Related papers: A closed-form filter for binary time series

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

In this paper, we aim to propose a consistent non-Gaussian Bayesian filter of which the system state is a continuous function. The distributions of the true system states, and those of the system and observation noises, are only assumed…

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…

Circular time series has received relatively little attention in statistics and modeling complex circular time series using the state space approach is non-existent in the literature. In this article we introduce a flexible Bayesian…

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…

In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…

Phase-averaged dilute bubbly flow models require high-order statistical moments of the bubble population. The method of classes, which directly evolve bins of bubbles in the probability space, are accurate but computationally expensive.…

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…

Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a…

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the…

We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors. Driven by the problem of…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are…

This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are…

Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that general nudging techniques can also tackle another crucial…