Related papers: Gaussian Processes for HRF estimation for BOLD fMR…
We study the problem of nonparametric estimation of linear multiplier function $\theta t)$ for processes satisfying stochastic differential equations of the type $dX_t=\theta(t)X_tdt+\epsilond\bar W_t^H, X_0=x_0, 0\leq t \leq T$ where…
Interactions between the brain and body are of fundamental importance for human behavior and health. Functional magnetic resonance imaging (fMRI) captures whole-brain activity noninvasively, and modeling how fMRI signals interact with…
The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The natural frequencies and damping behaviour can be easily and quickly detected from a Bode diagram. The modal…
Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM)…
Influence function (IF)-based estimators are widely used in mediation analysis due to their modeling flexibility, but standard implementations require direct estimation of the distribution functions of the mediator and treatment variables.…
After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also…
Functional Magnetic Resonance Imaging (fMRI) is a powerful non-invasive tool for localizing and analyzing brain activity. This study focuses on one very important aspect of the functional properties of human brain, specifically the…
Most brain disorders are very heterogeneous in terms of their underlying biology and developing analysis methods to model such heterogeneity is a major challenge. A promising approach is to use probabilistic regression methods to estimate…
Radio-frequency (RF) Radiance Field reconstruction is a challenging problem. The difficulty lies in the interactions between the propagating signal and objects, such as reflections and diffraction, which are hard to model precisely,…
Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian…
A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is…
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
In observational studies, unmeasured confounders present a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models for time-to-event outcomes, two-stage…
Motivated by modeling and analysis of mass-spectrometry data, a semi- and nonparametric model is proposed that consists of a linear parametric component for individual location and scale and a nonparametric regression function for the…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\xi_i, \: i=1,...,n $, with incomplete information, i.e. each real random variable $ \xi_i $ has a density $ g_{i} $ which is unknown to the…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…