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MARC 21

An Introduction to Probabilistic Modeling
Tag	Description
020	$a9781461210467$9978-1-4612-1046-7
082	$a519.2$223
099	$aOnline resource: Springer
100	$aBrémaud, Pierre.
245	$aAn Introduction to Probabilistic Modeling$h[EBook] /$cby Pierre Brémaud.
260	$aNew York, NY :$bSpringer New York :$bImprint: Springer,$c1988.
300	$aXVI, 208 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aUndergraduate Texts in Mathematics,$x0172-6056
505	$a1 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.
520	$aIntroduction 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aUndergraduate Texts in Mathematics,$x0172-6056
856	$uhttp://dx.doi.org/10.1007/978-1-4612-1046-7