer-LemeshowGoodnessofFitTest . . . . . . . . . . . . . 56
3.3 InteractiveHeatMapConfidenceIntervals . . . . . . . . . . . . . . . . . 60
3.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 CurrentBestPractices . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.3 ShinyImplementation . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 mapapp: AnRPackage . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 ApproachestoBigDataSpatialGeneralizedLinearMixedModels 72
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.1.1 SpatialGeneralizedLinearMixedModel(SGLMM) . . . . . . 73
4.1.2 ThreeApproachestothe“BigNProblem” . . . . . . . . . . . . 74
4.1.3 MarkovChainMonteCarlo(MCMC) . . . . . . . . . . . . . . 76
4.2 OptimizationinStan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.2 HamiltonianMonteCarlo(HMC) . . . . . . . . . . . . . . . . 77
4.2.3 TheHamiltonEquations . . . . . . . . . . . . . . . . . . . . . 79
4.2.4 OptimizationTechniques . . . . . . . . . . . . . . . . . . . . . 80
4.2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 DimensionReductionwithPredictiveProcessModels . . . . . . . . . . . 86
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.2 PPMProcedure . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4 IntegratedNestedLaplaceApproximations . . . . . . . . . . . . . . . . . 92
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.1.1 GaussianMarkovRandomFields . . . . . . . . . . . . 93
4.4.2 StochasticPartialDifferentialEquation(SPDE) . . . . . . . . . 93
4.4.2.1 PiecewiseLinearBasisRepresentation . . . . . . . . . 95
4.4.2.2 DeterministicBasisFunction . . . . . . . . . . . . . . 96
4.4.2.3 GaussianWeights . . . . . . . . . . . . . . . . . . . . 97
TABLE OF CONTENTS (Continued)
Page
4.4.3 IntegratedNestedLaplaceApproximations(INLA) . . . . . . . 100
4.4.3.1 Step1,GaussianApproximation . . . . . . . . . . . . 100
4.4.3.2 Step2,LaplaceApproximation . . . . . . . . . . . . . 101
4.4.3.3 Step3,NumericalIntegration . . . . . . . . . . . . . . 103
4.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5 Conclusion 107
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 DissertationSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4 NextSteps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Bibliography 111
Appendix 120
A BaseballBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
B StanCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
C INLARCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125