Some nonasymptotic results on resampling in high dimension, I: Confidence regions, II: Multiple tests

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two approaches, the first based on a concentration principle (valid for a large class of resampling weights) and the second on a resampled quantile, specifically using Rademacher weights. Several intermediate results established in the approach based on concentration principles are of interest in their own right. We also discuss the question of accuracy when using Monte Carlo approximations of the resampled quantities.Comment: Published in at http://dx.doi.org/10.1214/08-AOS667; http://dx.doi.org/10.1214/08-AOS668 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spatiotemporal techniques in multimodal imaging for brain mapping and epilepsy

Thesis (Ph.D.)--Boston UniversityThis thesis explored multimodal brain imaging using advanced spatiotemporal techniques. The first set of experiments were based on simulations. Much controversy exists in the literature regarding the differences between magnetoencephalography (MEG) and electroencephalography (EEG}, both practically and theoretically. The differences were explored using simulations that evaluated the expected signal-to-noise ratios from reasonable brain sources. MEG and EEG were found to be complementary, with each modality optimally suited to image activity from different areas of the cortical surface. Consequently, evaluations of epileptic patients and general neuroscience experiments will both benefit from simultaneously collected MEG/EEG. The second set of experiments represent an example of MEG combined with magnetic resonance imaging (MRI) and functional MRI (fMRI) applied to healthy subjects. The study set out to resolve two questions relating to shape perception. First, does the brain activate functional areas sequentially during shape perception, as has been suggested in recent literature? Second, which , if any, functional areas are active time-locked with reaction-time? The study found that functional areas are non-sequentially activated, and that area IT is active time-locked with reaction-time. These two points, coupled with the method for multimodal integration , can help further develop our understanding of shape perception in particular, and cortical dynamics in general for healthy subjects. Broadly, these two studies represent practical guidelines for epilepsy evaluations and brain mapping studies. For epilepsy studies, clinicians could combine MEG and EEG to maximize the probability of finding the source of seizures. For brain mapping in general, EEG, MEG, MRI and fMRI can be combined in the methods outlined here to obtain more sophisticated views of cortical dynamics

Cortical Reorganisation in Complex Regional Pain Syndrome (CRPS)

Complex Regional Pain Syndrome (CRPS) is a debilitating pain condition of unknown aetiology, usually occurring post-traumatically. Early diagnosis of CRPS remains a challenge with adverse implications on rehabilitation and recovery. The main goals of my research were to help develop clinically useful bedside tests as well as objective biomarkers to improve the early diagnosis of CRPS. The first research project in this thesis, ‘Novel signs in CRPS and their diagnostic clinical utility’ was a prospective observational cohort study which defined the four novel signs (finger misperception, abnormal hand laterality, astereognosis and abnormal body scheme report) in CRPS, examined their prevalence in CRPS and other chronic pain conditions and assessed their diagnostic utility (Sensitivity, Specificity, Predictive values and Likelihood ratios) for identifying patients at risk of CRPS within a Fracture cohort. This study demonstrates that novel signs are present in the majority of CRPS patients and can be reliably detected following simple training. They are practical and have significant clinical utility in diagnosing persistent pain in a fracture group. They can be used to identify patients at high risk of developing chronic pain post-fracture thereby allowing targeted early intervention. Cortical reorganisation, defined as structural and functional changes within the cerebral cortex, is implicated in many chronic pain conditions including CRPS. The second research project in this thesis ‘Cortical reorganisation and finger misperception in CRPS- a high density electroencephalogram study’ was a prospective case control design study which investigated the EEG parameters suggestive of cortical reorganisation in CRPS patients by studying the somatosensory ERPs (Event Related Potentials) elicited on painless finger stimulation. There was no significant difference in the GFP (Global Field Power) latency in the patient group compared to healthy subjects or between affected and unaffected sides of the patient group suggesting there was no impairment of somatosensory conduction from the periphery to the somatosensory cortex. However, GFP amplitude corresponding to P300 was significantly higher in the patient affected side compared to the healthy subjects suggesting cognitive dysfunction possibly related to increased allocation of attentional resources

EpiGauss : caracterização espacio-temporal da actividade cerebral em epilepsia

Doutoramento em Engenharia ElectrotécnicaA epilepsia é uma patologia cerebral que afecta cerca de 0,5% da população mundial. Nas epilepsias focais, o principal objectivo clínico é a localização da zona epileptogénica (área responsável pelas crises), uma informação crucial para uma terapêutica adequada. Esta tese é centrada na caracterização da actividade cerebral electromagnética do cérebro epiléptico. As contribuições nesta área, entre a engenharia e neurologia clínica, são em duas direcções. Primeiro, mostramos que os conceitos associados às pontas podem ser imprecisos e não ter uma definição objectiva, tornando necessária uma reformulação de forma a definir uma referência fiável em estudos relacionados com a análise de pontas. Mostramos que as características das pontas em EEG são estatisticamente diferentes das pontas em MEG. Esta constatação leva a concluir que a falta de objectividade na definição de ponta na literatura pode induzir utilizações erradas de conceitos associados ao EEG na análise de MEG. Também verificamos que o uso de conjuntos de detecções de pontas efectuadas por especialistas (MESS) como referência pode fornecer resultados enganadores quando apenas baseado em critérios de consenso clínico, nomeadamente na avaliação da sensibilidade e especificidade de métodos computorizados de detecção de pontas Em segundo lugar, propomos o uso de métodos estatísticos para ultrapassar a falta de precisão e objectividade das definições relacionadas com pontas. Propomos um novo método de neuroimagem suportado na caracterização de geradores electromagnéticos – EpiGauss – baseado na análise individual dos geradores de eventos do EEG que explora as suas estruturas espacio-temporais através da análise de “clusters”. A aplicação de análise de “clusters” à análise geradores de eventos do EEG tem como objectivo usar um método não supervisionado, para encontrar estruturas espacio-temporais dps geradores relevantes. Este método, como processo não supervisionado, é orientado a utilizadores clínicos e apresenta os resultados sob forma de imagens médicas com interpretação similar a outras técnicas de imagiologia cerebral. Com o EpiGauss, o utilizador pode determinar a localização estatisticamente mais provável de geradores, a sua estabilidade espacial e possíveis propagações entre diferente áreas do cérebro. O método foi testado em dois estudos clínicos envolvendo doentes com epilepsia associada aos hamartomas hipotalâmicos e o outro com doentes com diagnóstico de epilepsia occipital. Em ambos os estudos, o EpiGauss foi capaz de identificar a zona epileptogénica clínica, de forma consistente com a história e avaliação clínica dos neurofisiologistas, fornecendo mais informação relativa à estabilidade dos geradores e possíveis percursos de propagação da actividade epileptogénica contribuindo para uma melhor caracterização clínica dos doentes. A conclusão principal desta tese é que o uso de técnicas não supervisionadas, como a análise de “clusters”, associadas as técnicas não-invasivas de EMSI, pode contribuir com um valor acrescido no processo de diagnóstico clínico ao fornecer uma caracterização objectiva e representação visual de padrões complexos espaciotemporais da actividade eléctrica epileptogénica.Epilepsy is a brain pathology that affects 0.5% of the world population. In focal epilepsies, the main clinical objective is the localization of the epileptogenic zone (brain area responsible for the epileptic seizures – EZ), a key information to decide an adequate therapeutic approach. This thesis is centred on electromagnetic activity characterization of the epileptic brain. Our contribution to this boundary area between engineering and clinical neurology is two-folded. First we show that spike related clinical concepts can be unprecise and some do not have objective definitions making necessary a reformulation in order to have a reliable reference in spike related studies. We show that EEG spike wave quantitative features are statistically different from their MEG counterparts. This finding leads to the conclusion that the lack of objective spike feature definitions in the literature can induce the wrong usage of EEG feature definition in MEG analysis. We also show that the use of multi-expert spike selections sets (MESS) as gold standard, although clinically useful, may be misleading whenever defined solely in terms of clinical agreement criteria, namely as references for automatic spike detection algorithms in sensitivity and specificity method analysis. Second, we propose the use of statistical methods to overcome some lack of precision and objectivity in spike related definitions. In this context, we propose a new ElectroMagnetic Source Imaging (EMSI) method – EpiGauss – based on cluster analysis that explores both spatial and temporal information contained in individual events sources analysis characterisation. This automatic cluster method for the analysis of spike related electric generators based in EEG is used to provide an unsupervised tool to find their relevant spatio-temporal structures. This method enables a simple unsupervised procedure aimed for clinical users and presents its results in an intuitive representation similar to other brain imaging techniques. With EpiGauss, the user is able to determine statistically probable source locations, their spatial stability and propagation patterns between different brain areas. The method was tested in two different clinical neurophysiology studies, one with a group of Hypothalamic Hamartomas and another with a group of Occipital Epilepsy patients. In both studies EpiGauss identified the clinical epileptogenic zone, consistent with the clinical background and evaluation of neurophysiologists, providing further information on stability of source locations and their probable propagation pathways that enlarges their clinical interpretation. This thesis main conclusion is that the use of unsupervised techniques, such as clustering, associated with EMSI non-invasive techniques, can bring an added value in clinical diagnosis process by providing objective and visual representation of complex epileptic brain spatio-temporal activity patterns