相关论文: Substationarity in Spatial Point Processes

In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical…

We focus our attention on dynamical processes characterized by an entropic index Q<1. According to the probabilistic arguments of Tsallis and Bukman [C.Tsallis, D.J. Bukman, Phys. Rev. E 54,R2197 (1996)] these processes are subdiffusional…

In a newly introduced time scale $\tau$, much smaller than the usual $t$, any object is assumed to be a point-like particle, having a definite position. It fluctuates without dynamics and the wave function $\Psi$ is defined by averaging the…

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and…

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism…

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…

Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to…

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the…

We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…

Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate…

Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…

We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…

In this note we consider non-stationary cluster point processes and we derive their conditional intensity, i.e. the intensity of the process given the locations of one or more events of the process. We then provide some approximations of…

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity…

Literatures in state space models focus on parametric inference and prediction, which fail if the state space model is not fully specified and the maximum likelihood estimation does not work. In this paper, we assume the state transition…