Related papers: Central Limit Theorems for Coupled Particle Filter…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are…
This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling…
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…
Bootstrap particle filter (BPF) is the corner stone of many popular algorithms used for solving inference problems involving time series that are observed through noisy measurements in a non-linear and non-Gaussian context. The long term…
Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
A recently developed approach, conditional probability density functional theory (CP-DFT), yields direct access to the exchange-correlation hole of a system, an important correlation function that is not available from any standard DFT…
Particle Flow Filters perform the measurement update by moving particles to a different location rather than modifying the particles' weight based on the likelihood. Their movement (flow) is dictated by a drift term, which continuously…
This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…
Our previously developed Constrained-Pairing Mean-Field Theory (CPMFT) is shown to map onto an Unrestricted Hartree-Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation…
This paper introduces the {\it particle swarm filter} (not to be confused with particle swarm optimization): a recursive and embarrassingly parallel algorithm that targets an approximation to the sequence of posterior predictive…
Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient…
We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their…
We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume…
Current data from neutrino oscillation experiments are in good agreement with $\delta =-\frac{\pi}{2}$ and $\theta_{23}^{} = \frac{\pi}{4}$. We define the notion of "constrained maximal CP violation" (CMCPV) for predicting these features…
We present a consensus-based distributed particle filter (PF) for wireless sensor networks. Each sensor runs a local PF to compute a global state estimate that takes into account the measurements of all sensors. The local PFs use the joint…
We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a…
We consider the Kalman-filtering problem with multiple sensors which are connected through a communication network. If all measurements are delivered to one place called fusion center and processed together, we call the process centralized…