VOStat HEAD 2004

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VOStat Arming Astronomers with Advanced
Statistics

• Caltech A. Mahabal, M. Graham, S.G.Djorgovski,
• R. Williams
• Penn State J. Babu (PI), E. Feigelson
• CMU R. Nichol, D. Van DenBerk, L.Wasserman

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Use of statistics

• 15000 astronomical studies per year
• 5 have statistics in their abstract
• 20 treat variable objects or multivariate
  datasets

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Traditional methods

• Fourier transform (Fourier 1807)
• Least sq. and chisq (Legendre 1805, Pearson 1901)
• Kolmogorov-Smirnov test (Kolomogrov 1933)
• Principal Component Analysis (Hotelling 1936)

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VOStat

• Web based service
• Simple and sophisticated statistical routines
• Large datasets
• Public domain (R)/ specially written
• General purpose and Virtual Observatory

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VOStat

• ASCII / VOTABLE as input (can be used as an
  intermediate block for a VO based pipeline)
• CGI routines as prototypes (few 1000 lines)
• Webservices (Java GUI) - hundreds of thousands of
  lines (limited by Rs capabilities) -
  distributed, multi-OS, multi-language

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Examples of available functions

• Descriptive statistics (e.g. boxplot)
• Two- and k-sample tests (e.g. Wilcoxon rank-sum
  test)
• Density estimation (e.g. Kernel smoothing)
• Correlation and regression (e.g. PCA)
• Censored data (e.g. Survival)
• Multivariate classification (e.g. H clustering)
• External functions (e.g. K-density)

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User-friendly GUI

• Columns are autoselected (and can be deselected)
• Parameter choices for functions are conveniently
  placed
• Can be used from your own webpages on tables
  residing elsewhere

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Toy Demos

• Rediscovering HR diagram
• Rediscovering FP of Globular Clusters
• Looking for outliers in color-color space

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Rediscovering HR diagram

• Hyades stars (Hipparcus main catalog)
• Mean/median/boxplot
• Density estimation (Histogram)
• Kernel smoothing
• Correlation matrix
• X-Y plot
• Multivariate clustering

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• X-Y plot between Vmag and B-V reveals the famous
  structure in the dataset the color-magnitude of
  bright stars showing the main sequence, giant
  branch (with red clump stars), and a few Hyades
  white dwarfs.

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FP of Globular clusters

• Matrix of pairwise correlation coefficients
• Pairwise plots
• Principal Component Analysis

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• Core parameters as a group tend to be highly
  correlated, unlike the half-light parameters.
  This is indicative of the dynamical evolution
  driven by the core collapse.

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Exploring outliers

• Palomar-QUEST synoptic sky survey
• 9 mix-and-match colors from 8 filters
• Aim finding outliers in color-color space for
  spectroscopic follow-up
• 1000 random objects

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Boxplot

• Reveals relationships between colors
• (mean, median, overlap, outliers)

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Clustering

• K-means provides various cluster centers along
  with withinss and a list of possible outliers

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(No Transcript)
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K-density

• Probability - density association for outliers

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Visual confirmation(found from 1000 random
objects)
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Summary

• Web-based
• VO compatible
• Public domain and specialized routines