Related papers: Fast and Accurate Linear Fitting for Incompletely …
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
A general purpose fitting model for one-dimensional astrometric signals is developed, building on a maximum likelihood framework, and its performance is evaluated by simulation over a set of realistic image instances. The fit quality is…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
Many datasets are in the form of tables of binned data. Performing regression on these data usually involves either reading off bin heights, ignoring data from neighbouring bins or interpolating between bins thus over or underestimating the…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…
We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -- geometric fit, Kasa fit, Pratt fit, and Taubin fit -- is…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
In all applications of gamma-ray spectroscopy, one of the most important and delicate parts of the data analysis is the fitting of the gamma-ray spectra, where information as the number of counts, the position of the centroid and the width,…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…