Models and methods for computationally efficient analysis of large spatial and spatio-temporal data

With the development of technology, massive amounts of data are often observed at a large number of spatial locations (n). However, statistical analysis is usually not feasible or not computationally efficient for such large dataset. This is the so-called big n problem . The goal of this dissertation is to contribute solutions to the big n problem . The dissertation is devoted to computationally efficient methods and models for large spatial and spatio-temporal data. Several approximation methods to the big n problem are reviewed, and an extended autoregressive model, called the EAR model, is proposed as a parsimonious model that accounts for smoothness of a process collected over space. It is an extension of the Pettitt et a1. as well as Czado and Prokopenko parameterizations of the spatial conditional autoregressive (CAR) model. To complement the computational advantage, a structure removing orthonormal transformation named pre-whitening is described. This transformation is based on a singular value decomposition and results in the removal of spatial structure from the data. Circulant embedding technique further simplifies the calculation of eigenvalues and eigenvectors for the pre-whitening procedure. The EAR model is studied to have connections to the Matern class covariance structure in geostatistics as well as the integrated nested Laplace approximation (INLA) approach that is based on a stochastic partial differential equation (SPDE) framework. To model geostatistical data, a latent spatial Gaussian Markov random field (GMRF) with an EAR model prior is applied. The GMRF is defined on a fine grid and thus enables the posterior precision matrix to be diagonal through introducing a missing data scheme. This results in parameter estimation and spatial interpolation simultaneously under the Bayesian Markov chain Monte Carlo (MCMC) framework. The EAR model is naturally extended to spatio-temporal models. In particular, a spatio-temporal model with spatially varying temporal trend parameters is discussed

Probabilistic Modeling Paradigms for Audio Source Separation

This is the author's final version of the article, first published as E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley, M. E. Davies. Probabilistic Modeling Paradigms for Audio Source Separation. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 7, pp. 162-185. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch007file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners. Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene. Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models. In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models. They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling. They compare the merits of either paradigm and report objective performance figures. They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems

An Introduction to EEG Source Analysis with an illustration of a study on Error-Related Potentials

International audienceOver the last twenty years blind source separation (BSS) has become a fundamental signal processing tool in the study of human electroencephalography (EEG), other biological data, as well as in many other signal processing domains such as speech, images, geophysics and wireless communication (Comon and Jutten, 2010). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG, increasing the sensitivity and specificity of the signal received from the electrodes on the scalp. This chapter begins with a short review of brain volume conduction theory, demonstrating that BSS modeling is grounded on current physiological knowledge. We then illustrate a general BSS scheme requiring the estimation of second-order statistics (SOS) only. A simple and efficient implementation based on the approximate joint diagonalization of covariance matrices (AJDC) is described. The method operates in the same way in the time or frequency domain (or both at the same time) and is capable of modeling explicitly physiological and experimental source of variations with remarkable flexibility. Finally, we provide a specific example illustrating the analysis of a new experimental study on error-related potentials