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:
“And catch the gleaming of a random light,
That tells me that the ship I seek is passing, passing.”
—Paul Laurence Dunbar (1872–1906)
“The great object of Education should be commensurate with the object of life. It should be a moral one; to teach self-trust: to inspire the youthful man with an interest in himself; with a curiosity touching his own nature; to acquaint him with the resources of his mind, and to teach him that there is all his strength, and to inflame him with a piety towards the Grand Mind in which he lives. Thus would education conspire with the Divine Providence.”
—Ralph Waldo Emerson (1803–1882)