Enhances the reasoning skills needed for a valid algorithmic solution and the correct interpretation of computational resultsEncourages skills in algorithmic analysis and implementation that are essential in translating structural properties into equations and computer programsOffers an introduction to experimentation with visualization of stochastic processesEmphasizes the integration of knowledge required to derive recurrence relations or matrix -analytic equations appropriate for numerical implementation, requiring precise probabilistic reasoning and a careful structural analysis of the modelCovers topics including: the recognition of recursive relations and schemes, the numerical solutions of equations, derived probabilities, Markov chains, and computer experimental problems
This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes.
A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.
Table of Contents
Computational Probability: An Introduction
Functions of Random Variables
Discrete-Time Markov Chains
Continuous-Time Markov Chains
Experimentation and Visualization
Appendix 1: Some Topics from Matrix Analysis
Appendix 2: Phase-Type Distibutions
Appendix 3: The Markovian Arrival Process
Solution to Selected Problems