Table Of ContentContributions to Statistics
Forfurthervolumes:
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•
Matteo Grigoletto Francesco Lisi
(cid:2)
Sonia Petrone
Editors
Complex Models
and Computational Methods
in Statistics
123
Editors
MatteoGrigoletto SoniaPetrone
FrancescoLisi DepartmentofDecisionSciences
DepartmentofStatisticalSciences BocconiUniversity
UniversityofPadua Milan
Padua Italy
Italy
IncollaborationwithDepartmentofStatisticalSciences,UniversityofPadua,Italy
ISSN1431-1968
ISBN978-88-470-2870-8 ISBN978-88-470-2871-5(eBook)
DOI10.1007/978-88-470-2871-5
SpringerMilanHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012956315
JointlypublishedwithPhysica-VerlagHeidelberg,Germany
©Springer-VerlagItalia2013
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Preface
Theuseofcomputationalmethodsinstatisticstofacecomplexproblemsandhighly
dimensionaldata,aswellasthewidespreadavailabilityofcomputertechnology,is
nonews.Therangeofapplications,instead,isunprecedented.Asoftenoccurs,new
andcomplexdata typesrequirenew strategies,demandingfor thedevelopmentof
novelstatisticalmethodsandsuggestingstimulatingmathematicalproblems.
This volume presents the revised version of a selection of the papers given at
S.Co. 2011,the 7th ConferenceonStatisticalComputationandComplex Systems,
heldin Padua,Italy,September19–21,2011.TheS.Co. conferenceis a forumfor
the discussion of new developments and applications of statistical methods and
computationaltechniquesforcomplexandhigh-dimensionaldatasets.
Althoughthe topicscoveredin thisvolumeare diverse,the same themesrecur,
as research is mostly fueled by the need to analyse complicated data sets, for
which traditional methods do not provide viable solutions. Among the topics
presented we have estimation of traffic matrices in a communications network,
in the presence of long-range dependence; nonparametric mixed-effects models
for epidemiology; advanced methods for neuroimaging; efficient computations
and inference in environmental studies; hierarchical and nonparametric Bayesian
methodswithapplicationsingenomicstudies;Markovswitchingmodelstoexplain
regime changes in the evolution of realized volatility for financial returns; joint
modellingoffinancialreturnsandmultipledailyrealizedmeasures;classificationof
multivariatelinear–circulardata,withapplicationstomarinemonitoringnetworks;
forecastingofelectricitysupplyfunctions,usingprincipalcomponentanalysisand
reduced rank regression; clustering based on nonparametric density estimation;
surfaceestimationandspatialsmoothing,withapplicationstotheestimationofthe
blood-flowvelocity field. Whilst not exhaustive, this list should give a feel of the
rangeofissuesdiscussedattheconference.
This bookis addressedto researchersworkingat the forefrontof the statistical
analysis of complex systems and using computationally intensive statistical
methods.
v
vi Preface
Wewishtothankallcontributorswhomadethisvolumepossible.Finally,thanks
must go to the reviewers, who responded rapidly when put under pressure and
helpedimprovethepaperswiththeirvaluablecommentsandsuggestions.
Padua,Italy MatteoGrigoletto,FrancescoLisi
Milan,Italy SoniaPetrone
Contents
A New Unsupervised Classification Technique Through
NonlinearNonParametricMixed-EffectsModels ........................... 1
LauraAzzimonti,FrancescaIeva,andAnnaMariaPaganoni
EstimationApproachesfortheApparentDiffusionCoefficient
inRice-DistributedMRSignals ................................................ 13
Stefano Baraldo, Francesca Ieva, Luca Mainardi,
andAnnaMariaPaganoni
Longitudinal Patternsof Financial Product Ownership:
ALatentGrowthMixtureApproach .......................................... 27
FrancescaBassiandJose´ G.Dias
ComputationallyEfficient Inference Proceduresfor Vast
DimensionalRealizedCovarianceModels .................................... 37
LucBauwensandGiuseppeStorti
AGPUSoftwareLibraryforLikelihood-BasedInference
ofEnvironmentalModelswithLargeDatasets............................... 51
MichelaCamelettiandFrancescoFinazzi
Theoretical Regression Trees: A Tool for Multiple
Structural-ChangeModelsAnalysis ........................................... 63
CarmelaCappelliandFrancescaDiIorio
SomeContributionstotheTheoryofConditionalGibbsPartitions ....... 77
AnnalisaCerquetti
EstimationofTrafficMatricesforLRDTraffic .............................. 91
PierLuigiConti,LiviaDeGiovanni,andMaurizioNaldi
ANewton’sMethodforBenchmarkingTimeSeries......................... 109
TommasoDiFonzoandMarcoMarini
vii
viii Contents
SpatialSmoothingforDataDistributedover
Non-planarDomains............................................................. 123
Bree Ettinger, Tiziano Passerini, Simona Perotto,
andLauraM.Sangalli
VolatilitySwingsintheUSFinancialMarkets................................ 137
GiampieroM.GalloandEdoardoOtranto
SemicontinuousRegressionModelswithSkewDistributions............... 149
AnnaGottard,ElenaStanghellini,andRosaCapobianco
ClassificationofMultivariateLinear-CircularData
withNonignorableMissingValues............................................. 161
FrancescoLagonaandMarcoPicone
MultidimensionalConnectedSetDetectioninClusteringBased
onNonparametricDensityEstimation......................................... 175
GiovannaMenardi
UsingIntegratedNestedLaplaceApproximations
forModellingSpatialHealthcareUtilization ................................. 187
MonicaMusio,Erik-A.Sauleau,andValentinaMameli
SupplyFunctionPredictioninElectricityAuctions.......................... 203
MatteoPelagatti
AHierarchicalBayesianModelforRNA-SeqData.......................... 215
Davide Risso, Gabriele Sales, Chiara Romualdi,
andMonicaChiogna
A New Unsupervised Classification Technique
Through Nonlinear Non Parametric
Mixed-Effects Models
LauraAzzimonti,FrancescaIeva,andAnnaMariaPaganoni
Abstract In this work we propose a novel unsupervised classification technique
based on the estimation of nonlinear nonparametric mixed-effects models. The
proposedmethodisaniterativealgorithmthatalternatesanonparametricEMstep
andanonlinearMaximumLikelihoodstep.Weapplythisnewproceduretoperform
anunsupervisedclusteringoflongitudinaldataintwodifferentcasestudies.
1 Introduction
Unsupervisedclustering is one of the main topicsin data mining,i.e., the process
of finding useful information from data [4]. We focus our attention on highly
overdispersed longitudinal and repeated data, which are naturally described
through mixed-effects models. Nonlinear mixed-effects models (NLME models)
are mixed-effects models in which at least one of the fixed or random effects
appears nonlinearly in the model function. They are increasingly used in several
biomedicalandecologicalapplications,especiallyinpopulationpharmacokinetics,
pharmacodynamic, immune cells reconstruction and epidemiological studies
(see [6,7,13,21]). In these fields, statistical modeling based on NLME models
takes advantage of tools that allow to distinguish overall population effects from
drugs effects or unit specific influence. In general, mixed-effects models include
parameters associated with the entire population (fixed effects) and subject/group
specific parameters (random effects). For this reason, mixed-effects models are
able to describethe dynamicsof the phenomenonunderinvestigation,even in the
presence of high between subjects variability. When the random effects represent
a deviation from the common dynamics of the population, mixed-effects models
L.Azzimonti(cid:2)F.Ieva((cid:2))(cid:2)A.M.Paganoni
MOX-DepartmentofMathematics,PolitecnicodiMilano,Milan,Italy
e-mail:[email protected];[email protected];[email protected]
M.Grigolettoetal.(eds.),ComplexModelsandComputationalMethodsinStatistics, 1
ContributionstoStatistics,DOI10.1007/978-88-470-2871-5 1,
©Springer-VerlagItalia2013
2 L.Azzimontietal.
provide estimates both for the entire population’s model and for each subject’s
one. In this work random effects have a different meaning, in fact they describe
the common dynamics of different groups of subjects. In this framework, mixed-
effectsmodelsprovideonlyestimatesforeachgroup-specificmodel.Thankstothis
property, it will be possible to consider mixed-effects models as an unsupervised
clusteringtoolforlongitudinaldataandrepeatedmeasures.Forthisreasonwefocus
ourattentionontheestimationofthedistributionoftherandomeffectsP(cid:3).
A wide literature exists for parametric modelingof random effectsdistribution
in linear and non linear mixed-effects models. In this framework, Maximum
Likelihood(ML)estimatorsaregenerallypreferredbecauseoftheirconsistencyand
efficiency.However,duetothenonlinearityofthelikelihood,wearenotalwaysable
toprovideexplicitlytheparameterestimators.Ageneralandcompleteoverviewof
linearmultilevelmodelsisgivenin[12].Ananalogousoverviewfornonlinearcase
is given in [10]. In [9] it is shown how R and S-plus tools estimate linear and
generalized linear mixed-effects models with parametric, in particular Gaussian,
randomeffects.Concerningnonlinearmodels,in[11]aMLestimationofGaussian
randomeffectisprovidedforpeculiarnonlinearforms.Astochasticapproximation
of traditional EM algorithm (SAEM) for estimating Gaussian random effects is
suggested in [14], whereas an exact EM algorithm is described in [24]. Finally,
[25] introduces a Laplace approximation for nonlinear random effects marginal
distributions.However,parametricassumptionsmaysometimesresulttoorestrictive
todescribeveryheterogeneousorgroupedpopulations.Moreover,whenthenumber
of measurements for unit is small, predictions for random effects are strongly
influenced by the parametric assumptions. For these reasons nonparametric (NP)
framework, which allow P(cid:3) to live in an infinite dimensional space, is attractive.
Moreover,it providesin a verynaturalway a clusteringtool, as we will highlight
later.
Methodsfor the estimation of linear nonparametricrandomeffectsdistribution
inlinearandgeneralizedlinearmixed-effectsmodelshavebeenproposedin[1,2],
whereas[3,6,15,23],amongothers,dealwithnonparametricnonlinearmodels.
Inthisworkweproposeanovelestimationmethodfornonlinearnonparametric
mixed-effects models, aimed at unsupervised clustering. The proposed method is
an iterative algorithm that alternates a nonparametric EM step and a nonlinear
Maximum Likelihood step. The present algorithm is implemented in R program
(version2.13.0,RDevelopmentCoreTeam[20])andtheRsourcecodeisavailable
uponrequest.Tothebestofourknowledge,thisisthefirstexampleoffreesoftware
fortheestimationofnonlinearnonparametricmixed-effectsmodels.
InSect.2thegeneralframeworkoftheworkissketchedout,andinSect.3the
algorithmfortheestimationofnonlinearnonparametricrandomeffect(NLNPEM)
is described. Section 4 contains applications to case studies. Concluding remarks
and further developments of this work are finally discussed in Sect. 5. Technical
detailsintheestimationalgorithmarediscussedinAppendix.
