The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.

中文翻译：

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无限分解的贝叶斯累积收缩

在依赖分解的各种模型中，参数空间的维度通常是未知的。例如，在因子分析中，潜在因子的数量是未知的，必须从数据中推断出来。尽管经典的收缩先验在这种情况下很有用，但增加收缩先验可以提供一种更有效的方法，该方法逐渐惩罚复杂性增加的扩展。在本文中，我们提出了一种新的增加收缩先验，称为累积收缩过程，用于控制过完备公式中的尺寸的参数。我们的构造具有广泛的适用性，并且基于可解释的尖峰和板坯分布序列，随着模型复杂性的增加，尖峰分布的质量也随之增加。以因子分析为例，我们表明，与当前的竞争对手相比，该公式具有理论和实践优势，包括提高了恢复模型维度的能力。提出了一种自适应马尔可夫链蒙特卡罗算法，并在模拟和个性数据应用中概述了性能增益。