Related papers: Introduction to Geodetic Time Series Analysis

This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…

Atmospheric processes involve both space and time. This is why human analysis of atmospheric imagery can often extract more information from animated loops of image sequences than from individual images. Automating such an analysis requires…

Learning is a fundamental characteristic of living systems, enabling them to comprehend their environments and make informed decisions. These decision-making processes are inherently influenced by available information about their…

In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt…

We present here a general framework and a specific algorithm for predicting the destination, route, or more generally a pattern, of an ongoing journey, building on the recent work of [Y. Lassoued, J. Monteil, Y. Gu, G. Russo, R. Shorten,…

Time Series forecasting is critical in diverse domains such as weather forecasting, financial investment, and traffic management. While traditional numerical metrics like mean squared error (MSE) can quantify point-wise accuracy, they fail…

This paper derives practical algorithms, based on Bayesian inference methods, for several data analysis problems common in time series analysis of astronomical and other data. One problem is the determination of the lag between two time…

Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…

Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. Due to their multidimensional nature, time series often need to be embedded into a fixed-dimensional feature space to…

In recent years, spatio-temporal graph neural networks (GNNs) have attracted considerable interest in the field of time series analysis, due to their ability to capture, at once, dependencies among variables and across time points. The…

This paper introduces a novel two-dimensional (2D) time series forecasting model that integrates cohort behavior over time, addressing challenges in small data environments. We demonstrate its efficacy using multiple real-world datasets,…

Bayesian methods are increasingly being applied to parameterize mechanistic process models used in environmental prediction and forecasting. In particular, models describing ecosystem dynamics with multiple states that are linear and…

The purpose of this paper is to give an overview of the time series forecasting problem based on similarity of trajectories. Various methodologies are introduced and studied, and detailed discussions on hyperparameter optimization, outlier…

With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…

Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which,…

Geological process models simulate a range of dynamic processes to evolve a base topography into a final 2D cross-section or 3D geological scenario. In principle, process parameters may be updated to better align with observed geophysical…

In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition…

Learning time-series models is useful for many applications, such as simulation and forecasting. In this study, we consider the problem of actively learning time-series models while taking given safety constraints into account. For…

We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version…