论文标题
潜在因子模型中协方差矩阵的结构化先验分布
Structured prior distributions for the covariance matrix in latent factor models
论文作者
论文摘要
因子模型广泛用于缩小多元数据的分析。这是通过将P X P协方差矩阵分解为两个组成部分的总和来实现的。通过潜在因子表示，它们可以解释为特质方差的对角矩阵和共享变体矩阵，即P X K因子载荷矩阵及其转置的乘积。如果k << p，则定义了协方差矩阵的简约分解。从历史上看，几乎没有关注将先前的信息纳入贝叶斯分析中的因子模型，充其量是因子负载的先验是订单不变的。在这项工作中，开发了一类结构化的先验，可以编码有关共享变体矩阵的依赖性结构的想法。该构建允许数据信息收缩到明智的参数结构，同时还促进了对因子数量的推断。利用固定矢量自动加工的不受约束的重新聚集化，该方法扩展到固定动态因子模型。对于计算推断，提出了参数扩展的Markov链蒙特卡洛采样器，包括有效的自适应Gibbs采样器。两个实质性应用程序展示了该方法的范围及其推理益处。
Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p x k factor loadings matrix and its transpose. If k << p, this defines a parsimonious factorisation of the covariance matrix. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings is order invariant. In this work, a class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures while also facilitating inference over the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Two substantive applications showcase the scope of the methodology and its inferential benefits.
