AUTHOR=Wu Hau-Tieng , Lai Tze Leung , Haddad Gabriel G. , Muotri Alysson 

TITLE=Oscillatory Biomedical Signals: Frontiers in Mathematical Models and Statistical Analysis

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=7

YEAR=2021

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.689991

DOI=10.3389/fams.2021.689991

ISSN=2297-4687

ABSTRACT=<p>Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time–frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.</p>