Comments on John Rice

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Comments on John Rices paper On Detecting
Periodicity in Astronomical Point
Processes Jeff Scargle
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• This paper should be quite accessible to
  astronomers
• Clear description of a well-defined, practical
  problem
• Does not go off into asymptotia
• Choices for the analyst not overwhelming
• Nice description of problem of unspecified
  alternative -- geometrical view tests good in
  restricted sets of directions in parameter space
• Ideas have direct parallels with Bayesian
  methods
• Bretthorst periodogram is similar to Rices
  power formula for the case of fundamental only
  (no harnomics Rayleigh test)

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Sampling in frequency In periodogram/spectral
analysis with evenly spaced data, one normally
evaluates the power spectrum at the Fourier
frequencies fn n / T n 0, 1, 2,
(N/2) - 1 But often one is tempted to
oversample, to avoid missing a real peak For
uneven sampling or for point data as Rice
considers, the Nyquist frequency is not well
defined and it is not obvious how many and which
frequencies should be sampled. He proposes a
novel and potentially extremely useful procedure
to integrate over finite frequency bands. One
needs to carefully assess the statistical
significance of any peak found this way. Rices
analysis of this is a good beginning, but needs
more development examples, etc., the usual
stuff astronomers need to feel good about a
method.
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• Incorporating Frequency Drift
• Simple extension of model to include frequency
  derivative
• Power P( f, df/dt )
• Perhaps this can be interpreted as a
  time-frequency plot
• change of variables, such as
• ( f , df/dt ) ?? (f true , t ) where t
  ( f true f ) / df/dt
• This would be an excellent tool for astronomers,
  for not just pulsars, but for tracking QPOs in
  accreting black hole/neutron star systems, etc.!
• Photons in
• P( f, t ) out
• knob tunes time-frequency resolution trade-off

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Alice Harding
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Alice Harding
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(No Transcript)
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Bayesian Estimation of Time Series Lags and
Structure , J. Scargle, in Bayesian Inference and
Maximum Entropy in Science and Engineering, 2001.
AIP Conference Proceedings, ed. Robert L. Fry.
http//proceedings.aip.org/ (volume617),
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Bayesian Time Series Tools Periodogram sin( ?t
a ) Pr(?) exp( - P(?) / s2
) Bretthorst period/phase Cross-corr. f1(t),
f2( t t ) Pr(t) exp( - ?(t) / const
) Scargle Time Lag Scalegram s
scale Pr(s) exp( - W(s) / const ) Scargle,
Loredo Time-Freq. Bayesianization
of Rices frequency drift tracker? Distribution
Others ?