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Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
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-negative and the other is…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework,…
"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random…
We investigate the use of possibly the simplest scheme for the parallelisation of the standard particle filter, that consists in splitting the computational budget into $M$ fully independent particle filters with $N$ particles each, and…
Our article deals with Bayesian inference for a general state space model with the simulated likelihood computed by the particle filter. We show empirically that the partially or fully adapted particle filters can be much more efficient…
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 discrete-time observations, we…
Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration.…
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
We present a new approach-the ALVar estimator-to estimation of asymptotic variance in sequential Monte Carlo methods, or, particle filters. The method, which adjusts adaptively the lag of the estimator proposed in [Olsson, J. and Douc, R.…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
A standard approach to approximate inference in state-space models isto apply a particle filter, e.g., the Condensation Algorithm.However, the performance of particle filters often varies significantlydue to their stochastic nature.We…
Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in the comparison of these quantities as some…
The objective of this article is to study the asymptotic behavior of a new particle filtering approach in the context of hidden Markov models (HMMs). In particular, we develop an algorithm where the latent-state sequence is segmented into…
Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the…
Particle filtering is a powerful tool for target tracking. When the budget for observations is restricted, it is necessary to reduce the measurements to a limited amount of samples carefully selected. A discrete stochastic nonlinear…
We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for…