Commentary on Chris Genovese

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Commentary on Chris GenovesesNonparametric
inference and theDark Energy equation of state

• Eric Feigelson (Penn State)
• SCMA IV

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Nonparametrics today .

• is far more than the Kolmogorov-Smirnov test
  Kendalls t. More than the 2-point correlation
  function, the Kaplan-Meier estimator, etc.
• includes density estimation techniques
  histograms, smoothers, splines, lowess, kriging
• includes nonparametric regression techniques
  modeling continuous behavior from discrete data
  with variance derivative estimation.
  Computationally efficient.

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QuestionWhen should we use parametric models
vs. nonparametric methods in astronomy?
Note to statisticians The models I address
here are not your familiar heuristic models
linear, polynomial, exponential, Weibull. These
Are physical models based on the physical
laws of nature gravity, electromagnetism,
quantum mechanics ? fluid flows, stellar
structure, plasma physics, nuclear astrophysics,
concordance models of particle physics
cosmology, etc. Our job as astronomers is to
establish the conditions (parameters) in which
these physical processes are actualized in
planets, stars, galaxies and the Universe as a
whole.
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Historical example 1Eclipsing binary stars
Periodic brightness variation
HD 209458 hot Jupiter binary system
Periodic radial velocity variation
Interesting parameters aorb, Mp, Rp
Charbonneau et al. 2000
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A more complicated case V505 Sgr Triple,
partial eclipsing, tidally distorted,
asynchronous rotation, reflection 36 parameters,
least-squares fit
Lazaro et al. 2006
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• Although one can debate the statistics
  (chisq?), computational procedures (least
  squares? MCMC?), and model selection criteria
  (chisq? BIC?), there is no debate regarding the
  astrophysical model involved in binary star
  orbits (orbits following Newtonian gravity).
• There are many problems in astronomy where the
  link to astrophysical models is clear, and
  parametric methods are appropriate.

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Historical example 2Elliptical galaxy structure
W. Keel, WWW
M32, HST
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Radial profile of starlight in the elliptical M
32 with King model fit
King 1962
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A long history of incompatible parametric
models of elliptical galaxy radial profiles
(These five papers have 3,776 citations)
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• Hubbles and Kings models are based on simple
  physical
• Interpretation (truncated isothermal sphere).
  Hernquist NFW
• models have more complicated physical
  interpretation. The
• de Vaucouleurs model makes no physical sense.
• But the entire issue of elliptical galaxy
  structure models was
• rendered moot by several insights since the
  1980s
• the observed star distribution does not reflect
  the
• distribution of the dominant Dark Matter
• many ellipticals formed from multiple collisions
  of
• spiral galaxies
• their resulting structure is triaxial and can
  not be
• represented by any analytical formula.

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I suggest that the study of elliptical galaxy
structure was confused by the belief that any
interpretation of data must be based on a
parametric model, however heuristic or
implausible. Much fruitless debate might be been
avoided had simple density estimation
techniques, or preferably the new nonparametric
regression methods described by Prof. Genovese,
been applied.
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Conclusions

• Astronomers should use parametric models when the
  underlying physical processes and astrophysical
  situation is clear (e.g. binary stars/planets).
• When the astrophysics is not well-founded
  (e.g. elliptical galaxy structure),
  nonparametric approaches may be preferable to
  heuristic parametric modeling.
• For cosmology, one must decide whether the
  concordance LCDM model with Dark Energy is
  clear or whether alternatives (quintessence?
  Bianchi universes?) are viable.