Related papers: Filtering of stationary Gaussian statistical exper…
This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…
Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior…
We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
Despite the numerous applications that may be expeditiously modelled by counting processes, stochastic filtering strategies involving Poisson-type observations still remain somewhat poorly developed. In this work, we propose a Monte Carlo…
In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…
We establish results for the first sensitivity analysis of the stochastic fluid models (SFMs). We derive expressions for the sensitivity analysis of the key stationary and transient (time-dependent) quantities of this class of models. We…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…
This work studies networked agents cooperating to track a dynamical state of nature under partial information. The proposed algorithm is a distributed Bayesian filtering algorithm for finite-state hidden Markov models (HMMs). It can be used…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
This paper proposes a novel and efficient key conditional quotient filter (KCQF) for the estimation of state in the nonlinear system which can be either Gaussian or non-Gaussian, and either Markovian or non-Markovian. The core idea of the…
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…
We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a…
In this paper, we focus on the statistical filtering problem in dynamical models with jumps. When a particular application relies on physical properties which are modeled by linear and Gaussian probability density functions with jumps, an…
This paper is concerned with the nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any time t, the sigma-algebra…
In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears…