The investigator derives a logspline procedure to estimate the density and conditional density (for regression type of applications) functions for response variable subject to random truncation. In addition to bias adjustment due to random truncation, the estimators will be shown to possess optimal rates of convergence and important issues related to high-dimensional explanatory variables will be addressed via ANOVA type of decomposition. For functional magnetic resonance imaging (fMRI) data, the PI and his collaborators estimate the hemodynamic response function(HRF) via deconvolution and develop statistical inference for brain region activation. They also consider the problem of spatial-temporal feature extraction using independent component analysis (ICA). Under appropriate conditions, both parametric and non-parametric statistical inference for the mixing matrix and the latent temporal signals will be derived. Finally, for data involving simultaneous recording of an ensemble of neurons, the problem of feature extraction in identify a group of neurons that interact with the target neuron is examined by using a logspline methodology to estimate the conditional intensity function. The PI studies the statistical inference for firing probability by establishing optimal rates of convergence and the asymptotic distribution of the estimator. Software for all the projects will be developed and disseminated for public use.

Advance in computer technology has provided a fertile ground for many exciting research opportunities. A profound example is how scientists now use genomic data to study diseases that affect our health. Another is biomedical imaging in brain disease and cognitive studies. In order to conduct valid statistical inferences based on these types of data, it is important to account for the under-sampling issue during the data acquisition stage. The Principle Investigator (PI) develops a flexible statistical framework to address this problem and investigates the modelling validity in real world applications. In particular, the PI and his colleagues investigate how their statistical modelling of blood flow information can help scientists interpret the functional magnetic resonant imaging data for medical applications. They also construct brain images that capture the neural physiological activity or circuitry of a specific task, as a pathway to understand how the brain functions. Finally, the PI uses efficient and effective statistical methods to study the dynamics of the brain at a much higher temporal resolution by modelling the electro-potential or neuro-firing probability of a task-specific ensemble of neurons. These results help medical researchers advance their knowledge in their related fields so that treatments to various genetic or central nervous system diseases that affect our health can be developed.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Gabor J. Szekely
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University of North Carolina Chapel Hill
Chapel Hill
United States
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