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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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Learningfrom

spectropolarimetricobservations

A. Asensio Ramos

Instituto de Astrofísica de Canarias

aasensio.github.io/blog

@aasensior

github.com/aasensio


Learningfromobservationsisanill-posedproblem


Followthesefoursteps

  • Understandyourproblem

  • Understandthemodelthat ‘generates’ your data

  • Define a meritfunction

  • Compute the‘best’ fitbyoptimizingorsamplethismeritfunction

Thesolutiontoanymodelfitting

has to be probabilistic


Understandyourproblem

  • Your data has beenobtainedwithaninstrument

  • Yoursyntheticmodelmightnotexplainwhatyousee

  • You are surelynotunderstandingyourerrors

  • Systematics


Understandyourgenerativemodel

Thisisthemostimportantand complexpart of theinference

Example

Generativemodel

Assumptions

  • Weassumethat xi are fixed and givenwithzerouncertainty

  • Uncertainty in themeasurementisGaussianwithzero meanand diagonal covariance


Fromthegenerativemodeltothemeritfunction

Likelihood

Probabilitythatthemeasured data has been

generatedfromthemodel


Why do we do thec2fitting?

Thestandardleast-squaresfitting comes fromthe

maximization of a Gaussianlikelihood


Somesubtleties

  • Weights

    • Do notchangethe position of themaximum

    • Modifythecurvature at themaximum

  • Ifnoisestatisticschange, modifythelikelihood


Be aware of theassumptions

  • Errors are Gaussian

  • Youknowtheerrors itisdifficulttoestimateuncertaintiesin theerrorsbecauseerrors are already a 2ndorderstatistics

  • Errors are onlyonthe y axis  x locations are givenwithinfiniteprecision

  • Themodelincludesthetruth


Whatifwe break theassumptions?

Any of ourassumptionsmight be broken

  • Errors are notGaussian

  • Wedon’tknowtheerrors

  • Errors are alsoonthex axis

  • Themodeldoesnotincludethetruth


Withoutoutliers


Withoutliers

Wegetbiasedresults


Modeleverything

Ifyoumodelthe data points and theoutliers, youautomatically

have a generativemodel and a meritfunctiontooptimize

pointsfromthe line

badpoint


Fitting He I 10830 Å profiles


Hazel

github.com/aasensio/hazel

MIT license


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


3d3D

3p3P

3s3S

2p3P

10830 Å

2s3S


Forward modelling


Problemswithinversion

  • Robustness

  • Sensitivitytoparameters

  • Ambiguities


Robustness: 2-step inversion

Global convergence DIRECT

Refinement Levenberg-Marquardt

Step 1

Step 2

Step 3

DIRECT algorithm (Jones et al 93)


Sensitivitytoparameters: cycles

Modifyweights and do cycles

Cycle 1

Invertthermodynamicalproperties

t, Dvth, vDopp, …

Stokes I

Cycle 2

Invertmagneticfield vector

Stokes Q, U, V



Ambiguities: off-limbapproach

  • Do a firstinversionwithHazel

  • Saturationregime findtheambiguoussolutions (<8)

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


Ambiguities: off-limbapproach

  • Do a firstinversionwithHazel

  • Saturationregime findtheambiguoussolutions (<8)

  • Foreachsolution, use Hazelto refine theinversion

  • NowalmostautomaticallywithHazel


Wheretogofromhere?

  • Do full Bayesianinversion

  • Modelcomparison

  • Inversionswithconstraints

Modeleverything, includingsystematics, and

integrateoutnuisanceparameters


Bayesianinference

PyHazel+PyMultinest


Modelcomparison

H0 : simple Gaussian

H1 : twoGaussians of equalwidthbutunknownamplitude ratio


Modelcomparison

H0 : simple Gaussian

H1 : twoGaussians of equalwidthbutunknownamplitude ratio


Modelcomparison


Modelcomparison

ln R=2.22  weak-moderateevidence

in favor of model 1



Central stars of planetarynebulae


Bayesianhierarchicalmodel

Model

FV

B1,μ1

Model

FV

b0

B2,μ2

Model

FV

B3,μ3


Bayesianhierarchicalmodel


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


Coincidencewithtornadoes in AIA


``Vertical’’ solutions

Field inclination


``Horizontal’’ solutions

Field inclination


Magneticfieldisrobust

  • Fields are statisticallybelow 20 G

  • Someregionsreach 50-60 G

  • Filamentary vertical structures in magneticfieldstrength


Conclusions

  • Be aware of yourassumptions

  • Modeleverythingifpossible

  • Hazelisfreelyavailable

  • Ambiguities can be problematic

  • More worktoputchromosphericinversionsat thelevel of photosphericinversions


Announcement

IAC Winter SchoolonBayesianAstrophysics

La Laguna, November 3-14, 2014


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