Credal Set
In mathematics, a credal set is a set of probability distributions or, more generally, a set of (possibly only finitely additive) probability measures. A credal set is often assumed or constructed to be a closed convex set. It is intended to express uncertainty or doubt about the probability model that should be used, or to convey the beliefs of a Bayesian agent about the possible states of the world.Cozman, Fabio (1999)Theory of Sets of Probabilities (and related models) in a Nutshell. If a credal set K(X) is closed and convex, then, by the Krein–Milman theorem, it can be equivalently described by its extreme points \mathrm (X)/math>. In that case, the expectation for a function f of X with respect to the credal set K(X) forms a closed interval .html" ;"title="underline[f">underline[f\overline[f, whose lower bound is called the lower prevision of f, and whose upper bound is called the upper prevision of f: :\underline \min_ \int f \, d\mu=\min_ \int f \, d\mu where \mu deno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Probability Distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |