Related papers: A Brownian Motion Model and Extreme Belief Machine…

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…

The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…

For many real time applications, it is important to validate the information received from the sensors before entering higher levels of reasoning. This paper presents an any time probabilistic algorithm for validating the information…

Motion correlation interfaces are those that present targets moving in different patterns, which the user can select by matching their motion. In this paper, we re-formulate the task of target selection as a probabilistic inference problem.…

The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…

We combine traditional pointer-based simultaneous measurements of conjugate observables with the concept of quantum Brownian motion of multipartite systems to phenomenologically model simultaneous measurements of conjugate observables in a…

The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting…

The purpose of this note is to collect in one place a few results about simple random walk and Brownian motion which are often useful. These include standard results such as Beurling estimates, large deviation estimates, and a method for…

Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…

In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a L\'evy process. More specifically, we investigate the asymptotic theory for the conditional mean…

We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution…

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…

Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging…

Computer codes are widely used to describe physical processes in lieu of physical observations. In some cases, more than one computer simulator, each with different degrees of fidelity, can be used to explore the physical system. In this…

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC)…

Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…

The application of machine learning (ML) techniques in wireless communication domain has seen a tremendous growth over the years especially in the wireless sensing domain. However, the questions surrounding the ML model's inference…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

We describe and experimentally investigate a method to construct forecasting algorithms for stationary and ergodic processes based on universal measures (or so-called universal data compressors). Using some geophysical and economical time…

Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals.…