Robert og Casella: Monte Carlo Statistical Methods, 2004. Springer. ISBN:?0-387-21239-6.
General comments about the book:
The book contain both presentation of methods for doing Monte Carlo and discussion on theoretical properties of the methods. We will in this course consentrate on presentation of methods, and not go through all the details in the mathematical theory.
Preliminary syllabus:
Ch 1: Mainly motivation for the rest of the book
Ch 2: 2.1-2.3 (sketchy)
Ch 3: 3.1, 3.2 (not example 3.14) and 3.4
Ch 4: 4.2 and 4.4
Ch 6: Only the main results as given in the note "Markov chian Theory - essentials".
Ch 7: 7.1, 7.2, 7.3.1, 7.3.2 (not the proof of the results, but you should understand the main content of the results), 7.4.1 (not the proof of Th 7.8, not example 7.12), 7.5 (until Th 7.15)
Ch 9: 9.1 (only 9.1.2), 9.2 (only 9.2.1)
Ch 10: 10.1 (not 10.1.2 nor 10.1.3), 10.2.1 (only Th 10.6 and its proof), 10.2.2
Ch 12: 12.1, 12.2.1, 12.2.2, 12.3.1, 12.3.4
Ch 14: 14.1, 14.2, 14.3 (14.3.1-14.3-4)
All given exercises,
Geir Storvik: Markov chain theory - essentials, 2009. This is a note containing the main theory needed from chapter 6 in the textbook. pdf-file.
The paper by Chib and Greenberg (1995) is not part of the syllabus but might be a usefull supplement regarding the Metropolis-Hastings algorithm.
The paper by Casella and George (1992) is not part of the syllabus but might be a usefull supplement regarding the Gibbs sampler