Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants]
Abstract
This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model. We look at cases where the nonparametric part of the construction is a Dirichlet process or relatives thereof. (2) Express the density as an additive expansion of orthogonal basis functions, and place priors on the coefficients. Here attention is given to a certain robust Hermite expansion around the normal distribution. Multiplicative expansions are also considered. (3) Express the unknown density as locally being of a certain parametric form, then construct suitable local likelihood functions to express information content, and place local priors on the local parameters.
Keywords
Cite
@article{arxiv.2604.20238,
title = {Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants]},
author = {Nils Lid Hjort},
journal= {arXiv preprint arXiv:2604.20238},
year = {2026}
}
Comments
29 pages, no figures. Statistical Research Report, Department of Mathematics, University of Oslo, 1995; invited discussion paper for the Fifth Valencia Meeting on Bayesian Statistics. Published version in "Bayesian Statistics" (1995, eds. J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F. Smith), Proceedings of the Fifth Valencia International Meeting (vol. 5), 223-254