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A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
Measures of local and global spatial association are key tools for exploratory spatial data analysis. Many such measures exist including Moran's $I$, Geary's $C$, and the Getis-Ord $G$ and $G^*$ statistics. A parametric approach to testing…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
In low-level video analyses, effective representations are important to derive the correspondences between video frames. These representations have been learned in a self-supervised fashion from unlabeled images or videos, using carefully…
In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation…
Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some…
Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of…
Class-imbalance is an inherent characteristic of multi-label data which affects the prediction accuracy of most multi-label learning methods. One efficient strategy to deal with this problem is to employ resampling techniques before…
Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion…
Astronomers often deal with data where the covariates and the dependent variable are measured with heteroscedastic non-Gaussian error. For instance, while TESS and Kepler datasets provide a wealth of information, addressing the challenges…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range,…
Machine learning is gaining popularity in a broad range of areas working with geographic data, such as ecology or atmospheric sciences. Here, data often exhibit spatial effects, which can be difficult to learn for neural networks. In this…
Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency…
Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…
Astronomical observations, physical experiments as well as computer simulations often involve discrete data sets supposed to represent a fair sample of an underlying smooth and continuous field. Reconstructing the underlying fields from a…
We consider a high-dimensional model in which variables are observed over time and space. The model consists of a spatio-temporal regression containing a time lag and a spatial lag of the dependent variable. Unlike classical spatial…
Integral field spectroscopy can map astronomical objects spatially and spectroscopically. Due to instrumental and atmospheric effects, it is common for integral field instruments to yield a sampling of the sky image that is both irregular…