Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Contribution of the North Atlantic subtropical high to regional climate model (RCM) skill in simulating southeastern United States summer precipitation

© 2014, Springer-Verlag Berlin Heidelberg.This study assesses the skill of advanced regional climate models (RCMs) in simulating southeastern United States (SE US) summer precipitation and explores the physical mechanisms responsible for the simulation skill at a process level. Analysis of the RCM output for the North American Regional Climate Change Assessment Program indicates that the RCM simulations of summer precipitation show the largest biases and a remarkable spread over the SE US compared to other regions in the contiguous US. The causes of such a spread are investigated by performing simulations using the Weather Research and Forecasting (WRF) model, a next-generation RCM developed by the US National Center for Atmospheric Research. The results show that the simulated biases in SE US summer precipitation are due mainly to the misrepresentation of the modeled North Atlantic subtropical high (NASH) western ridge. In the WRF simulations, the NASH western ridge shifts 7° northwestward when compared to that in the reanalysis ensemble, leading to a dry bias in the simulated summer precipitation according to the relationship between the NASH western ridge and summer precipitation over the southeast. Experiments utilizing the four dimensional data assimilation technique further suggest that the improved representation of the circulation patterns (i.e., wind fields) associated with the NASH western ridge substantially reduces the bias in the simulated SE US summer precipitation. Our analysis of circulation dynamics indicates that the NASH western ridge in the WRF simulations is significantly influenced by the simulated planetary boundary layer (PBL) processes over the Gulf of Mexico. Specifically, a decrease (increase) in the simulated PBL height tends to stabilize (destabilize) the lower troposphere over the Gulf of Mexico, and thus inhibits (favors) the onset and/or development of convection. Such changes in tropical convection induce a tropical–extratropical teleconnection pattern, which modulates the circulation along the NASH western ridge in the WRF simulations and contributes to the modeled precipitation biases over the SE US. In conclusion, our study demonstrates that the NASH western ridge is an important factor responsible for the RCM skill in simulating SE US summer precipitation. Furthermore, the improvements in the PBL parameterizations for the Gulf of Mexico might help advance RCM skill in representing the NASH western ridge circulation and summer precipitation over the SE US.