Sta$s$csinastronomyand

theSAMSI ASTRO Program

G. Jogesh Babu(with input from Eric Feigelson)

PennState

Whyastrosta$s$cs?Astronomersencounterasurprisingvarietyofsta$s$calproblemsintheirresearch:

–  Theskyhasvastnumbersofstars&galaxiesandgasonallscales.–  Moststarshaveorbi$ngplanets,mostgalaxieshaveamassiveblackhole–  Astronomersacquirehugedatasetsofimages,spectra&$meseriesof

planets,stars,galaxies,quasars,supernovae,etc.–  Variousproper$esofcosmicpopula$onsobservedandempiricallystudied

withallkindsoftelescopes(n>>p)–  Proper$esaremeasuredrepeatedlybutwithirregularspacing.–  Spa$aldistribu$onsinsky(2D),space(3D),andparameterspace(pD)is

complex(MVNassump$onusuallyinapplicable)EricFeigelsonandIstartedcollabora$nginlate1980sandtheterm`Astrosta$s$cs’wascoinedinmid1990s,whenwepublishedabookbythesamename.

•  Modern statistics is vast in its scope and methodology. It is difficult to find what may be useful (jargon problem!), and there are usually several ways to proceed. Very confusing.

•  Some statistical procedures are based on mathematical proofs which

determine the applicability of established results. It is perilous to violate mathematical truths! Some issues are debated among statisticians, or have no known solution.

•  Scientific inferences should not depend on arbitrary choices in methodology & variable scale. Prefer nonparametric & scale-invariant methods. Try multiple methods.

•  It can be difficult to interpret the meaning of a statistical result with respect to the scientific goal. Statistics is only a tool towards understanding nature from incomplete information.

We should be knowledgeable in our use of statistics

and judicious in its interpretation

Astronomy & Statistics: A glorious past For most of western history,

the astronomers were the statisticians! Ancient Greeks to 18th century

Best estimate of the length of a year from discrepant data? •  Middle of range: Hipparcos (4th century B.C.) •  Observe only once! (medieval) •  Mean: Brahe (16th c), Galileo (17th c), Simpson (18th c) •  Median (20th c)

19th century Discrepant observations of planets/moons/comets used to estimate orbital parameters using Newtonian celestial mechanics

•  Legendre, Laplace & Gauss develop least-squares regression and normal error theory (c.1800-1820)

•  Prominent astronomers contribute to least-squares theory (c.1850-1900)

The lost century of astrostatistics….

In the late-19th and 20th centuries, statistics moved towards human sciences (demography, economics, psychology, medicine, politics) and industrial applications (agriculture, mining, manufacturing). During this time, astronomy recognized the power of modern physics: electromagnetism, thermodynamics, quantum mechanics, relativity. Astronomy & physics were wedded into astrophysics. Thus, astronomers and statisticians substantially broke contact; e.g. the curriculum of astronomers heavily involved physics but little statistics. Statisticians today know little modern astronomy.

Astrosta$s$csatSAMSIAstrostatistics Program at SAMSI January 2006�

•  Opening workshop January18-20,2006–  Bayesian astrostatistics–  Nonparametric inference–  Astronomy for Statisticians

•  Working groups –  Exoplanets, surveys & population studies–  Gravitational Lensing–  Source detection & feature detection–  Particle physics

•  Concluded with SCMA IV at Penn State in June 2006

Astrosta$s$csatSAMSIAstrostatistics sub Program Fall 2012

Statistical and Computational Methodology for Massive Datasets •  Workshop September19-21,2012

–  Thesearchfortransients– Missions(Fermi,SDSS.DES,Plank,LSST,LIGO)–  Sparsity(high-dimensionaldata,butlow-dimsignal)–  Datamining

•  Working groups –  Discovery&Classifica$oninSynop$cSurveys;–  Inference&Simula$oninComplexModels,–  Stochas$cProcesses&AstrophysicalInference–  GraphicalModels&GraphicsProcessors

Astrosta$s$csatSAMSI

Exoplanets Summer 2013

ModernSta$s$calandComputa$onalMethodsforAnalysisofKeplerData

June10-28,2013

Astrosta$s$csatSAMSI

Sta4s4cal,Mathema4calandComputa4onalMethodsforAstronomy 2016-2017�

•  Opening workshop August22-26,2016–  TimeDomainAstronomy(TDA)–  Exoplanetdataanalysis,hierarchicalmodeling–  Uncertainty,selec$oneffectsforgravita$onalwaves(GW)–  Pulsar$mingarraysanddetec$onofGWs–  Non-sta$onary,non-Gaussian,irregularlysampledprocesses–  Sta$s$calissuesincosmology

SAMSIASTROProgramis$mely

•  Gravita$onalwavesdetected100yearsaderEinstein’spredic$on

•  FirstGW(GW150914)detectedbyLaserInterferometerGravita$onal-WaveObservatory(LIGO)confirmedEinstein’s1915generaltheoryofrela$vityappliedtoinspiralingbinaryblackholes.

•  Theplanningmee$ngonSeptember21,2015includedLIGOscien$stswhohadonlyjustlearnedofthecandidatedetec$on,andhadtokeepitsecretun$lconfirmedandannouncedonFebruary11,2016.AsecondGWevent(GW151226)wasannouncedonJune15,2016.ItwasrecordedonDecember26,2015.

SAMSI2016-17WorkingGroups

•  Synop$cTimeDomainSurveys

•  Mul$variateandIrregularlySampledTimeSeries

•  UncertaintyQuan$fica$onandAstrophysicalEmula$on

•  AstrophysicalPopula$ons

•  Sta$s$cs,Computa$on,andModelinginCosmology

Synop$cTimeDomainSurveys•  TDAhasbeengeingricherwithdatasetsspanningdecades,

manyspectralbands.Includesbothdenseandsparselight-curvesforhundredsofmillionsofsources.

•  Thevariety,volumeandvelocitysquarelyfallinBigDataregime.•  Thelight-curvesodenhavelargegaps,areheteroskedas$c,and

theintrinsicvariability–odenpoorlyunderstood–addsanelementofuncertaintywhenmul$-banddataarenotobtainedsimultaneously.–  binaryblack-holesearchesfromCRTTransientSurvey–  Kepler-typeplanetsearch/characteriza$on(alsoinotherWGs)

GroupLeaders:AshishMahabal(Astro,Caltech),G.JogeshBabu(Stat,PSU)

BigQues$ons•  Whatmathema$calandsta$s$calapproachescanbeusedtobestcharacterizeandquan$fysalientfeaturesofirregular,heteroscedas$c,gapped$meseries?

•  Canweiden$fyspecificfeaturesets,templatesandmodels?Howcanweiden$fymanyweakfeaturesorafewstrongonesinsuchhighdimensional$meseriesBigData?Aretherespecificdomain-knowledgebasedfeaturesthatcanbeiden$fiedtoimproveclassdiscrimina$on?

•  Howcansignificantoutliers/anomaliesandsubclassesbedetected?

Subgroups•  Datachallenges•  Crea$ngdesignerfeaturesforclassifica$on•  Whereshouldthenextpointbe?Schedulingandop$mizingobserva$ons.

•  Interpola$ng$me-series•  Smart/fastwaysofincorpora$ngnon-structuredancillaryinforma$on

•  Outlierdetec$on(clustering)•  DomainAdapta$onforclassifica$on(combiningdiversedatasets)

•  Light-curvedecomposi$on(e.g.ARIMA&ARFIMA)

Exoplanets•  Amajorproblemforplanetdetec$onisstellarvariability•  KeplerAutoRegressivePlanetSearch(KARPS)uses

ARIMA-typemodelstoremoveaperiodicstellarvaria$onsfollowedbytransitcombfiltertofindperiodicplanettransits

•  PreliminaryKARPSanalysisofirregularlyspaced$meseriesusingcadencesfromHungarianAutomatedTelescopeSouth(HATS)network.

Two methods for detecting planets orbiting stars

Photometric2meserieswithperiodictransitswhenplanetpassesinfrontofstar

Radialvelocity2meserieswithperiodicvaria2onswhenplanetpullsstartowardsandawayfromus

A significant challenge is that astronomical time series are usually acquired with irregularly spaced observations.

Statistical challenges in planet detection

The discovery of planets in astronomical radial velocity or photometric time series (light curves) involves 3 statistical stages:

•  Time domain removal/suppression of variations intrinsic to the star

•  Frequency domain periodogram to reveal periodic signature of planetary orbit

ButthestaritselfoFenshowsvariabilityinbrightnessorradialvelocityduetomagne4cac4vity.Thishasbeenwell-studiedonourSunandstronglymagne4callyac4vestars.Butun4lthesensi4vephotometryoftheKeplermission,itwasnotrecognizedhowstellarmagne4cac4vityissopervasive.

Planetsandstellarac$vity:HideandseekintheCoRoT-7systemHaywoodetal.2014

GPlocalregressionfit

“[E]xoplanets may still be detected by exploiting differences in timescale, shape and wavelength dependence between the planetary and stellar signals. ... However, [stellar] variability, combined with residual instrumental systematics, is still limiting the detection of habitable planets by Kepler. ... [A] better understanding of, and ability to mitigate, stellar variability, continues to be crucial for the continued development of exoplanet studies.”

Suzanne Aigrain IAU 2015

Stellarvariabilityreduc2onmethodsNonparametricmodeling§  IndependentComponentAnalysis(Waldmannetal.2012)§  Waveletdecomposi4on(KeplerTeampipeline;Jenkinsetal.2010)§  GaussianProcessesregression(Aigrainetal.2012&manyothers)§  Correntropy,trendentropy,EmpiricalModeDecomposi4on,

SingularSpectrumAnalysis,…(Huijseetal.2012,Robertsetal.2013,Grecoetal.2016)

Parametricmodeling§  Principalcomponentsanalysis§  Autoregressivemodeling

PeriodicitysearchmethodsAcommontaskisthesearchforperiodicityfromexoplanetaryorbitsinstellar$meseries.Sta$s$caltechniquesinclude§  FastFourierTransformInfinite,sta$onary,evenlyspaced,Gaussiandatawith

sinusoidalsignal§  Lomb-Scargleperiodogram(Scargle1982)Least-squaresfiingofsinusoidsto

irregularlyspaced$meseries§  Phasedispersionminimiza4on(Stellingwerf1977)Binnedvariance-based

measuredesignedfornon-sinusoidalshapes,irregulardata&heteroscedas$cmeasurementerrors

§  Minimumstrengthlength(Dworetzky2003)UnbinnedmeasuresimilartoPDM§  Step-func4on(Gregory&Loredo1992)Bayesiansimultaneousmodellingof

signalshape&strength§  Boxleastsquares(Kovacsetal.2002)Matchedfilterforperiodicboxshape

expectedfromplanetarytransits§  TransitCombFilter(Caceresetal.2017)Matchedfilterforperiodicdouble-

spikeexpectedfromtransitsaderdifferencingoperatorisapplied

Mul$variateandIrregularlySampledTimeSeries

•  ThenoisefromGWdetectorschangesonlong$mescaleswithfrequent“glitches”.Howcanwebuildrobustnoisemodelsandexploitinforma$oninauxiliaryenvironmentalchannels?

•  Ground-basedphotometricsurveys,withbillionsofirregularlightcurves,detectstellarvariabilityfromamul$tudeofsources,fromvariablestarstosupernovae.Howdoweeffec$velyseparatetheseclassesinirregularlysampleddata?

•  Howcanwemaximizethesensi$vityofspace-basedphotometricsurveys(Kepler,TESS)fordetec$ngsmallplanetsinthepresenceofstellarac$vity?

•  Howdoweinferplanetmassesfromobserva$onaldataaffectedbystellarac$vity‘jiser’?GroupLeaders:BenFarr(Astro,U.Chicago),SoumenLahiri(Stat,NCSU)

GWfromPulsarTiming

•  GWbackgroundproducesafluctua$oninthepulse$mesofarrival(TOAs)fromagivenpulsar.Studyusingcross-correla$onsofpulsarpairs.

•  Trypar$alautocorrela$onsandmul$plecorrela$onstoextracttheeffectoftheGWB?

•  Demorestetal.(ApJ2016)useBayesianmethodstocomputeupperlimitsontheIsotropicStochas$cGWBfrom9yeardataset.

UncertaintyQuan$fica$onandAstrophysicalEmula$on

•  UncertaintyQuan$fica$on(UQ)andReducedOrderModeling(ROM)areatthecoreofmanyproblemsingravita$onandcosmology,fromdirectsimula$onsoftheEinsteinequa$onstotheinverseproblem.

•  Leverageexper$sefromareassuchasgeneralizedpolynomialchaosandsimulatoremula$onbasedonstochas$cprocessestoapplytogravita$on,astrophysics,andcosmology.GroupLeaders:DerekBingham(SimonFraser),EarlLawrence(LANL)

AstrophysicalPopula$ons•  Improvethesta$s$calmethodologytoinfertheunderlying

popula$onofexoplanets&gravita$onalwaves(GW)sources.•  Theexoplanetscommunityneedstorobustlydetectandcharacterize

planetsinthepresenceofstellarac$vityfromphotometricandDopplersurveyswithoutafirst-principlesmodel.

•  TheGWcommunityisinterestedindetec$nggravita$onalwavesourcesforwhichthedetailsoftheprimaryGWsignaland/orbackgroundsareunknown.

•  Bothapplica$onsrequirealgorithmstoefficientlyexplorehigh-dimensionalparameterspacesandtoestablishconfidenceindetec$ons,despitecomplexandunknownsourcesofuninteres$ngbackgroundsignals.GroupLeaders:JessiCisewski(Stat,Yale);EricFord(Astro,PennState)

Sta$s$cs,Computa$on,andModelingin

Cosmology•  Seektobringtogetherleadingresearchersin

cosmology,computa$onalspa$alandBayesiansta$s$cs,experimentaldesign,andcomputermodelingtodevelopmethodologynecessaryforansweringfundamentalques$onsabouttheoriginandlargescalestructureoftheuniverse.

•  Howcanwemakeinferencesfordeterminis$cnonlineardynamicalsystems(inferenceofini$alcondi$onsandmodelparameters)?

GroupLeaders:JeffJewell(Astro,JPL),JoeGuinness(Stat,NCSU)

ConclusionSomeofthemostimportantscien$ficproblemsinastronomy&astrophysicsraisechallengingissuesinsta$s$calmethodology:exoplanets,gravita$onalwaves,cosmologyThelargesttelescopeprojectsproduceenormousimaging,$meseriesandtabulardatasetsrequiringsophis$catedmethodsOverthepastdecade,theSAMSIorganiza$onprovidesaforumwheretheseissuescanbepursuedbycross-disciplinaryteamsofsta$s$cians&astronomers