Related papers: Nonparametric tests of structure for high angular …
We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to…
Over the past few decades, magnetic resonance imaging has been utilized as a powerful imaging modality to evaluate the structure and function of various organs in the human body,such as the brain. Additionally, diffusion and perfusion MR…
In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.
Change point tests for abrupt changes in the mean of functional data, i.e., random elements in infinite-dimensional Hilbert spaces, are either based on dimension reduction techniques, e.g., based on principal components, or directly based…
In the last decade Diffusing Wave Spectroscopy (DWS) has emerged as a powerful tool to study turbid media. In this article we develop the formalism to describe light diffusion in general anisotropic turbid media. We give explicit formulas…
Brownian motion of water molecules provides an essential length scale, the diffusion length, commensurate with cell dimensions in biological tissues. Measuring the diffusion coefficient as a function of diffusion time makes in vivo…
We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It…
We calculate the one-point probability distribution function (PDF) for cosmic density in non-linear regime of the gravitational evolution. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…
Many developmental processes, such as plasticity and aging, or pathological processes such as neurological diseases are characterized by modulations of specific cellular types and their microstructures. Diffusion-weighted Magnetic Resonance…
Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their…
Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of…
Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, our new approach takes into account suitable weighted action functionals…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Diffusion models (DMs) are generative models that learn to synthesize images from Gaussian noise. DMs can be trained to do a variety of tasks such as image generation and image super-resolution. Researchers have made significant…
Cross-term spatiotemporal encoding (xSPEN) is a recently introduced imaging approach delivering single-scan 2D NMR images with unprecedented resilience to field inhomogeneities. The method relies on performing a pre-acquisition encoding and…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
Parcellation of white matter tractography provides anatomical features for disease prediction, anatomical tract segmentation, surgical brain mapping, and non-imaging phenotype classifications. However, parcellation does not always reach…