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Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
A growing interest has developed in the problem of training models of EEG features to predict brain activity measured using fMRI, i.e. the problem of EEG-to-fMRI synthesis. Despite some reported success, the statistical significance and…
This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome…
Functional data analysis finds widespread application across various fields. While functional data are intrinsically infinite-dimensional, in practice, they are observed only at a finite set of points, typically over a dense grid. As a…
A common concern in the field of functional data analysis is the challenge of temporal misalignment, which is typically addressed using curve registration methods. Currently, most of these methods assume the data is governed by a single…
Functional graphical models explore dependence relationships of random processes. This is achieved through estimating the precision matrix of the coefficients from the Karhunen-Loeve expansion. This paper deals with the problem of…
We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…
Instrumental variables are widely used to adjust for measurement error bias when assessing associations of health outcomes with ME prone independent variables. IV approaches addressing ME in longitudinal models are well established, but few…
Localizing neuronal activity in the brain, both in time and in space, is a central challenge to advance the understanding of brain function. Because of the inability of any single neuroimaging techniques to cover all aspects at once, there…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
We consider the problem of extracting features from passive, multi-channel electroencephalogram (EEG) devices for downstream inference tasks related to high-level mental states such as stress and cognitive load. Our proposed method…
EEG is a non-invasive technique for recording brain bioelectric activity, which has potential applications in various fields such as human-computer interaction and neuroscience. However, there are many difficulties in analyzing EEG data,…
We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models,…
Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…
Estimation of brain functional connectivity from EEG data is of great importance both for medical research and diagnosis. It involves quantifying the conditional dependencies among the activity of different brain areas from the time-varying…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
In multi-condition EEG experiments, brain activity is recorded as subjects perform various tasks or are exposed to different stimuli. The recorded signals are commonly transformed into time-frequency representations, which often display…
Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…
Heterogeneous treatment effect estimation is an important problem in precision medicine. Specific interests lie in identifying the differential effect of different treatments based on some external covariates. We propose a novel…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…