Jeffrey's Prior for Unknown Sinusoidal Noise Model via Cramer-Rao Lower Bound
This paper employs the Jeffrey's prior technique in the process of estimating the periodograms and frequency of sinusoidal model for unknown noisy time variants or oscillating events (data) in a Bayesian setting. The non-informative Jeffrey's prior was adopted for the posterior trigonometric function of the sinusoidal model such that Cramer-Rao Lower Bound (CRLB) inference was used in carving-out the minimum variance needed to curb the invariance structure effect for unknown noisy time observational and repeated circular patterns. An average monthly oscillating temperature series measured in degree Celsius (0C) from 1901 to 2014 was subjected to the posterior solution of the unknown noisy events of the sinusoidal model via Markov Chain Monte Carlo (MCMC). It was not only deduced that two minutes period is required before completing a cycle of changing temperature from one particular degree Celsius to another but also that the sinusoidal model via the CRLB-Jeffrey's prior for unknown noisy events produced a miniature posterior Maximum A Posteriori (MAP) compare to a known noisy events.
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 K. Roy, J. Shelton, A. Esterline. A brief Survey on Multispectral Iris Recognition, International Journal of Applied Pattern Recognition Vol.3 (4), 2016, pp. 2049-8888.
 T. Proietti, A. Luati. Generalised linear cepstral models for the spectrum of a time series. Center for Research in Econometric Analysis of Time Series (CREATES), 2014, DNRF78.
 P. Bloomeld. Fourier analysis of time series: An Introduction, 2nd Edition. Wiley, New York, 2000.
 O. Rosen, S. Wood, D.S. Stoffer. AdaptSPEC: Adaptive spectral estimation for non-stationary time series, Journal of the American Statistical Association, Vol. 107, 2012, pp. 15751589.
 S. Vaughan. A Bayesian test for periodic signals in red noise, Monthly Notices of the Royal Astronomical Society, Vol. 402, 2010, pp. 307320. doi:10.1111/j.1365-2966.2009.15868.x
 K. Fokianos, A. Savvides. On comparing several spectral densities, Technometrics, Vol. 50, 2008, pp. 317331.
 T. Aksenova, V. Volkovych, A. Villa. Detection of spectral instability in EEG recordings during the parietal period, Journal of Neural Engineering, Vol. 4, 2007, pp.173178.
 J. Durbin, S.J. Koopman. Time Series Analysis by State Space Methods, 2001, Oxford: Oxford University Press.
 M. Gierlinski, M. Middleton, M. Ward, C. Done 2008, Nat, 455, 369
 C.A.L. Bailer-Jones. Bayesian time series analysis of terrestrial impact cratering, Monthly Notices of the Royal Astronomical Society, Vol. 416, pp. 11631180, 2011.
 R. O. Olanrewaju. Bayesian Approach: An alternative to periodogram and time axes estimation for known and unknown white noise. International Journal of Mathematical Sciences and Computing, Vol. 2(5), 2018, 22 - 33. doi: 10.5815/ijmsc.2018.02.03.
 H. Cramer. Mathematical methods of statistics. Princeton, NJ; Princeton University Press, 1946. ISBN 0-691-08004-6. OCLC 185436716
 V. Mladen. On the Cramer-Rao Lower Bound for RSS-based positioning in wireless cellular networks, AEU-International Journal of Electronics and Communications, Vol. 68(8), pp. 730-736, 2014.
 B.R. Frieden. Science from Fisher information: unification. Cambridge University Press. ISBN0-521-100911-1, 2004.
 B.R. Frieden, R.A. Gatenby. Principle of maximum Fisher information from Hardys axioms applied to statistical systems, Physical Review E. Vol. 88 (4), 2013, 042144.arXiv:1405.0007.
 G.L. Bretthorst. Bayesian Spectrum Analysis and Parameter Estimation. Lecture notes in statistics vol. 48, Springer: 1998.