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Statistical astrophysics

  1. Feb 19, 2004 #1


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    PhyStat 2003: Statistical Problems in Particle Physics, Astrophysics, and Cosmology
    Statistical Challenges in Modern Astronomy
    E. D. Feigelson
    Department of Astronomy & Astrophysics, Penn State University, University Park PA 16802, USA
    G. J. Babu
    Department of Statistics, Penn State University, University Park PA 16802, USA
    Despite centuries of close association, statistics andastronomyare surprisingly distant today. Most observational
    astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial:
    astronomy encounters sophisticated problems involving sampling theory, survival analysis, multivariate classification and analysis, time series analysis, wavelet analysis, spatial point processes, nonlinear regression, bootstrap
    resampling and model selection. We review the recent resurgence of astrostatistical research, and outline new
    challenges raised by the emerging Virtual Observatory. Our essay ends with a list of research challenges and
    arXiv:astro-ph/0401404 v1 20 Jan 2004
    infrastructure for astrostatistics in the coming decade.
    1. The glorious history of astronomy and statistics
    Astronomy is perhaps the oldest observational science1 . The effort to understand the mysterious luminous objects in the sky has been an important element of human culture for at least 104years.Quantitative
    measurements of celestial phenomena were carried out
    by many ancient civilizations. The classical Greeks
    were not active observers but were unusually creative
    in the applications of mathematical principles to as
    tronomy. The geometric models ofthe Platonists with
    crystalline spheres spinning around the static Earth
    were elaborated in detail, and this model endured in
    Europe for 15 centuries. But it was another Greek
    natural philosopher, Hipparchus, who made one of the
    first applications of mathematical principles that we
    now consider to be in the realm of statistics. Finding
    scatter in Bablylonian measurements of the length of
    a year, defined as the time between solstices, he took
    the middle of the range – rather than the mean or
    median – for the best value.
    This is but one of many discussions of statistical issues in the history of astronomy. Ptolemy estimated
    parameters of a non-linear cosmological model using a
    minimax goodness-of-fit method. Al-Biruni discussed
    the dangers of propagating errors from inaccurate in
    struments and inattentive observers. While some Medieval scholars advised against the acquisition of repeated measurements, fearing that errors would compound rather than compensate for each other, the usefulnes of the mean to increase precision was demonstrated with great success by Tycho Brahe.
    During the 19thcentury, several elements of modern
    mathematical statistics were developed in the context
    1The historical relationship between astronomy and statistics is described in references [15], [38] and elsewhere. Our
    Astrostatistics monograph gives more detail and contemporary
    examples of astrostatistical problems [3].
    of celestial mechanics, where the application of Newtonian theory to solar system phenomena gave astonishingly precise and self-consistent quantitative inferences. Legendre developed L2 least squares parameter estimation to model cometary orbits. The least
    squares method became an instant success in European astronomy and geodesy.Other astronomers and
    physicists contributed to statistics: Huygens wrote a
    book on probability in games of chance; Newton developed an interpolation procedure; Halley laid foundations of actuarial science; Quetelet worked on statistical approaches to social sciences; Bessel first used the
    concept of ”probable error”; and Airy wrote a volume
    on the theory of errors.
    But the two fields diverged in the late-19thand 20th
    centuries. Astronomy leaped onto the advances of
    physics – electromagnetism, thermodynamics, quantum mechanics and general relativity – to understand
    the physical nature of stars, galaxies and the Universe
    as a whole. A subfield called “statistical astronomy”
    was still present but concentrated on rather narrow issues involving star counts and Galactic structure [30].
    Statistics concentrated on analytical approaches. It
    found its principle applications in socialsciences, biometrical sciences and in practical industries (e.g., Sir
    R. A. Fisher’s employment by the British agricultural
    2. Statistical needs of astronomy today
    Contemporary astronomy abounds in questions of
    a statistical nature. In addition to exploratory data
    analysis and simple heuristic (usually linear)modeling
    common in other fields, astronomers also often interpret data in terms of complicated non-linear models
    based on deterministic astrophysical processes. The phenomena studied must obey known behaviors of atomic and nuclear physics, gravitation and mechanics, thermodynamics and radiative processes, and so forth. ‘Modeling’ data may thus involves both the selection of a model family based on an astrophysical--------------------
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