Related papers: Optimal parameters for anomalous diffusion exponen…
Recent studies found that many channels are affected by additive noise that is impulsive in nature and is best explained by heavy-tailed symmetric alpha-stable distributions. Dealing with impulsive noise environments comes with an added…
Countless systems in biology, physics, and finance undergo diffusive dynamics. Many of these systems, including biomolecules inside cells, active matter systems and foraging animals, exhibit anomalous dynamics where the growth of the mean…
Periodic autoregressive (PAR) time series with finite variance is considered as one of the most common models of second-order cyclostationary processes. However, in the real applications, the signals with periodic characteristics may be…
Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and…
We propose a general framework for optimizing noise schedules in diffusion models, applicable to both training and sampling. Our method enforces a constant rate of change in the probability distribution of diffused data throughout the…
We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
We analyze the effect of lossy compression in the processing of sensor signals that must be used to detect anomalous events in the system under observation. The intuitive relationship between the quality loss at higher compression and the…
Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…
In the previous paper an adaptive filtering based on a reference recursive recipe was developed and tested on a simulated dynamics of a spring, mass, and damper with a weak nonlinear spring. In this paper the above recipe is applied to a…
We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…
Regression discontinuity designs assess causal effects in settings where treatment is determined by whether an observed running variable crosses a pre-specified threshold. Here we propose a new approach to identification, estimation, and…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
To develop a machine sound monitoring system, a method for detecting anomalous sound is proposed. Exact likelihood estimation using Normalizing Flows is a promising technique for unsupervised anomaly detection, but it can fail at…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…
Digital sensors can lead to noisy results under many circumstances. To be able to remove the undesired noise from images, proper noise modeling and an accurate noise parameter estimation is crucial. In this project, we use a…
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…