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Learning from spectropolarimetric observations

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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  1. Learningfrom spectropolarimetricobservations A. Asensio Ramos Instituto de Astrofísica de Canarias aasensio.github.io/blog @aasensior github.com/aasensio

  2. Learningfromobservationsisanill-posedproblem

  3. Followthesefoursteps • Understandyourproblem • Understandthemodelthat ‘generates’ your data • Define a meritfunction • Compute the‘best’ fitbyoptimizingorsamplethismeritfunction Thesolutiontoanymodelfitting has to be probabilistic

  4. Understandyourproblem • Your data has beenobtainedwithaninstrument • Yoursyntheticmodelmightnotexplainwhatyousee • You are surelynotunderstandingyourerrors • Systematics • …

  5. Understandyourgenerativemodel Thisisthemostimportantand complexpart of theinference Example Generativemodel Assumptions • Weassumethat xi are fixed and givenwithzerouncertainty • Uncertainty in themeasurementisGaussianwithzero meanand diagonal covariance

  6. Fromthegenerativemodeltothemeritfunction Likelihood Probabilitythatthemeasured data has been generatedfromthemodel

  7. Why do we do thec2fitting? Thestandardleast-squaresfitting comes fromthe maximization of a Gaussianlikelihood

  8. Somesubtleties • Weights • Do notchangethe position of themaximum • Modifythecurvature at themaximum • Ifnoisestatisticschange, modifythelikelihood

  9. Be aware of theassumptions • Errors are Gaussian • Youknowtheerrors itisdifficulttoestimateuncertaintiesin theerrorsbecauseerrors are already a 2ndorderstatistics • Errors are onlyonthe y axis  x locations are givenwithinfiniteprecision • Themodelincludesthetruth

  10. Whatifwe break theassumptions? Any of ourassumptionsmight be broken • Errors are notGaussian • Wedon’tknowtheerrors • Errors are alsoonthex axis • Themodeldoesnotincludethetruth

  11. Withoutoutliers

  12. Withoutliers Wegetbiasedresults

  13. Modeleverything Ifyoumodelthe data points and theoutliers, youautomatically have a generativemodel and a meritfunctiontooptimize pointsfromthe line badpoint

  14. Fitting He I 10830 Å profiles

  15. Hazel github.com/aasensio/hazel MIT license

  16. 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

  17. 3d3D 3p3P 3s3S 2p3P 10830 Å 2s3S

  18. Forward modelling

  19. Problemswithinversion • Robustness • Sensitivitytoparameters • Ambiguities

  20. Robustness: 2-step inversion Global convergence DIRECT Refinement Levenberg-Marquardt Step 1 Step 2 Step 3 DIRECT algorithm (Jones et al 93)

  21. Sensitivitytoparameters: cycles Modifyweights and do cycles Cycle 1 Invertthermodynamicalproperties t, Dvth, vDopp, … Stokes I Cycle 2 Invertmagneticfield vector Stokes Q, U, V

  22. Ambiguities

  23. Ambiguities: off-limbapproach • Do a firstinversionwithHazel • Saturationregime findtheambiguoussolutions (<8) In thesaturationregime(above~40 G for He I 10830)

  24. Ambiguities: off-limbapproach • Do a firstinversionwithHazel • Saturationregime findtheambiguoussolutions (<8) • Foreachsolution, use Hazelto refine theinversion • NowalmostautomaticallywithHazel

  25. Wheretogofromhere? • Do full Bayesianinversion • Modelcomparison • Inversionswithconstraints Modeleverything, includingsystematics, and integrateoutnuisanceparameters

  26. Bayesianinference PyHazel+PyMultinest

  27. Modelcomparison H0 : simple Gaussian H1 : twoGaussians of equalwidthbutunknownamplitude ratio

  28. Modelcomparison H0 : simple Gaussian H1 : twoGaussians of equalwidthbutunknownamplitude ratio

  29. Modelcomparison

  30. Modelcomparison ln R=2.22  weak-moderateevidence in favor of model 1

  31. Constraints

  32. Central stars of planetarynebulae

  33. Bayesianhierarchicalmodel Model FV B1,μ1 Model FV b0 B2,μ2 Model FV B3,μ3

  34. Bayesianhierarchicalmodel

  35. 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

  36. Coincidencewithtornadoes in AIA

  37. ``Vertical’’ solutions Field inclination

  38. ``Horizontal’’ solutions Field inclination

  39. Magneticfieldisrobust • Fields are statisticallybelow 20 G • Someregionsreach 50-60 G • Filamentary vertical structures in magneticfieldstrength

  40. Conclusions • Be aware of yourassumptions • Modeleverythingifpossible • Hazelisfreelyavailable • Ambiguities can be problematic • More worktoputchromosphericinversionsat thelevel of photosphericinversions

  41. Announcement IAC Winter SchoolonBayesianAstrophysics La Laguna, November 3-14, 2014

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