论文标题
基于树的可靠集估计
Tree based credible set estimation
论文作者
论文摘要
随着尺寸变大，估计多元后密度的联合最高后密度可靠设置是具有挑战性的。通常会出现单变量边缘的可靠间隔，以易于计算和可视化。通常有两个近似层，因为我们可能需要计算目标密度的可靠集，而目标密度本身仅是对真实后部密度的近似值。我们获得了由Li等人给出的密度估计树的联合最高后密度可靠集。 （2016年）近似于截断的密度与r^d的紧凑子集，因为这比copula构造更优选。这些树使用由顺序二进制分裂定义的分段常数函数近似于后样品的联合后验分布。我们使用一致的估计器来衡量我们可靠的集合估计与目标密度样本的真实HPD集之间的对称差异。可以计算此质量度量，而无需知道真实集合。我们展示了如何在没有后验样品的双重棘手的情况下估算估计近似目标密度的近似可信集的真实覆盖。我们通过模拟研究说明了我们的方法，并发现我们的估计器与现有方法具有竞争力。
Estimating a joint Highest Posterior Density credible set for a multivariate posterior density is challenging as dimension gets larger. Credible intervals for univariate marginals are usually presented for ease of computation and visualisation. There are often two layers of approximation, as we may need to compute a credible set for a target density which is itself only an approximation to the true posterior density. We obtain joint Highest Posterior Density credible sets for density estimation trees given by Li et al. (2016) approximating a density truncated to a compact subset of R^d as this is preferred to a copula construction. These trees approximate a joint posterior distribution from posterior samples using a piecewise constant function defined by sequential binary splits. We use a consistent estimator to measure of the symmetric difference between our credible set estimate and the true HPD set of the target density samples. This quality measure can be computed without the need to know the true set. We show how the true-posterior-coverage of an approximate credible set estimated for an approximate target density may be estimated in doubly intractable cases where posterior samples are not available. We illustrate our methods with simulation studies and find that our estimator is competitive with existing methods.
