Related papers: Matrix Fisher-Gaussian Distribution on $\mathrm{SO…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…
Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle…
Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g.,~for regular…
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space…
The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…
This article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
Data assimilation is the process of estimating the state of a dynamical system over time by combining model predictions with measurements. This task becomes challenging when the system is nonlinear and high-dimensional. To address this,…
Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
We revisit the nonlinear complimentary filter on $SO(3)$, previously proposed in the literature, and provide the (time-explicit) solution to the matrix ODE governing the attitude estimation error in the absence of measurement errors. The…
Multi-robot systems must have the ability to accurately estimate relative states between robots in order to perform collaborative tasks, possibly with no external aiding. Three-dimensional relative pose estimation using range measurements…
The filtering of a Markov diffusion process on a manifold from counting process observations leads to `large' changes in the conditional distribution upon an observed event, corresponding to a multiplication of the density by the intensity…
With the advance in computational resources, Bayesian inference is increasingly becoming the standard tool of practise in GW astronomy. However, algorithms such as Markov Chain Monte Carlo (MCMC) require a large number of iterations to…