Physics – Data Analysis – Statistics and Probability
Scientific paper
2011-05-02
Astrophysics and Space Science, Volume 338, Issue 1 (2012), Page 35-48
Physics
Data Analysis, Statistics and Probability
15 pages, 13 figures, 1 table, major revision, final version, Accepted for publication in Astrophysics & Space Science
Scientific paper
10.1007/s10509-011-0922-4
The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in the spectrum when faced with imperfect data. Several arguments are presented suggesting that the arbitrary prefactor should not be introduced to the entropy term. The introduction of that factor is not required when a continuous Poisson distribution is used for the amplitude coefficients. We compare the formalism for when the variance of the data is known explicitly to that for when the variance is known only to lie in some finite range. The result of including the entropic measure factor is to suggest a spectrum consistent with the variance of the data which has less structure than that given by the forward transform. An application of the methodology to example data is demonstrated.
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