Bayesian nonparametric modeling using mixtures of triangular distributions.

F Perron; K Mengersen

doi:10.1111/j.0006-341x.2001.00518.x

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PubMed · 11414578

Bayesian nonparametric modeling using mixtures of triangular distributions.

F Perron·K Mengersen

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Abstract

Nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical Bayesian context, using the entire posterior distribution rather than particular expectations, increases its flexibility. In this article, the focus is on nonparametric estimation through a mixture of triangular distributions. The optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived. Although our approach is more widely applicable, we focus for simplicity on estimation of a monotone nondecreasing regression on [0, 1] with additive error, effectively approximating the function of interest by a function having a piecewise linear derivative. Computationally accessible methods of estimation are described through an amalgamation of existing Markov chain Monte Carlo algorithms. Simulations and examples illustrate the approach.

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Algorithms Bayes Theorem Models, Statistical Statistics, Nonparametric Journal Article Research Support, Non-U.S. Gov't

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F Perron, K Mengersen. 2001. Bayesian nonparametric modeling using mixtures of triangular distributions.. https://doi.org/10.1111/j.0006-341x.2001.00518.x

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