This is the first chapter specifically about simulation techniques, even though some prin-

ciples have already been discussed. Simulation work in applied statistics replaces analytical

work on behalf of the researcher with repetitious, low-level effort by the computer. The key

advantage is that when a model specification leads to a posterior form that is difficult or

impossible to manipulate analytically, then it is often possible to create a set of simulated

values that share the same distributional properties. So we describe the posterior by using

empirical summaries of these simulated values rather than perform some uncomfortable

integration or other operation. This is actually an old idea (see the really interesting 1951

chronicle: “Report on a Monte Carlo Calculation Performed with the Eniac,” by Mayer),

but one that is particularly easy to implement now that computers are ubiquitous and fast

(and getting more so every day). Excellent references in addition to those specifically cited

in this chapter include: Fang, Hickernell, and Niederreiter (2002), Fishman (2003), Lange

(2000), Rubinstein (1981), and Sobol (1994).