A test for isotropy of images modeled as stationary or intrinsically stationary random fields on a lattice is developed. The test is based on wavelet theory, and can operate on the horizontal and vertical scale of choice, or on any combination of scales. Scale is introduced through the wavelet variances (sometimes referred to as the wavelet power spectrum), which decompose the variance over ...

Consider the Earth’s global mean surface temperature time series (GMST) as a realization of a stochastic process. Based on a number of studies, a long-range memory (LRM) stochastic process seems to describe the GMST better than a shortrange memory model, such as the AR(1)-process. We want to study the persistence in climate model simulations, to find out if simulated temperature data exhibit the ...

Climate change poses challenges for decision makers across society, not just in preparing for the climate of the future but even when planning for the climate of the present day. When making climate sensitive decisions, policy makers and adaptation planners would benefit from information on local scales and for user-specific quantiles (e.g. the hottest/coldest 5% of days) and thresholds (e.g. ...

The paper explores the hypothesis that the temporal global temperature response can be modeled as a long-range memory (LRM) stochastic process characterized by a Hurst exponent 0.5 < H≲1.0 on time scales from months to decades. The LRM is a mathematical representation of the multitude of response times associated with the various subsystems. By analysis of instrumental and reconstructed temperature ...

The paper proposes an approach to assessment of timescale errors in proxy-based series with chronological uncertainties. The method relies on approximation of the physical process(es) forming a proxy archive by a random Gamma process. Parameters of the process are partly data-driven and partly determined from prior assumptions. For a particular case of a linear accumulation model and absolutely dated ...

Kernel density estimation and kernel regression are useful ways to visualize and assess the structure of data. Using these techniques we define a temporal scale space as the vector space spanned by bandwidth and a temporal variable. In this space significance regions that reflect a significant derivative in the kernel smooth similar to those of SiZer (Significant Zero-crossings of derivatives) are ...

This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by considering constructed covariates. This enables us to use integrated nested Laplace approximation and to considerably speed up the inferential task. In addition, ...

We present several fundamental duality theorems for matroids and more general combinatorial structures. As a special case, these results show that the maximal cardinalities of fixed-ranked sets of a matroid determine the corresponding maximal cardinalities of the dual matroid. Our main results are applied to perfect matroid designs, graphs, transversals, and linear codes over division rings, in each ...

A 2800-yr-long August sea surface temperature (aSST) record based on fossil diatom assemblages is generated from a marine sediment core from the northern subpolar North Atlantic. The record is compared with the aSST record from the Norwegian Sea to explore the variability of the aSST gradient between these areas during the late Holocene. The aSST records demonstrate the opposite climate tendencies ...