Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials

Ding Jianhua; Zhang Zhongzhan

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Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials

机译：形状受限伯恩斯坦多项式的非参数混合效应模型的贝叶斯回归

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摘要

We develop a Bayesian estimation method to non-parametric mixed-effect models under shape-constrains. The approach uses a hierarchical Bayesian framework and characterizations of shape-constrained Bernstein polynomials (BPs). We employ Markov chain Monte Carlo methods for model fitting, using a truncated normal distribution as the prior for the coefficients of BPs to ensure the desired shape constraints. The small sample properties of the Bayesian shape-constrained estimators across a range of functions are provided via simulation studies. Two real data analysis are given to illustrate the application of the proposed method.

机译：我们针对形状约束下的非参数混合效应模型开发了贝叶斯估计方法。该方法使用分层贝叶斯框架和形状受限伯恩斯坦多项式（BPs）的特征。我们采用马尔可夫链蒙特卡罗方法进行模型拟合，使用截断正态分布作为BP系数的先验值，以确保所需的形状约束。通过模拟研究提供了一系列函数中的贝叶斯形状约束估计量的小样本属性。两次实际数据分析说明了该方法的应用。

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来源
《Journal of applied statistics》 |2016年第16期|2524-2537|共14页
作者
Ding Jianhua; Zhang Zhongzhan;
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Shanxi Datong Univ, Dept Stat, Datong, Peoples R China;

Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China;

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正文语种 eng
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关键词
Bernstein polynomials; shape constrains; truncated normal distribution; Markov chainMonte Carlo sampler;

机译：Bernstein多项式形状约束截断正态分布马尔可夫链蒙特卡洛采样器;

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3. Comparison of nonlinear mixed-effect and non-parametric expectation maximisation modelling for Bayesian estimation of carboplatin clearance in children. [J] . Patoux A, Bleyzac N, Boddy AV, European journal of clinical pharmacology . 2001,第4期

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5. Bayesian Noninferiority Testing and Nonparametric Survival Regression using Bernstein Polynomials. [D] . Osman, Muhtarjan. 2011

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6. Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration with an application to alcohol and mortality [O] . Christen M. Gray, Raymond J. Carroll, Marleen A. H. Lentjes, -1

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8. Analysis of Bayesian Inference for Non-Parametric Regression [R] . Cox, D. D. 1986

机译：非参数回归的贝叶斯推断分析

Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials

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