Related papers: Bridge Simulation and Metric Estimation on Lie Gro…

Group-formation experiments, in which experimental units are randomly assigned to groups, are a powerful tool for studying peer effects in the social sciences. Existing design and analysis approaches allow researchers to draw inference from…

We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the…

In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input…

Diffusion bridge models and stochastic interpolants enable high-quality image-to-image (I2I) translation by creating paths between distributions in pixel space. However, the proliferation of techniques based on incompatible mathematical…

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between the sets in terms of their distributions. Indices for this task are usually derived by…

The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…

We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additional equivalence transformation on the space (x,y,z,u,f),…

We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the…

It is known that a connected and simply-connected Lie group admits only one left-invariant Riemannian metric up to scaling and isometry if and only if it is isomorphic to the Euclidean space, the Lie group of the real hyperbolic space, or…

Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…

We introduce a novel approximation to the same marginal Schr\"{o}dinger bridge using the Langevin diffusion. As $\varepsilon \downarrow 0$, it is known that the barycentric projection (also known as the entropic Brenier map) of the…

We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…

The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…

Deep Ensemble (DE) approach is a straightforward technique used to enhance the performance of deep neural networks by training them from different initial points, converging towards various local optima. However, a limitation of this…