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This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…
We apply a recently developed stochastic method to the Shastry-Sutherland model on 4x4 and 8x8 lattices. This method, which we call the Stochastic State Selection Method here, enables us to evaluate expectation values of powers of the…
Research in NLP is often supported by experimental results, and improved reporting of such results can lead to better understanding and more reproducible science. In this paper we analyze three statistical estimators for expected validation…
We prove the asymptotic mixed normality of the least absolute deviation (LAD) estimator for a locally $\alpha$-stable stochastic differential equation (SDE) observed at high frequency, where $\alpha\in(0,2)$. We investigate both ergodic and…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
We propose a partition-based state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state…
Robust stability of moving-horizon estimators is investigated for nonlinear discrete-time systems that are detectable in the sense of incremental input/output-to-state stability and are affected by disturbances. The estimate of a…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…
The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
This paper discusses minimum distance estimation method in the linear regression model with dependent errors which are strongly mixing. The regression parameters are estimated through the minimum distance estimation method, and asymptotic…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
This paper summarizes an optimal state estimation that previously has been used in power systems and discusses the robustness of the by using a system-state controller. Static state estimation (SSE) traditionally tries to linearize power…
We study the least square estimator, in the framework of simple linear regression, when the deviance term $\varepsilon$ with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator,…
Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions or local transport properties from molecular simulations, we show that the variance can be…
Optimal experiment design for parameter estimation is a research topic that has been in the interest of various studies. A key problem in optimal input design is that the optimal input depends on some unknown system parameters that are to…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
In this paper, an approach to estimating a nonlinear deterministic model is presented. We introduce a stochastic model with extremely small variances so that the deterministic and stochastic models are essentially indistinguishable from…
We consider the optimal control design problem for discrete-time LTI systems with state feedback, when the actuation signal is subject to unmeasurable switching propagation delays, due to e.g. the routing in a multi-hop communication…