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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 ...
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 ...
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 ).
2 Examples. 3 Uniqueness. 4 Literature. Toggle the table of contents. Simple point process. ... A simple point process is a special type of point process in ...
Point processes have a number of interpretations, which is reflected by the various types of point process notation. [4] [9] For example, if a point belongs to or is a member of a point process, denoted by , then this can be written as: [4], and represents the point process being interpreted as a random set.
Point Processes is a book on the mathematics of point processes, randomly located sets of points on the real line or in other geometric spaces. It was written by David Cox and Valerie Isham , and published in 1980 by Chapman & Hall in their Monographs on Applied Probability and Statistics book series.
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.
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 ...