Related papers: Bayesian Radio Map Estimation: Fundamentals and Im…

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…

The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

The Bayes error rate (BER) is a fundamental concept in machine learning that quantifies the best possible accuracy any classifier can achieve on a fixed probability distribution. Despite years of research on building estimators of lower and…

We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of $\mathbf{s}\mathbf{s}^T$, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference…

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…

Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for…

Environmental model performances need to be assessed using some statistical parameters, such as mean absolute error (MAE) and root mean square error (RMSE). The advantages and disadvantages of these parameters are still in controversial.…

The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior…

Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…

The Bayesian Cram\'er-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed…

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error…

In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…

This paper addresses the classic problem of parameter estimation (PE) in multimachine power system models. Such models are typically described by a set of nonlinear differential-algebraic equations (DAE), where generator physics and network…

Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

The Bayesian Land Surface Temperature estimator previously developed has been extended to include the effects of imperfectly known gain and offset calibration errors. It is possible to treat both gain and offset as nuisance parameters and,…

Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…

Radio Map Prediction (RMP), aiming at estimating coverage of radio wave, has been widely recognized as an enabling technology for improving radio spectrum efficiency. However, fast and reliable radio map prediction can be very challenging…