论文标题
为一类空间潜在高斯过程模型直接从后分布中生成独立重复
Generating Independent Replicates Directly from the Posterior Distribution for a Class of Spatial Latent Gaussian Process Models
论文作者
论文摘要
马尔可夫链蒙特卡洛（MCMC）允许人们从后部分布中产生依赖的重复，以有效任何贝叶斯分层模型。但是，MCMC可以产生重大的计算负担。这促使我们考虑查找后验分布的表达式，这些表达式在计算上直接从直接获得独立重复。我们专注于广泛的贝叶斯潜在高斯工艺（LGP）模型，这些模型允许空间依赖数据。首先，我们得出了新的分布类别，我们称为广义共轭多变量（GCM）分布。 GCM分布的理论发展与CM分布的理论发展相似，其中有两个主要差异。即，（1）GCM允许进行潜在的高斯过程假设，（2）GCM通过边缘化明确考虑了超参数。需要GCM的开发以直接从具有有效投影/回归形式的确切后验分布中获得独立的重复。因此，我们将我们的方法称为精确的后验回归（EPR）。提供了说明性的示例，包括模拟研究，用于弱固定的空间过程和空间基函数扩展。提出了对有条件自回旋模型的美国人口普查局美国社区调查（ACS）的贫困发生率数据的附加分析。
Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to consider finding expressions of the posterior distribution that are computationally straightforward to obtain independent replicates from directly. We focus on a broad class of Bayesian latent Gaussian process (LGP) models that allow for spatially dependent data. First, we derive a new class of distributions we refer to as the generalized conjugate multivariate (GCM) distribution. The GCM distribution's theoretical development is similar to that of the CM distribution with two main differences; namely, (1) the GCM allows for latent Gaussian process assumptions, and (2) the GCM explicitly accounts for hyperparameters through marginalization. The development of GCM is needed to obtain independent replicates directly from the exact posterior distribution, which has an efficient projection/regression form. Hence, we refer to our method as Exact Posterior Regression (EPR). Illustrative examples are provided including simulation studies for weakly stationary spatial processes and spatial basis function expansions. An additional analysis of poverty incidence data from the U.S. Census Bureau's American Community Survey (ACS) using a conditional autoregressive model is presented.
