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Information contained in design points of experiments with correlated observations

Andrej Pázman (2010)

Kybernetika

A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected...

Kriging and masurement errors

István Fazekas, Alexander G. Kukush (2005)

Discussiones Mathematicae Probability and Statistics

A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations aremeasured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.

Lévy Processes, Saltatory Foraging, and Superdiffusion

J. F. Burrow, P. D. Baxter, J. W. Pitchford (2008)

Mathematical Modelling of Natural Phenomena

It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...

Moment estimation methods for stationary spatial Cox processes - A comparison

Jiří Dvořák, Michaela Prokešová (2012)

Kybernetika

In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation study in...

Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries

Ludovic Menneteau (2008)

ESAIM: Probability and Statistics

In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided.

On an estimation problem for type I censored spatial Poisson processes

Jan Hurt, Petr Lachout, Dietmar Pfeifer (2001)

Kybernetika

In this paper we consider the problem of estimating the intensity of a spatial homogeneous Poisson process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.

Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution

Wolfgang Kühne, Peter Neumann, Dietrich Stoyan, Helmut Stoyan (1994)

Applicationes Mathematicae

The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical...

Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction

Tomáš Mrkvička, François Goreaud, Joël Chadoeuf (2011)

Kybernetika

We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...

Spatial structure analysis using planar indices.

José Miguel Albert, Jorge Mateu, J. C. Pernías (2000)

Qüestiió

Spatial planar indices have become a useful tool to analyze patterns of points. Despite that, no simulation study has been reported in literature in order to analyze the behaviour of these quantities under different pattern structures. We present here an extensive Monte Carlo simulation study focused on two important indices: the Index of Dispersion and the Index of Cluster Size, usually used to detect lack of homogeneity in a spatial point model. Finally, an application is also presented.

Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference

Blažena Frcalová, Viktor Beneš (2009)

Kybernetika

The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A...

Statistical procedures for spatial point pattern recognition.

Jorge Mateu (2002)

Qüestiió

Spatial structures in the form of point patterns arise in many different contexts, and in most of them the key goal concerns the detection and recognition of the underlying spatial pattern. Particularly interesting is the case of pattern analysis with replicated data in two or more experimental groups. This paper compares design-based and model-based approaches to the analysis of this kind of spatial data. Basic questions about pattern detection concern estimating the properties of the underlying...

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