-
Article
Bayesian parameter inference for partially observed stochastic volterra equations
In this article we consider Bayesian parameter inference for a type of partially observed stochastic Volterra equation (SVE). SVEs are found in many areas such as physics and mathematical finance. In the latte...
-
Article
Open AccessMulti-index Sequential Monte Carlo Ratio Estimators for Bayesian Inverse problems
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalising constant, and where even the un-normalised target needs to be approximated at finite resolut...
-
Article
Bayesian parameter inference for partially observed stochastic differential equations driven by fractional Brownian motion
In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion models. The approach we follow is to time-discretize the hidden process and then to design Markov chain ...
-
Article
Open AccessA 4D-Var method with flow-dependent background covariances for the shallow-water equations
The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations ove...
-
Article
Multilevel estimation of normalization constants using ensemble Kalman–Bucy filters
In this article we consider the application of multilevel Monte Carlo, for the estimation of normalizing constants. In particular we will make use of the filtering algorithm, the ensemble Kalman–Bucy filter (E...
-
Article
Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parall...
-
Chapter and Conference Paper
Randomized Multilevel Monte Carlo for Embarrassingly Parallel Inference
This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next...
-
Article
Open AccessUncertainty modelling and computational aspects of data association
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially obs...
-
Article
Open AccessUnbiased estimation of the gradient of the log-likelihood in inverse problems
We consider the problem of estimating a parameter \(\theta \in \Theta \subseteq {\mathbb {R}}^{d_{\theta }}\) ...
-
Article
Multilevel particle filters for the non-linear filtering problem in continuous time
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but d...
-
Article
Open AccessCorrection to: Multilevel particle filters for Lévy-driven stochastic differential equations
The article Multilevel particle filters for Lévy-driven stochastic differential equations, written by Ajay Jasra, Kody J. H. Law, Prince Peprah Osei, was originally published electronically on the publisher’s ...
-
Article
Open AccessMultilevel particle filters for Lévy-driven stochastic differential equations
We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations driven by pure Lévy processes. We consider filtering such processes as well a...
-
Article
Open AccessOptimization Based Methods for Partially Observed Chaotic Systems
In this paper we consider filtering and smoothing of partially observed chaotic dynamical systems that are discretely observed, with an additive Gaussian noise in the observation. These models are found in a w...
-
Article
A method for high-dimensional smoothing
We consider the problem of the computation of smoothed additive functional, which are some integrals with respect to the joint smoothing distribution. It is a key issue in inference for general state-space mod...
-
Article
On coupling particle filter trajectories
Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps...
-
Article
Multilevel particle filters: normalizing constant estimation
In this article, we introduce two new estimates of the normalizing constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non...
-
Article
Biased Online Parameter Inference for State-Space Models
We consider Bayesian online static parameter estimation for state-space models. This is a very important problem, but is very computationally challenging as the state-of-the art methods that are exact, often h...
-
Article
Variational inference for sparse spectrum Gaussian process regression
We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty i...
-
Article
Monte Carlo algorithms for computing \(\alpha \) -permanents
We consider the computation of the \(\alpha \) α ...
-
Article
Sequential Monte Carlo methods for Bayesian elliptic inverse problems
In this article, we consider a Bayesian inverse problem associated to elliptic partial differential equations in two and three dimensions. This class of inverse problems is important in applications such as hy...
