Sparse regression methods with measurement-error for magnetoencephalography - Davies, Jonathan (2017)
Magnetoencephalography (MEG) is a neuroimaging method for mapping brain activity based on magnetic field recordings. The inverse problem associated with MEG is severely ill-posed and is complicated by the presence of high collinearity in the forward (leadfield) matrix. This means that accurate source localisation can be challenging. The most commonly used methods for solving the MEG problem do not employ sparsity to help reduce the dimensions of the problem. In this thesis we review a number of the sparse regression methods that are widely used in statistics, as well as some more recent methods, and assess their performance in the context of MEG data. Due to the complexity of the forward model in MEG, the presence of measurement-error in the leadfield matrix can create issues in the spatial resolution of the data. Therefore we investigate the impact of measurement-error on sparse regression methods as well as how we can correct for it. We adapt the conditional score and simulation extrapolation (SIMEX) methods for use with sparse regression methods and build on an existing corrected lasso method to cover the elastic net penalty. These methods are demonstrated using a number of simulations for different types of measurement-error and are also tested with real MEG data. The measurement-error methods perform well in simulations, including high dimensional examples, where they are able to correct for attenuation bias in the true covariates. However the extent of their correction is much more restricted in the more complex MEG data where covariates are highly correlated and there is uncertainty over the distribution of the error.