This article discusses Bayesian nonparametric models, arguing that all Bayesians are constructing probability distributions (the prior) on spaces of density functions. The parametric Bayesian can be seen to be making restrictive assumptions about the choice of density for modelling data. In contrast, the nonparametric Bayesian constructs a probability distribution on as many densities as possible. The model is infinite dimensional, yet inference is possible, including density estimation and the implementation of decision rules, such as the maximization of expected utility. An example of a nonparametric model is given and a means by which to make inference provided by simulation techniques.
KeywordsBayesian nonparametrics Density functions Expected utility Latent variables Likelihood Markov chain Monte Carlo methods Parametric models Probability distribution Statistical inference Uncertainty
- Escobar, M.D. 1988. Estimating the means of several normal populations by nonparametric estimation of the distribution of the means. Ph.D. thesis, Department of Statistics, Yale University.Google Scholar
- Lindley, D.V. 1978. The Bayesian approach (with discussion). Scandinavian Journal of Statistics 5: 1–26.Google Scholar
- Lindsey, J.K. 1999. Some statistical heresies. The Statistician 48: 1–40.Google Scholar
- Smith, A.F.M., and G.O. Roberts. 1993. Bayesian computations via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B 55: 3–23.Google Scholar