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The simplest and most ubiquitous example of a point process is the Poisson point process, which is a spatial generalisation of the Poisson process. A Poisson (counting) process on the line can be characterised by two properties : the number of points (or events) in disjoint intervals are independent and have a Poisson distribution. A Poisson ...
The thinning operation entails using some predefined rule to remove points from a point process to form a new point process .These thinning rules may be deterministic, that is, not random, which is the case for one of the simplest rules known as -thinning: [1] each point of is independently removed (or kept) with some probability (or ).
A point process is often denoted by a single letter, [1] [7] [8] for example , and if the point process is considered as a random set, then the corresponding notation: [1], is used to denote that a random point is an element of (or belongs to) the point process . The theory of random sets can be applied to point processes owing to this ...
A visual depiction of a Poisson point process starting. In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
A simple point process is a special type of point process in probability theory. In simple point processes, every point is assigned the weight one. In simple point processes, every point is assigned the weight one.
In mathematics, a determinantal point process is a stochastic point process, the probability distribution of which is characterized as a determinant of some function. They are suited for modelling global negative correlations, and for efficient algorithms of sampling, marginalization, conditioning, and other inference tasks.
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In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.