Bayesian nonparametric modeling using mixtures of triangular distributions
Bayesian nonparametric modeling using mixtures of triangular distributions
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DOI：
10.1111/j.0006-341x.2001.00518.x
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发表时间：
2001-06-01
期刊：
影响因子：
1.9
通讯作者：
Mengersen, K
中科院分区：
文献类型：
--
作者：
Perron, F;Mengersen, K
非参数建模是许多应用中不可或缺的工具，其在分层贝叶斯环境中的表述，使用整个后验分布而不是特定期望，增加了其灵活性。在本文中，重点是通过混合三角分布进行非参数估计。讨论了该方法的最优性，并推导了该近似精度的界限。尽管我们的方法应用更广泛，但为了简单起见，我们重点关注[0, 1]上具有加性误差的单调非递减回归的估计，通过具有分段线性导数的函数有效地逼近感兴趣的函数。通过现有马尔可夫链蒙特卡罗算法的合并来描述可计算的估计方法。模拟和示例说明了该方法。
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.