PRACTICAL ANALYTICS 7/19/2012. Tamás Budavári / The Johns Hopkins University
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1 PRACTICAL ANALYTICS / The Johns Hopkins University
2 Statistics Of numbers Of vectors Of functions Of trees
3 Statistics Description, modeling, inference, machine learning Bayesian / Frequentist / Pragmatist? Supervised Unsupervised Discrete Classification Clustering Continuous Regression Dimensional Reduction
4 What s Large? VOLUME Say >100TB today but tomorrow? Moving target COMPLEXITY The raw dataset are simple unlike their derivatives DEFINITION? Large when you cannot apply the usual tools
5 Data LARGE!!
6 Data LARGE!!
7 Large? Sample size
8 Large? Sample size
9 Large? Dimensions Ratio of surface/volume grows all points are lonely in high dimensions
10
11 Keeping Up? Image processing Catalog extraction O(n) What is difficult? O(n log n) O(n 2 ), Worse w/ Moore s law
12 Fundamental Challenges Cross-identification of sources To assemble multicolor catalogs Drop-outs from sky coverage To constrain fluxes not detected Constraining physical properties To interpret the data
13 Cross-Identification From long-tail science to the largest experiments
14 Recording Observations Astronomers drew it Now kids do it on SkyServer #1 by Haley
15 Multicolor Universe
16 Eventful Universe
17 Cross-Identification One of the most fundamental analysis steps
18 What is the Right Question? Cross-identification is a hard problem Computationally, Scientifically & Statistically Need symmetric n-way solution Need reliable quality measure Same or not? Distance threshold? Maximum likelihood?
19 Tabletop Astronomy Imagine the observed sky has only 6 pixels One object: one die Observing: rolling a die Locality: die is loaded Sky: a bag of dice
20 Model Comparison: Same or Not? Crossmatch: draw two dice with replacement Same or not? Bayes Factor is the ratio of the Likelihood of Same Likelihood of Not Likelihood of a hypothesis? Sum over all possibilities
21 Model Comparison: Same or Not? Crossmatch: draw two dice with replacement Same or not? Bayes Factor is the ratio of the Likelihood of Same Likelihood of Not Likelihood of a hypothesis? Sum over all possibilities
22 Model Comparison: Same or Not? Model for loaded dice is matrix of probabilities E.g., loaded toward l =1 Etc. for l =2 6 2-way case Same: Not: n-way: same
23 Model Comparison: Same or Not? Model for loaded dice is matrix of probabilities E.g., loaded toward l =1 Etc. for l =2 6 2-way case Same: Not: n-way: same
24 Model Comparison: Same or Not? Model for loaded dice is matrix of probabilities E.g., loaded toward l =1 Etc. for l =2 6 2-way case Same: Not: n-way: same
25 Celestial Sphere Continuous functions General formalism Accuracy is a density fn on sky
26 Modeling the Astrometry Astrometric precision A simple function Where on the sky? Anywhere really
27 NOT SAME OR Same or Not? The Bayes factor H: all observations of the same object at m K: might be from separate objects at {m i }
28 NOT SAME OR Same or Not? The Bayes factor H: all observations of the same object at m K: might be from separate objects at {m i }
29 NOT SAME OR Same or Not? The Bayes factor H: all observations of the same object at m K: might be from separate objects at {m i }
30 NOT SAME OR Same or Not? The Bayes factor H: all observations of the same object at m On the sky K: might be from separate objects at {m i } Astrometry
31 NOT SAME OR Same or Not? The Bayes factor H: all observations of the same object at m On the sky K: might be from separate objects at {m i } Astrometry
32 Analytic Results Normal distribution Flat and spherical Gauss and Fisher 2-way results
33 Normal Distribution Astrometric precision: Fisher distribution: Analytic results: For high accuracies:
34 Wikipedia: Interpretation
35 Probability of a Match Same or not?
36 From Priors to Posteriors Bayes factor is the connection
37 From Priors to Posteriors Posterior probability from prior & Bayes factor Prior probability of a match Like dice in a bag: 1/N and N 1 n In general?
38 From Priors to Posteriors Different selections Nearby / Distant Red / Blue But only 1 number
39 Self-Consistent Estimates Prior has an unknown fudge-factor Educated guess Or solve for it: TB & Szalay (2008)
40 Simulations Mock objects With correct clustering U 01 values as properties 0 1 Simulated sources Subsets: N 1 N 2 Overlap: N
41 Simulations Mock objects With correct clustering U 01 values as properties 0 1 Simulated sources Subsets: N 1 N 2 Overlap: N
42 Simulations Quality Multiple matches Explained by simple model of point sources! Heinis, TB, Szalay (2009)
43 Proper Motion Same hypotheses but different parameters Just need prior to integrate Sources from SDSS
44 Proper Motion Same hypotheses but different parameters Just need prior to integrate Kerekes, TB+ (2010) Sources from SDSS
45 Matching Events Streams of events in time and space E.g., thresholded peaks in signal-to-noise (1) (2) (x)
46 Dropouts from Sky Coverage
47 Drawing with Equations TB, Szalay & Fekete (2010) r = 0.6 r = 0.5
48 Matching in Practice
49 Open SkyQuery Following our 1 st prototype Successful Not bayesian Limitations
50 SkyQuery The 3 rd Generation Dynamic federation of astronomy databases Query the collection as if they were one The 3 rd gen tool coming this summer Cluster of machines running partitioned jobs Proper probabilistic exec with variable errors
51 SkyQuery Almost pure standard SQL
52 SkyQuery Almost pure standard SQL
53 SkyQuery Almost pure standard SQL
54 SkyQuery Almost pure standard SQL Added XMATCH Verifiable Flexible
55
56 HST Crossmatch Catalog RELEASE AT AAS SQL pipeline Astrometric correction Subpixel precision TB & Lubow (2012)
57 HST Crossmatch Catalog RELEASE AT AAS FoF groups Possible chains Bayesian model selection Chainbreaker
58 HST Crossmatch Catalog RELEASE AT AAS Lots of matching sources during HST s long life TB & Lubow (2012) TB & Lubow (2012)
59 HST Crossmatch Catalog RELEASE AT AAS Lots of matching sources during HST s long life TB & Lubow (2012) TB & Lubow (2012)
60 Zone Algorithm Constant Declination zones Sort by R.A. within Fast SQL code SDSS-GALEX in 1 hour CPU limited!
61 Parallel on GPUs Recent Github release Multi-GPU implementation Search in 5 great perf! NVIDIA GTX GB 29M 29M in 11 seconds C2050 Teslas 400M 150M in 3 minutes
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