Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants]

Nils Lid Hjort

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arXiv · 2604.20238

Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants]

Nils Lid Hjort

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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.

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Nils Lid Hjort. 2026-04-22. Bayesian approaches to non- and semiparametric density estimation [with a rejoinder to my discussants]. https://arxiv.org/abs/2604.20238

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