Related papers: On fixed gain recursive estimators with discontinu…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
This paper considers the simultaneous state and unknown input estimation for continuous-discrete stochastic systems. Two types of approaches (with and without modeling of unknown inputs) which can address this issue are investigated. A…
The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-field PDE model in which the Young's modulus is an affine…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…
For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple…
This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…
We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
We discuss a class of difference-based estimators for the autocovariance in nonparametric regression when the signal is discontinuous (change-point regression), possibly highly fluctuating, and the errors form a stationary $m$-dependent…
Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We investigate the problem of estimating the drift parameter from $N$ independent copies of the solution of a stochastic differential equation driven by a multiplicative fractional Brownian noise with Hurst parameter $H\in (1/3,1)$.…
We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…