论文标题
贝叶斯自适应选择功能数据表示的基础功能
Bayesian Adaptive Selection of Basis Functions for Functional Data Representation
论文作者
论文摘要
考虑到功能数据分析的上下文，我们通过Gibbs采样器开发并应用了一种新的贝叶斯方法，以选择功能数据有限表示的基础功能。所提出的方法使用Bernoulli潜在变量将零分配给具有正概率的某些基本函数系数。此过程允许自适应基础选择，因为它可以确定碱的数量，并且应选择其代表功能数据。此外，提出的程序测量了选择过程的不确定性，可以同时应用于多个曲线。开发的方法可以处理观察到的曲线，这些曲线可能由于实验误差和受试者之间的随机个体差异而有所不同，这可以在实际数据集应用中观察到，涉及巴西每天数量的COVID-19案例。仿真研究显示了所提出方法的主要特性，例如它在估计程序的系数和强度以找到真正的基础函数集的准确性。尽管在功能数据分析的背景下开发了，但我们还通过模拟与已建立的套索和贝叶斯套索进行了比较，这是用于非功能数据的方法。
Considering the context of functional data analysis, we developed and applied a new Bayesian approach via Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent variables to assign zero to some of the basis function coefficients with a positive probability. This procedure allows for an adaptive basis selection since it can determine the number of bases and which should be selected to represent functional data. Moreover, the proposed procedure measures the uncertainty of the selection process and can be applied to multiple curves simultaneously. The methodology developed can deal with observed curves that may differ due to experimental error and random individual differences between subjects, which one can observe in a real dataset application involving daily numbers of COVID-19 cases in Brazil. Simulation studies show the main properties of the proposed method, such as its accuracy in estimating the coefficients and the strength of the procedure to find the true set of basis functions. Despite having been developed in the context of functional data analysis, we also compared the proposed model via simulation with the well-established LASSO and Bayesian LASSO, which are methods developed for non-functional data.
