D.2 Nonparametric methods

Throughout this book, it is assumed that the data we are analyzing comes from some parametric family, so that the density p(x|θ) of any observation x depends on one or more parameters θ (e.g. x is normal of mean θ and known variance). In classical statistics, much attention has been devoted to developing methods which do not make any such assumption, so that you can, for example, say something about the median of a set of observations without assuming that they come from a normal distribution. Some attempts have been made to develop a Bayesian form of nonparametric theory, though this is not easy as it involves setting up a prior distribution over a very large class of densities for the observations. Useful references are Ferguson (1973), Florens et al. (1983), Dalal (1980), Hill (1988), Lenk (1991), Ghosh and Ramamoorthi (2003) and Hjort et al. (2010). A brief account is given by Müller and Quintana (2004).