I have obtained my Ph.D. in the Oxford-Warwick Statistics Programme (OxWaSP), working under the supervision of Professor Bärbel Finkenstädt Rand (University of Warwick, UK) and collaboration with Dr. Mark Fiecas (University of Minnesota, MN, USA). My area of research lies in the connection between Bayesian statistics and medical life sciences, where I am particularly interested in the development of methodologies for the automated analysis of nonstationary time series.
Statistical methodologies for identifying periodicities in time series is important for studying oscillatory systems and can provide meaningful information about the underlying physical process. As a core part of my PhD, I have introduced a novel Bayesian approach for analysing nonstationary periodic processes and implemented a reversible-jump MCMC based algorithm that simultaneously identifies the change-points and the changing periodicities in the data. The methodology is successfully applied in two applications relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in respiratory traces.
I have also developed a full Bayesian approach to model time-varying periodic and oscillatory processes by means of a hidden Markov model (HMM) where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. I have addressed this inference problem by using a Bayesian nonparametric HMM assuming a sticky hierarchical Dirichlet processes for the switching dynamics between different states while the periodicities characterising each state are explored by means of a trans-dimensional MCMC sampling step. The use of the proposed methodology is applied in respiratory research which focuses on the detection of apnea instances in human breathing traces.
- Hadj-Amar, B., Finkenstädt, B., Fiecas, M., Levi, F. & Huckstepp, R., Bayesian Model Search for Nonstationary Periodic Time Series, Journal of the American Statistical Association, 2019.
- Hadj-Amar, B., Finkenstädt, B., Fiecas, M. & Huckstepp, R., A Spectral Hidden Markov Model for Nonstationary Oscillatory Processes (in preparation).
- AutoNOM: (Automatic Nonstationary Oscillatory Modelling) which includes Julia scripts to model nonstationary periodic time series.
- PeakSpectraHMM: a Julia software to model time-varying periodic and oscillatory processes by means of a spectral HMM
- Spring 2017, 2018, 2019
ST104 - Statistical Laboratory
- Autumn 2016, 2017, 2018
ST220 - Introduction to Mathematical Statistics