1: Excellent review of simulation techniques at an intermediate level.
According to the books I have consulted by S. M. Ross, I consider him to
be a tremendous author, with this book being my absolute favourite. It
is inspirational, clear, creative and (most of all) fun to read.
Starting off from the very basics regarding probability, random numbers
and generation of random variables, Professor Ross steadily guides the
reader through, for instance, simulation with respect to some queueing
systems, validation techniques (e.g. goodness-of-fit tests;
Kolmogorov-Smirnov tests), the standard MCMC-methods and various variance
reduction techniques. The latter chapter is the one that I found most
enlightening including, for instance, a certainly rewarding section on
importance sampling (weighted simulation). Throughout, a lot of
well-chosen examples enhance students/readers understanding and interest
of the subject.
One might note that this is by no means the most advanced or complete book
on Monte Carlo simulation out there, see e.g.
Monte Carlo Statistical Methods (Springer Texts in Statistics)
or
Stochastic Simulation: Algorithms and Analysis (Stochastic Modelling and Applied Probability),
rather it evolves at an intermediate level covering a few more advanced
concepts as, for example, coupling from the past. But, having this in
mind, this is the book to get. Pure concentrated fun (xiii+274 pages).
Final note: In 2006 the fourth edition was launched. [Simulation, Fourth Edition]
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