An Introduction to Probabilistic Modeling
Published on 17. October 2012
Book
Paperback/Softback
XVI, 208 pages
978-1-4612-6996-0 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1988
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Professional/practitioner
Illustrations
XVI, 208 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 13 mm
Weight
353 gr
ISBN-13
978-1-4612-6996-0 (9781461269960)
DOI
10.1007/978-1-4612-1046-7
Schweitzer Classification
Other editions
Additional editions
Pierre Bremaud
An Introduction to Probabilistic Modeling
Book
08/1988
Springer
€71.64
Shipment within 5-7 days
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: 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.