Pierre Bremaud

An Introduction to Probabilistic Modeling (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 208
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461210467
• Artikelnr.: 43993021

Inhaltsangabe

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.