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Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions
Author(s) -
Perron F.,
Mengersen K.
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00518.x
Subject(s) - markov chain monte carlo , nonparametric statistics , computer science , bayesian probability , context (archaeology) , mathematical optimization , mathematics , parametric statistics , markov chain , piecewise , nonparametric regression , algorithm , focus (optics) , flexibility (engineering) , machine learning , econometrics , statistics , artificial intelligence , paleontology , mathematical analysis , physics , optics , biology
Summary. 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.