Related papers: On Parametric Misspecified Bayesian Cram\'{e}r-Rao…
Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the…
Virtually any model we use in machine learning to make predictions does not perfectly represent reality. So, most of the learning happens under model misspecification. In this work, we present a novel analysis of the generalization…
Parameter estimates in misspecified models converge to pseudo-true parameter values, which minimize a population objective function. Pseudo-true values often differ from quantities of economic interest, raising questions of how, if at all,…
Quantum Cram\'er--Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain…
Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
In this paper, we consider the multicollinearity problem in the gamma regression model when model parameters are linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories…
This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…
Meta-backscatter system that utilizes meta-material sensors is a promising enabler for future environmental sensing, offering distinct advantages such as low cost, zero-power consumption, and robustness. Specifically, the electromagnetic…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
In his 2005 paper, S.T. Smith proposed an intrinsic Cram\'er-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…