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AuthorBrรฉmaud, Pierre. author
TitleAn Introduction to Probabilistic Modeling [electronic resource] / by Pierre Brรฉmaud
ImprintNew York, NY : Springer New York : Imprint: Springer, 1988
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1046-7
Descript XVI, 208 p. online resource

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


CONTENT

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: Mendelโ{128}{153}s Law and Hardyโ{128}{148}Weinbergโ{128}{153}s Theorem -- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle -- Illustration 3. Bertrandโ{128}{153}s Paradox -- 2 Discrete Probability -- 1. Discrete Random Elements -- 2. Variance and Chebyshevโ{128}{153}s Inequality -- 3. Generating Functions -- Illustration 4. An Introduction to Population Theory: Galtonโ{128}{148}Watsonโ{128}{153}s Branching Process -- Illustration 5. Shannonโ{128}{153}s 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. Buffonโ{128}{153}s 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


Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes



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