Related papers: Computable infinite dimensional filters with appli…
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
We investigate the impact of filter choice on forecast accuracy in state space models. The filters are used both to estimate the posterior distribution of the parameters, via a particle marginal Metropolis-Hastings (PMMH) algorithm, and to…
We study the problem of distributed Kalman filtering for sensor networks in the presence of model uncertainty. More precisely, we assume that the actual state-space model belongs to a ball, in the Kullback-Leibler topology, about the…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is…
Independent cascade (IC) model is a widely used influence propagation model for social networks. In this paper, we incorporate the concept and techniques from causal inference to study the identifiability of parameters from observational…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual…
A time-invariant, linear, distributed observer is described for estimating the state of an $m>0$ channel, $n$-dimensional continuous-time linear system of the form $ \dot{x} = Ax,\ y_i = C_i x,\ i \in \{1,2,\cdots, m\}$. The state $x$ is…
In this paper, a cooperative diffusion-based molecular communication system is considered where distributed receivers collaboratively determine a transmitter's signal. In this system, the receivers first make local hard decisions about the…
We develop a generalization of unobserved components models that allows for a wide range of long-run dynamics by modelling the permanent component as a fractionally integrated process. The model does not require stationarity and can be cast…
Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…
The paper discusses fundamental detectability properties associated with the problem of distributed state estimation using networked observers. The main result of the paper establishes connections between detectability of the plant through…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…
This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…