D.6 Numerical methods

This is the area in which most progress in Bayesian statistics has been made in recent years. Although Chapter is devoted to numerical methods, a mere sketch of the basic ideas has been given. Very useful texts with a wealth of examples and full programs in WinBUGS available on an associated website are Congdon (2002, 2005, 2006 and 2010). Those seriously interested in the application of Bayesian methods in the real world should consult Tanner (1993), Gelman et al. (2004), Carlin and Louis (2008), Gilks et al. (1996), French and Smith (1997) and Brooks (1998).

More recently books giving a useful and comprehensible treatment of Bayesian numerical methods using and WinBUGS include Albert (2009) (a particularly attractive treatment), Marin and Robert (2007), Robert and Casella (2010) and Ntzoufras (2009).

At a much lower level, Albert (1994) is a useful treatment of elementary Bayesian ideas using Minitab.