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An Introduction to Probabilistic Modeling Pierre Bremaud

An Introduction to Probabilistic Modeling By Pierre Bremaud

An Introduction to Probabilistic Modeling by Pierre Bremaud

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Summary

Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory.

An Introduction to Probabilistic Modeling Summary

An Introduction to Probabilistic Modeling by Pierre Bremaud

Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory.

Table of Contents

1 Basic Concepts and Elementary Models.- 1. The Vocabulary of Probability Theory.- 2. Events and Probability.- 3. Random Variables and Their Distributions.- 4. Conditional Probability and Independence.- 5. Solving Elementary Problems.- 6. Counting and Probability.- 7. Concrete Probability Spaces.- Illustration 1. A Simple Model in Genetics: Mendels Law and HardyWeinbergs Theorem.- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle.- Illustration 3. Bertrands Paradox.- 2 Discrete Probability.- 1. Discrete Random Elements.- 2. Variance and Chebyshevs Inequality.- 3. Generating Functions.- Illustration 4. An Introduction to Population Theory: GaltonWatsons Branching Process.- Illustration 5. Shannons Source Coding Theorem: An Introduction to Information Theory.- 3 Probability Densities.- I. Expectation of Random Variables with a Density.- 2. Expectation of Functionals of Random Vectors.- 3. Independence.- 4. Random Variables That Are Not Discrete and Do Not Have a pd.- Illustration 6. Buffons Needle: A Problem in Random Geometry.- 4 Gauss and Poisson.- 1. Smooth Change of Variables.- 2. Gaussian Vectors.- 3. Poisson Processes.- 4. Gaussian Stochastic Processes.- Illustration 7. An Introduction to Bayesian Decision Theory: Tests of Gaussian Hypotheses.- 5 Convergences.- 1. Almost-Sure Convergence.- 2. Convergence in Law.- 3. The Hierarchy of Convergences.- Illustration 8. A Statistical Procedure: The Chi-Square Test.- Illustration 9. Introduction to Signal Theory: Filtering.- Additional Exercises.- Solutions to Additional Exercises.

Additional information

NPB9780387964607
9780387964607
0387964606
An Introduction to Probabilistic Modeling by Pierre Bremaud
Pierre Bremaud
Undergraduate Texts in Mathematics
New
Hardback
Springer-Verlag New York Inc.
1988-08-01
208
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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