The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented. The Canadian Journal of Statistics 38: 256–270; 2010 © 2010 Statistical Society of Canada

中文翻译：

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通过随机近似蒙特卡罗的纵向函数主成分建模。

作者考虑了基于功能主成分方法的分层纵向功能数据的分析。与选择主成分数量的标准频率论方法相比，作者使用贝叶斯公式进行模型平均。相对简单的可逆跳跃马尔可夫链蒙特卡罗公式具有较差的混合特性，并且在模拟数据中经常陷入错误数量的主成分。为了克服这个问题，作者展示了如何将随机近似蒙特卡罗 (SAMC) 应用于这个问题，这种方法有可能探索整个空间并且不会陷入局部极值。通过主成分的极坐标表示简化了可逆跳跃方法和 SAMC 在分层纵向功能数据中的组合。该方法易于实现，并且在确定主成分数量分布的模拟数据中表现良好，并且在其频率估计特性方面表现良好。还介绍了实证应用。加拿大统计杂志 38：256-270；2010 © 2010 加拿大统计学会