## Bayesian nonparametric methods for data from a unimodal density.(English)Zbl 0806.62038

Summary: A strongly unimodal density with mode $$\theta$$ is one that is non- decreasing on $$(-\infty, \theta)$$ and non-increasing on $$(\theta, \infty)$$. L. J. Brunner and A. Y. Lo [Ann. Stat. 17, No. 4, 1550-1566 (1989; Zbl 0697.62003)] have described Bayesian procedures for sampling from a unimodal density, assuming only that it is symmetric about an unknown mode $$\theta$$. Here, the case where the unimodal density need not be symmetric is considered. The unimodal density is first written as a mixture with mixing distribution $$G$$. Placing a Dirichlet process prior on the unknown mixing distribution $$G$$ and an arbitrary prior on the unknown model $$\theta$$, the posterior distribution of the pair $$(\theta, G)$$ is obtained; the marginal posterior distribution of $$\theta$$ and the posterior expectation of $$G$$ are expressed in terms of sums over partitions of the set of integers $$\{1,\dots, n\}$$.

### MSC:

 62G99 Nonparametric inference 62C10 Bayesian problems; characterization of Bayes procedures

Zbl 0697.62003
Full Text:

### References:

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