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Learning from spectropolarimetric observations. A. Asensio Ramos Instituto de Astrofísica de Canarias. aasensio.github.io/blog. @ aasensior. github.com/ aasensio. Learning from observations is an ill-posed problem. Follow these four steps. Understand your problem

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Learning from spectropolarimetric observations

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Learning from spectropolarimetric observations

Learningfrom

spectropolarimetricobservations

A. Asensio Ramos

Instituto de Astrofísica de Canarias

aasensio.github.io/blog

@aasensior

github.com/aasensio


Learning from spectropolarimetric observations

Learningfromobservationsisanill-posedproblem


Learning from spectropolarimetric observations

Followthesefoursteps

  • Understandyourproblem

  • Understandthemodelthat ‘generates’ your data

  • Define a meritfunction

  • Compute the‘best’ fitbyoptimizingorsamplethismeritfunction

Thesolutiontoanymodelfitting

has to be probabilistic


Learning from spectropolarimetric observations

Understandyourproblem

  • Your data has beenobtainedwithaninstrument

  • Yoursyntheticmodelmightnotexplainwhatyousee

  • You are surelynotunderstandingyourerrors

  • Systematics


Learning from spectropolarimetric observations

Understandyourgenerativemodel

Thisisthemostimportantand complexpart of theinference

Example

Generativemodel

Assumptions

  • Weassumethat xi are fixed and givenwithzerouncertainty

  • Uncertainty in themeasurementisGaussianwithzero meanand diagonal covariance


Learning from spectropolarimetric observations

Fromthegenerativemodeltothemeritfunction

Likelihood

Probabilitythatthemeasured data has been

generatedfromthemodel


Learning from spectropolarimetric observations

Why do we do thec2fitting?

Thestandardleast-squaresfitting comes fromthe

maximization of a Gaussianlikelihood


Learning from spectropolarimetric observations

Somesubtleties

  • Weights

    • Do notchangethe position of themaximum

    • Modifythecurvature at themaximum

  • Ifnoisestatisticschange, modifythelikelihood


Learning from spectropolarimetric observations

Be aware of theassumptions

  • Errors are Gaussian

  • Youknowtheerrors itisdifficulttoestimateuncertaintiesin theerrorsbecauseerrors are already a 2ndorderstatistics

  • Errors are onlyonthe y axis  x locations are givenwithinfiniteprecision

  • Themodelincludesthetruth


Learning from spectropolarimetric observations

Whatifwe break theassumptions?

Any of ourassumptionsmight be broken

  • Errors are notGaussian

  • Wedon’tknowtheerrors

  • Errors are alsoonthex axis

  • Themodeldoesnotincludethetruth


Learning from spectropolarimetric observations

Withoutoutliers


Learning from spectropolarimetric observations

Withoutliers

Wegetbiasedresults


Learning from spectropolarimetric observations

Modeleverything

Ifyoumodelthe data points and theoutliers, youautomatically

have a generativemodel and a meritfunctiontooptimize

pointsfromthe line

badpoint


Learning from spectropolarimetric observations

Fitting He I 10830 Å profiles


Learning from spectropolarimetric observations

Hazel

github.com/aasensio/hazel

MIT license


Learning from spectropolarimetric observations

Assumptions+ properties

  • Multi-term atom

  • Simplified but realistic radiativetransfer effects

  • One or two components (along LOS or inside pixel)

  • Magneto-optical effects

  • MIT license

  • MPI using master-slavescheme

  • Scalesalmostlinearlywith N-1 (testedwithup to 500 CPUs)

  • Pythonwrapperforsynthesis


Learning from spectropolarimetric observations

3d3D

3p3P

3s3S

2p3P

10830 Å

2s3S


Learning from spectropolarimetric observations

Forward modelling


Learning from spectropolarimetric observations

Problemswithinversion

  • Robustness

  • Sensitivitytoparameters

  • Ambiguities


Learning from spectropolarimetric observations

Robustness: 2-step inversion

Global convergence DIRECT

Refinement Levenberg-Marquardt

Step 1

Step 2

Step 3

DIRECT algorithm (Jones et al 93)


Learning from spectropolarimetric observations

Sensitivitytoparameters: cycles

Modifyweights and do cycles

Cycle 1

Invertthermodynamicalproperties

t, Dvth, vDopp, …

Stokes I

Cycle 2

Invertmagneticfield vector

Stokes Q, U, V


Learning from spectropolarimetric observations

Ambiguities


Learning from spectropolarimetric observations

Ambiguities: off-limbapproach

  • Do a firstinversionwithHazel

  • Saturationregime findtheambiguoussolutions (<8)

In thesaturationregime(above~40 G for He I 10830)


Learning from spectropolarimetric observations

Ambiguities: off-limbapproach

  • Do a firstinversionwithHazel

  • Saturationregime findtheambiguoussolutions (<8)

  • Foreachsolution, use Hazelto refine theinversion

  • NowalmostautomaticallywithHazel


Learning from spectropolarimetric observations

Wheretogofromhere?

  • Do full Bayesianinversion

  • Modelcomparison

  • Inversionswithconstraints

Modeleverything, includingsystematics, and

integrateoutnuisanceparameters


Learning from spectropolarimetric observations

Bayesianinference

PyHazel+PyMultinest


Learning from spectropolarimetric observations

Modelcomparison

H0 : simple Gaussian

H1 : twoGaussians of equalwidthbutunknownamplitude ratio


Learning from spectropolarimetric observations

Modelcomparison

H0 : simple Gaussian

H1 : twoGaussians of equalwidthbutunknownamplitude ratio


Learning from spectropolarimetric observations

Modelcomparison


Learning from spectropolarimetric observations

Modelcomparison

ln R=2.22  weak-moderateevidence

in favor of model 1


Learning from spectropolarimetric observations

Constraints


Learning from spectropolarimetric observations

Central stars of planetarynebulae


Learning from spectropolarimetric observations

Bayesianhierarchicalmodel

Model

FV

B1,μ1

Model

FV

b0

B2,μ2

Model

FV

B3,μ3


Learning from spectropolarimetric observations

Bayesianhierarchicalmodel


Learning from spectropolarimetric observations

Are solar tornadoes and barbsthesame?

Coreof the He I line at 1083.0 nm (~0.8’’)

  • Full Stokes He I line at 1083.0 nm (VTT+TIP II)

  • Imaging at thecore of the Hα line (VTT - diffractionlimited MOMFBD)

  • Imaging at thecore of the Ca II K (VTT - diffractionlimited MOMFBD)

  • Imagingfrom SDO


Learning from spectropolarimetric observations

Coincidencewithtornadoes in AIA


Learning from spectropolarimetric observations

``Vertical’’ solutions

Field inclination


Learning from spectropolarimetric observations

``Horizontal’’ solutions

Field inclination


Learning from spectropolarimetric observations

Magneticfieldisrobust

  • Fields are statisticallybelow 20 G

  • Someregionsreach 50-60 G

  • Filamentary vertical structures in magneticfieldstrength


Learning from spectropolarimetric observations

Conclusions

  • Be aware of yourassumptions

  • Modeleverythingifpossible

  • Hazelisfreelyavailable

  • Ambiguities can be problematic

  • More worktoputchromosphericinversionsat thelevel of photosphericinversions


Learning from spectropolarimetric observations

Announcement

IAC Winter SchoolonBayesianAstrophysics

La Laguna, November 3-14, 2014


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