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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...

Steady state and scaling limit for a traffic congestion model

Ilie Grigorescu, Min Kang (2010)

ESAIM: Probability and Statistics

In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...

Stein’s method in high dimensions with applications

Adrian Röllin (2013)

Annales de l'I.H.P. Probabilités et statistiques

Let h be a three times partially differentiable function on ℝ n , let X = ( X 1 , ... , X n ) be a collection of real-valued random variables and let Z = ( Z 1 , ... , Z n ) be a multivariate Gaussian vector. In this article, we develop Stein’s method to give error bounds on the difference 𝔼 h ( X ) - 𝔼 h ( Z ) in cases where the coordinates of X are not necessarily independent, focusing on the high dimensional case n → ∞ . In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy,...

Stereology of dihedral angles

Vratislav Horálek (2000)

Applications of Mathematics

The paper presents a short survey of stereological problems concerning dihedral angles, their solutions and applications, and introduces a graph for determining the distribution functions of planar angles under the hypothesis that dihedral angles in ℝ 3 are of the same size and create a random field.

Stereology of extremes; size of spheroids

Daniel Hlubinka (2003)

Mathematica Bohemica

The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of appropriate...

Stereology of grain boundary precipitates

Vratislav Horálek (1989)

Aplikace matematiky

Precipitates modelled by rotary symmetrical lens-shaped discs are situated on matrix grain boundaries and the homogeneous specimen is intersected by a plate section. The stereological model presented enables one to express all basic parameters of spatial structure and moments of the corresponding probability distributions of quantitative characteristics of precipitates in terms of planar structure parameters the values of which can be estimated from measurements carried out in the plane section....

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