International Journal of Mathematical Sciences and Computing(IJMSC)
ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)
Published By: MECS Press
IJMSC Vol.4, No.2, Apr. 2018
Bayesian Approach: An Alternative to Periodogram and Time Axes Estimation for Known and Unknown White Noise
Full Text (PDF, 766KB), PP.22-33
This study describes the Bayesian approach as an alternative approach for estimating time axes parameters and the periodogram (power spectrum) associated with sinusoidal model when the white noise (sigma) is known or unknown. The conventional method of estimating the time axes parameters and the periodogram has been via the Schuster method that relies solely on Maximum Likelihood Estimation (MLE). The Bayesian alternative approach proposed in this work, on the other hand, adopted the Maximum A Posteriori (MAP) via the Markov Chain Monte Carlo (MCMC) in order to checkmate the problem of re-parameterization and over- parameterization associated with MLE in the conventional practice. The rates of heartbeat variability at exactly an hour and two hours after birth of one thousand eight hundred (1800) newly born babies in a state hospital were recorded and subjected to both the Bayesian approach and Schuster approach for inferences. The periodogram estimates, exactly an hour and two hours of after birth, were estimated to be 0.7395 and 0.7549, respectively - and it was deduced that rates of heartbeat (frequency) variability moderated and stabilized the pulse among the babies after two hours of birth. In addition, MAP mean estimates of the parameters approximately equals to the true mean of estimates when round up to curb the problem of re-parameterization and over- parameterization that do affect Schuster method via MLE.
Cite This Paper
Olanrewaju Rasaki Olawale,"Bayesian Approach: An Alternative to Periodogram and Time Axes Estimation for Known and Unknown White Noise", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.4, No.2, pp.22-33, 2018.DOI: 10.5815/ijmsc.2018.02.03
Bailer-Jones C.A.L. Bayesian time series analysis and stochastic processes. Max Planck Institute for Astronomy, Heidelberg (2013), 1-31.
Alexandrov, T. A. Method of trend extraction using singular spectrum analysis. Statistical Journal. 7(1), (2009), 1–22. doi: arXiv: 0804.33667v3
Choudhuri, N., Ghosal, S., Roy, A. Bayesian estimation of the spectral density of a time series. Journal of the American Statistical Association. 99 (468), (2004), 1050-1059.
Bhattacharya, B., Saha, B. Analysis of signaling time of community model, International Journal of Mathematical Sciences and Computing. 2(2), (2015), 8-21. doi:10.5815/ijmsc.2015.02.02.
Roy, K., Shelton, J., Esterline, A. A brief survey on multispectral iris recognition. International Journal of Applied Pattern Recognition. 3(4), (2016), 2049-8888. doi:.org/10.1504/IJAPR.2016.082235
Wu, L., Ying, X., Wu, X. Examining spectral space of complex networks with positive and negative links. International Journal of Social Network Mining. 1(1) (2012), 91-111.
Dias, C.N., Maurice, A., Prata, J.N. A reﬁnement of the Robertson–Schrodinger uncertainty principle and a Hirschman–Shannon inequality for Wigner distributions. Journal of Fourier analysis Application. 2(3) (201), 1-32.
Pantazis, Y., Oliver, R., Stylianous, Y. Iterative estimation of sinusoidal signal parameters. IEEE Signal Processing Letters. (2010).
Prasad, A., Kundu, D., Mitra, A. Sequential estimation of the parameters of sum of sinusoidal model. Journal of Statistical planning and Inference. 3(38), (2008), 1297-1313.
Bretthorst G.L. Bayesian spectrum analysis and parameter estimation. Lecture notes in statistics, Springer: (1998).
Carson. C Chow. Bayesian Model Comparison. Scientific clearing house (2010):. https://sciencehouse.wordpress.com/2010/08/06/bayesian-model-comparison.
Statisticat, LLC. Laplaces Demon: Complete Environment for Bayesian Inference (2015): Rpackage version 15.03.19,https://web.archive.org/web/20141224051720/http://www.bayesian-inference.com/index