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Article summary:

1. Periodic data, such as speech signals, ECG signals, and vibration signals, are commonly encountered in scientific research and industrial applications.

2. The Periodic Gaussian Process (PGP) has been increasingly used to model signals under strong noise environments due to its ability to model the circulant within-period correlation.

3. Various approximation methods have been proposed to address the challenge of high computational complexity of PGP, including low-rank GP, inducing-point GP, local GP, covariance tapering, and sparse GP.

Article analysis:

The article is generally reliable and trustworthy in terms of its content and sources. It provides a comprehensive overview of the current literature on periodic data analysis using the Periodic Gaussian Process (PGP), including linear models such as Maximum Likelihood Pitch Estimation (MLPE) and Noise Resistant Correlation (NRC), nonlinear models such as Nonlinear Least Square (NLS), and various approximation methods for addressing the challenge of high computational complexity of PGP. The article also provides examples of how PGP has been used in various applications such as change point detection, periodicity detection in genomes, robust object detection, long-term forecasting of periodic processes, and error control.

The article does not appear to be biased or one-sided in its reporting; it presents both sides equally by providing an overview of both linear and nonlinear models for periodic data analysis as well as various approximation methods for addressing the challenge of high computational complexity of PGP. Furthermore, it provides evidence for its claims by citing relevant research papers throughout the text.

The only potential issue with this article is that it does not explore any counterarguments or alternative approaches to periodic data analysis that may be more suitable than PGP in certain cases. However, this is understandable given that the focus of this article is on PGP specifically rather than other approaches to periodic data analysis.