Titlebook: Computational Probability; Algorithms and Appli John H. Drew,Diane L. Evans,Lawrence M. Leemis Book 2017Latest edition Springer Internation

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Bayesian ApplicationsThis chapter considers Bayesian applications of APPL. Section?14.1 introduces Bayesian statistics and motivates the use of a computer algebra system to derive posterior distributions. Section?14.2 develops algorithms in the case of a single unknown parameter. Section?14.3 develops algorithms in the case of multiple unknown parameters.

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Other ApplicationsThis chapter contains miscellaneous computational probability applications. Section?. concerns algorithms for calculating the probability distribution of the longest path of a series-parallel stochastic activity network with continuous activity durations.

Conspiracy

Data Structures and Simple Algorithmsy are defined with a somewhat simpler data structure than that for discrete random variables. The development described here gives a probabilist the ability to automate the instantiation and processing of continuous random variables—key elements of computational probability.

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Transformations of Random Variablesheorem from Casella and Berger [16] for many–to–1 transformations, we consider more general univariate transformations. Specifically, the transformation can range from 1–to–1 to many–to–1 on various subsets of the support of the random variable of interest. We also present an implementation of the theorem in APPL and present four examples.

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Data Structures and Simple Algorithmsdiscrete random variables. The first section will show that the nature of the support of discrete random variables makes the data structures required much more complicated than for continuous random variables.

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