Adaptive Bayesian procedures using random series prior
Adaptive Bayesian procedures using random series prior
复制标题
使用随机序列先验的自适应贝叶斯过程
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Ghosal
中科院分区：
文献类型：
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作者：
Weining Shen;S. Ghosal
我们考虑非参数贝叶斯估计的先验，它使用具有随机项数的有限随机序列。先验是通过基函数数量和相关系数的分布构建的。通过构建适当的“筛子”并应用后验收敛率的一般理论，我们得出了真实模型中函数的所有平滑度级别的自适应后验收敛率的一般结果。我们将此一般结果应用于几个统计问题，例如信号处理、密度估计、各种非参数回归、分类、谱密度估计、函数回归等。先验可以被视为常用高斯过程先验的替代方案，但后验分布的属性可以通过相对更简单的技术进行分析，并且在许多情况下允许更简单的计算方法，而无需使用马尔可夫链蒙特卡罗（MCMC）方法。仿真研究表明，基于随机序列先验的贝叶斯估计量与高斯过程先验的贝叶斯估计量具有可比性。我们将该方法应用于两个有趣的函数回归数据集。
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We derive a general result on adaptive posterior convergence rates for all smoothness levels of the function in the true model by constructing an appropriate “sieve” and applying the general theory of posterior convergence rates. We apply this general result on several statistical problems such as signal processing, density estimation, various nonparametric regressions, classification, spectral density estimation, functional regression etc. The prior can be viewed as an alternative to the commonly used Gaussian process prior, but properties of the posterior distribution can be analyzed by relatively simpler techniques and in many cases allows a simpler approach to computation without using Markov chain Monte-Carlo (MCMC) methods. A simulation study is conducted to show that the accuracy of the Bayesian estimators based on the random series prior and the Gaussian process prior are comparable. We apply the method on two interesting data sets on functional regression.
影响因子：
1.1
作者：
Goldsmith J;Wand MP;Crainiceanu C
通讯作者：
Crainiceanu C