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Field name	Details
Dewey Class	519.2
Title	An Introduction to Probabilistic Modeling ([EBook] /) / by Pierre Brémaud.
Author	Brémaud, Pierre
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York : : Imprint: Springer, , 1988.
Physical Details	XVI, 208 p. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9781461210467
Summary Note	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.:
Contents note	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: Mendel’s Law and Hardy—Weinberg’s Theorem -- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle -- Illustration 3. Bertrand’s Paradox -- 2 Discrete Probability -- 1. Discrete Random Elements -- 2. Variance and Chebyshev’s Inequality -- 3. Generating Functions -- Illustration 4. An Introduction to Population Theory: Galton—Watson’s Branching Process -- Illustration 5. Shannon’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. Buffon’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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-1046-7
Links to Related Works	Subject References: Mathematics . Probabilities . Probability theory and stochastic processes . Authors: Brémaud, Pierre . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 519.2 .

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An Introduction to Probabilistic Modeling

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