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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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#### Presentation Transcript

Learningfrom

spectropolarimetricobservations

A. Asensio Ramos

Instituto de Astrofísica de Canarias

aasensio.github.io/blog

@aasensior

github.com/aasensio

Learningfromobservationsisanill-posedproblem

Followthesefoursteps

• Understandyourproblem

• Define a meritfunction

• Compute the‘best’ fitbyoptimizingorsamplethismeritfunction

Thesolutiontoanymodelfitting

has to be probabilistic

Understandyourproblem

• 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

Fitting He I 10830 Å profiles

Hazel

github.com/aasensio/hazel

Assumptions+ properties

• Multi-term atom

• Simplified but realistic radiativetransfer effects

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

• Magneto-optical effects

• 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

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

Constraints

Central stars of planetarynebulae

Bayesianhierarchicalmodel

Model

FV

B1,μ1

Model

FV

b0

B2,μ2

Model

FV

B3,μ3

Bayesianhierarchicalmodel

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

``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