Related papers: A practical example for the non-linear Bayesian fi…

This paper presents a performance comparison of different estimation and prediction techniques applied to the problem of tracking multiple robots. The main performance criteria are the magnitude of the estimation or prediction error, the…

A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…

Particle filters are applicable to a wide range of nonlinear, non-Gaussian state-space models and have already been applied to a variety of problems. However, there is a problem in the calculation of smoothed distributions, where particles…

Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…

Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them…

Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…

Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…

Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…

We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…

The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical…

Particle filters are a group of algorithms to solve inverse problems through statistical Bayesian methods when the model does not comply with the linear and Gaussian hypothesis. Particle filters are used in domains like data assimilation,…

A fundamental problem in statistical neuroscience is to model how neurons encode information by analyzing electrophysiological recordings. A popular and widely-used approach is to fit the spike trains with an autoregressive point process…

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the…

State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…