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Review on John Rice’s Paper: Detecting Periodicity in Astronomical Point Processes

A helpful review of John Rice's accessible paper providing practical solutions for analyzing periodicity in astronomical data, emphasizing Bayesian methods and innovative frequency integration techniques. Jeff Scargle's insights and potential advancements for frequency drift tracking are discussed, offering valuable tools for astronomers.

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Review on John Rice’s Paper: Detecting Periodicity in Astronomical Point Processes

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  1. Comments on John Rice’s paper “On Detecting Periodicity in Astronomical Point Processes” Jeff Scargle

  2. 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 Rice’s power formula for the case of fundamental only (no harnomics; Rayleigh test)]

  3. 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. Rice’s analysis of this is a good beginning, but needs more development … examples, etc., the usual stuff astronomers need to feel good about a method.

  4. 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

  5. Alice Harding

  6. Alice Harding

  7. 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),

  8. Bayesian Time Series Tools Periodogram sin( ωt + a ) Pr(ω) ~ exp( - P(ω) / σ2 ) Bretthorst period/phase Cross-corr. f1(t), f2( t – τ ) Pr(τ) ~ exp( - ρ(τ) / const ) Scargle Time Lag Scalegram s = scale Pr(s) ~ exp( - W(s) / const ) Scargle, Loredo Time-Freq. Bayesianization of Rice’s frequency drift tracker? Distribution Others ?

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