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Probability mass function

About: Probability mass function is a research topic. Over the lifetime, 2853 publications have been published within this topic receiving 101710 citations. The topic is also known as: pmf.


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Journal ArticleDOI
TL;DR: In this article, the authors show that the median probability model is often the optimal predictive model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model.
Abstract: Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is the model with highest posterior probability, but this is not necessarily the case. In this paper we show that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model. The median probability model often differs from the highest probability model.

881 citations

Journal ArticleDOI
TL;DR: In this paper, the operation of a cumulative sum control scheme is regarded as forming a Markov chain and the transition probability matrix for this chain is obtained and then the properties of this matrix used to determine not only the average run lengths for the scheme, but also moments and percentage points of the run-length distribution and exact probabilities of run length.
Abstract: The classical method of studying a cumulative sum control scheme of the decision interval type has been to regard the scheme as a sequence of sequential tests, to determine the average sample number for these component tests and hence to study the average run length for the scheme. A different approach in which the operation of the scheme is regarded as forming a Markov chain is set out. The transition probability matrix for this chain is obtained and then the properties of this matrix used to determine not only the average run lengths for the scheme, but also moments and percentage points of the run-length distribution and exact probabilities of run length. The method may be used with any discrete distribution and also, as ani accurate approximation, with any continuous distribution for the random variable which is to be controlled. Examples are given for the cases of a Poisson random variable and a normal random variable.

851 citations

Journal ArticleDOI
TL;DR: Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately for convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P.
Abstract: We consider convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P, i.e., finitely many scenarios. The behaviour of such stochastic programs is stable with respect to perturbations of P measured in terms of a Fortet-Mourier probability metric. The problem of optimal scenario reduction consists in determining a probability measure that is supported by a subset of supp P of prescribed cardinality and is closest to P in terms of such a probability metric. Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately. Compared to earlier versions, the computational performance (accuracy, running time) of the new algorithms has been improved considerably. Numerical experience is reported for different instances of scenario trees with computable optimal lower bounds. The test examples also include a ternary scenario tree representing the weekly electrical load process in a power management model.

851 citations

Book ChapterDOI
01 Jan 2002
TL;DR: In this paper, the authors extend the definition of coherent risk measures to general probability spaces and show how to define such measures on the space of all random variables, and give examples that relate the theory of coherent risks to game theory and to distorted probability measures.
Abstract: We extend the definition of coherent risk measures, as introduced by Artzner, Delbaen, Eber and Heath, to general probability spaces and we show how to define such measures on the space of all random variables. We also give examples that relates the theory of coherent risk measures to game theory and to distorted probability measures. The mathematics are based on the characterisation of closed convex sets Pσ of probability measures that satisfy the property that every random variable is integrable for at least one probability measure in the set Pσ.

835 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202311
202227
202161
202088
201991
201870