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:
“Novels as dull as dishwater, with the grease of random sentiments floating on top.”
—Italo Calvino (1923–1985)
“I often used to think myself in the case of the fox-hunter, who, when he had toiled and sweated all day in the chase as if some unheard-of blessing was to crown his success, finds at last all he has got by his labor is a stinking nauseous animal. But my condition was yet worse than his; for he leaves the loathsome wretch to be torn by his hounds, whilst I was obliged to fondle mine, and meanly pretend him to be the object of my love.”
—Sarah Fielding (1710–1768)