用贝叶斯推断推理为稀疏和不规则间距数据的功能主要组件模型
1Department of Statistics, University of Akron, Akron, OH, USA.
Journal of applied statistics
|June 5, 2024
概括
本研究引入了一种新的贝叶斯函数主要组件分析 (FPCA) 方法,用于稀疏,不规则的数据. 该方法证明了竞争性表现,并应用于身体质量指数 (BMI) 数据.
科学领域:
- 统计 统计 统计 统计
- 功能数据分析 功能数据分析
- 贝叶斯的推理是贝叶斯的推理.
背景情况:
- 功能主要组件分析 (FPCA) 的贝叶斯贡献是有限的.
- 稀少且间隔不规则的功能数据给分析带来了挑战.
研究的目的:
- 开发FPCA的贝叶斯方法,容纳连续和二进制稀疏,不规则的数据.
- 为使用贝叶斯推理分析功能数据提供灵活的框架.
主要方法:
- 一个马尔科夫链蒙特卡洛 (MCMC) 方法,使用吉布斯采样进行参数更新.
- 在一个通用的功能混合模型中,利用对平均值和自函数轨迹的处罚分线.
- 使用可逆跳转MCMC (RJ-MCMC) 算法来确定主要组件的数量.
主要成果:
- 拟议的贝叶斯式FPCA方法在模拟中显示了与非贝叶斯式方法相比的竞争性性能.
- 该模型有效地处理连续和二进制结果的稀疏和不规则间隔的函数数据.
- 成功应用到按性别和种族分层的身体质量指数 (BMI) 数据.
结论:
- 开发的贝叶斯式FPCA框架为分析复杂的功能数据提供了一个强大的方法.
- 这种方法将FPCA的适用性扩展到观察数量有限且分布不均的场景.
- 该研究强调了贝叶斯推理在功能数据分析中的实用性,对健康数据研究有实际意义.
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