Bayesian modeling, Bayesian nonparametrics, time series analysis, spectral analysis, spatial statistics, mixture models.
My research is focused on developing hierarchical models for multiple related time series in the spectral domain, applicable to fields where the frequency behavior is relevant and several time series are recorded simultaneously, e.g. neuroscience, econometrics, geoscience. A substantial component of my work is implementing algorithms for efficient MCMC posterior simulation.
1) Overview: Flexible spectral modeling of complex brain signals
EEGs record electrical fluctuation induced by neuronal activity. The signals are recorded in multpile locations/channels on a subject’s scalp. Each signal is composed by periodic components and noise. Neuroscientists call these periodic components brain waves
and are interested in which brain waves are active at each channel. The goal of my research is building a Bayesian hierarchical model a model that allows us to borrow strength among the different locations, while providing accurate information for every single channel.
For a quick summary on the motivations and applications of my research, you can take a look at my presentation for the first UCSC Grad Slam (3 Minutes Thesis Competition), that won the People’s Choice Award!