Related papers: Exploring Positive Noise in Estimation Theory
The reconstruction of a deterministic data field from binary-quantized noisy observations of sensors which are randomly deployed over the field domain is studied. The study focuses on the extremes of lack of deterministic control in the…
The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry--Esseen bound of the so-called alternative estimator of the mean reversion parameter. The…
The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…
We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
We develop a novel framework for costly information acquisition in which a decision-maker learns about an unobserved state by choosing a signal distribution, with the cost of information determined by the distribution of noise in the…
Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…
Noise Contrastive Estimation (NCE) is a powerful parameter estimation method for log-linear models, which avoids calculation of the partition function or its derivatives at each training step, a computationally demanding step in many cases.…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…
In this paper, we consider a novel machine learning problem, that is, learning a classifier from noisy label distributions. In this problem, each instance with a feature vector belongs to at least one group. Then, instead of the true label…
A problem of online estimation of unknown parameters is considered for a linear regression equation, which is affected by an additive perturbation that can be caused by measurement noise (that corrupts regressor and regressand), as well as…