Gaussian approximation of general non-parametric posterior distributions
Gaussian approximation of general non-parametric posterior distributions
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一般非参数后验分布的高斯近似
DOI：
10.1093/imaiai/iax017
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Cheng, Guang
中科院分区：
文献类型：
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作者：
Shang, Zuofeng;Cheng, Guang
在一般的贝叶斯非参数模型中，我们证明了后验分布可以用高斯过程（GP）渐近近似。我们的结果适用于非参数指数族，其中包含高斯和非高斯回归，也适用于有效（根）和无效（非根）估计。我们的一般逼近定理不依赖于后共轭，并可以在一类GP先验，具有平滑样条解释验证。特别是，限制后验测度成为先验自由下的贝叶斯版本的“下平滑”条件。最后，我们应用我们的近似定理来研究贝叶斯过程的渐近频率论性质，如可信区域和可信区间。
In a general class of Bayesian non-parametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process (GP). Our results apply to non-parametric exponential family that contains both Gaussian and non-Gaussian regression and also hold for both efficient (root-) and inefficient (non-root-) estimations. Our general approximation theorem does not rely on posterior conjugacy and can be verified in a class of GP priors that has a smoothing spline interpretation. In particular, the limiting posterior measure becomes prior free under a Bayesian version of ‘under-smoothing’ condition. Finally, we apply our approximation theorem to examine the asymptotic frequentist properties of Bayesian procedures such as credible regions and credible intervals.