Random Object
What is meant by a random object? A complete answer to this question requires the theory of random closed sets, which makes contact with advanced concepts from measure theory. The key idea is to focus on the probabilities of the given random closed set hitting specified test sets. There arise questions of inference (for example, estimate the set which encloses a given point pattern) and theories of generalizations of means etc. to apply to random sets. Connections are now being made between this latter work and recent developments in geometric mathematical analysis concerning general metric spaces and their geometry. Good parametrizations of specific random sets can allow us to refer random object processes to the theory of marked point processes; object-point pairs are viewed as points in a larger product space formed as the product of the original space and the space of parametrization.
Read more about this topic: Stochastic Geometry
Famous quotes containing the words random and/or object:
“... the random talk of people who have no chance of immortality and thus can speak their minds out has a setting, often, of lights, streets, houses, human beings, beautiful or grotesque, which will weave itself into the moment for ever.”
—Virginia Woolf (1882–1941)
“If the heart beguiles itself in its choice [of a wife], and imagination will give excellencies which are not the portion of flesh and blood:Mwhen the dream is over, and we awake in the morning, it matters little whether ‘tis Rachael or Leah,—be the object what it will, as it must be on the earthly side ... of perfection,—it will fall short of the work of fancy, whose existence is in the clouds.”
—Laurence Sterne (1713–1768)