Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.
• Clear and accessible introduction to algorithmic applications of Markov chains • Relevant to computer scientists as well as mathematicians
1. Basics of probability theory; 2. Markov chains; 3. Computer simulation of Markov chains; 4. Irreducible and aperiodic Markov chains; 5. Stationary distributions; 6. Reversible Markov chains; 7. Markov chain Monte Carlo; 8. Fast convergence of MCMC algorithms; 9. Approximate counting; 10. Propp-Wilson algorithm; 11. Sandwiching; 12. Propp-Wilson with read once randomness; 13. Simulated annealing; 14. Further reading.
'Has climbing up onto the MCMC juggernaut seemed to require just too much effort? This delightful little monograph provides an effortless way in. The chapters are bite-sized with helpful, do-able exercises (by virtue of strategically placed hints) that complement the text.' Publication of the International Statistical Institute
'… a very nice introduction to the modern theory of Markov chain simulation algorithms.' R. E. Maiboroda, Zentralblatt MATH
' … extremely elegant. I am sure that students will find great pleasure in using the book - and that teachers will have the same pleasure in using it to prepare a course on the subject.' Mathematics of Computation
'This elegant little book is a beautiful introduction to the theory of simulation algorithms, using (discrete) Markov chains (on finite state spaces) … highly recommended to anyone interested in the theory of Markov chain simulation algorithms.' Nieuw Archief voor Wiskunde