ADAPTIVE BAYESIAN ESTIMATION OF CONDITIONAL DENSITIES
ADAPTIVE BAYESIAN ESTIMATION OF CONDITIONAL DENSITIES
复制标题
条件密度的自适应贝叶斯估计
DOI：
10.1017/s0266466616000220
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发表时间：
2014
影响因子：
0.8
通讯作者：
D. Pati
中科院分区：
文献类型：
--
作者：
Andriy Norets;D. Pati
我们考虑一个条件密度的非参数贝叶斯模型。该模型是一个有限的混合正态分布协变量依赖多项式logit混合概率。混合物组分数的先验是在正整数上指定的。协变量的边缘分布未建模。研究了该模型后验概率的渐近频率论行为。具体来说，我们表明，当真正的条件密度有一定的平滑水平，然后后收缩率周围的真理是等于一个对数因子的频率最小最大估计率。协变量空间是无界的情况下，也建立了一个扩展。由于我们的结果在没有真密度的平滑水平的先验知识的情况下成立，因此所建立的后验收缩率是自适应的。此外，我们表明，在模型中包含不相关的协变量的速度不受影响。在蒙特卡罗模拟中，该模型的一个版本与交叉验证的核条件密度估计相比是有利的。
We consider a nonparametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is specified on positive integers. The marginal distribution of covariates is not modeled. We study asymptotic frequentist behavior of the posterior in this model. Specifically, we show that when the true conditional density has a certain smoothness level, then the posterior contraction rate around the truth is equal up to a log factor to the frequentist minimax rate of estimation. An extension to the case when the covariate space is unbounded is also established. As our result holds without a priori knowledge of the smoothness level of the true density, the established posterior contraction rates are adaptive. Moreover, we show that the rate is not affected by inclusion of irrelevant covariates in the model. In Monte Carlo simulations, a version of the model compares favorably to a cross-validated kernel conditional density estimator.