Related papers: Variance estimation in the particle filter
Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the…
Sequential Monte Carlo methods are typically not straightforward to implement on parallel architectures. This is because standard resampling schemes involve communication between all particles. The $\alpha$-sequential Monte Carlo method was…
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated…
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…
Sequential Monte Carlo algorithms, or particle filters, are widely used for approximating intractable integrals, particularly those arising in Bayesian inference and state-space models. We introduce a new variance reduction technique, the…
Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle…
This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expected memory cost by $T + C N \log N$ where…
Particle filters are a widely used Monte Carlo based data assimilation technique that estimates the probability distribution of a system's state conditioned on observations through a collection of weights and particles. A known problem for…
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…
We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models.…
Particle Markov chain Monte Carlo techniques rank among current state-of-the-art methods for probabilistic program inference. A drawback of these techniques is that they rely on importance resampling, which results in degenerate particle…
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…
We introduce a new sequential Monte Carlo algorithm we call the particle cascade. The particle cascade is an asynchronous, anytime alternative to traditional particle filtering algorithms. It uses no barrier synchronizations which leads to…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…