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

We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure.…

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the…

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This…

We present a scheme for simulating conditioned semimartingales taking values in Riemannian manifolds. Extending the guided bridge proposal approach used for simulating Euclidean bridges, the scheme replaces the drift of the conditioned…

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…

The main message in this paper is that there are surprisingly many different Brownian bridges, some of them - familiar, some of them - less familiar. Many of these Brownian bridges are very close to Brownian motions. Somewhat loosely…

Stochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian…

Monitoring contact pressure in hospital beds is essential for preventing pressure ulcers and enabling real-time patient assessment. Current methods can predict pressure maps but often lack physical plausibility, limiting clinical…

Billera-Holmes-Vogtmann (BHV) tree space is a geodesic metric space of edge-weighted phylogenetic trees with a fixed leaf set. Constructing parametric distributions on this space is challenging due to its non-Euclidean geometry and the…

We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed to calculate steady state probabilities of order…

We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random…

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the…

We show how Langevin diffusions can be interpreted in the context of stochastic Hamiltonian systems with structure-preserving noise and dissipation on reductive Lie groups. Reductive Lie groups provide the setting in which the Lie group…

We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we use the Gleason-Iwasawa-Montgomery-Yamabe-Zippin structure…

We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…

We consider an empirical process based upon ratio of selected pair of the non-overlapping $m$-spacings generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on…

We show that simple explicit formulas can be obtained for several relevant quantities related to the laws of the uniformly sampled Brownian bridge, Brownian meander and three dimensional Bessel process. To prove such results, we use the…

This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…

Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability…