对于依赖的随机概率与β边际的逻辑-β过程
Changwoo J Lee1, Alessandro Zito2, Huiyan Sang3
1Department of Statistical Science, Duke University.
概括
我们介绍了逻辑-β过程,这是一种用于建模依赖概率的新型统计方法. 这种灵活的方法增强了贝叶斯非参数模型的各种应用.
科学领域:
- 统计 统计 统计 统计
- 机器学习 机器学习
- 贝叶斯的非参数学.
背景情况:
- 贝塔分布广泛用于概率,但缺乏对依赖随机概率的灵活扩展.
- 对于依赖概率的现有方法通常在计算上不方便.
研究的目的:
- 提出一种新的随机过程,即逻辑-β过程,用于建模依赖概率.
- 为贝叶斯非参数模型开发一个灵活和可计算的框架.
主要方法:
- 逻辑-β过程通过逻辑转换来定义,产生β边际值.
- 它使用相关性内核结合了灵活的依赖结构.
- 一个正常的差值-平均值混合物表示方便后置推理.
主要成果:
- 逻辑-β过程使得可计算可处理的依赖贝叶斯非参数模型的设计成为可能.
- 在依赖的迪里克莱特过程和扩展中证明了有效性.
- 在非参数二进制回归和条件密度估计中成功应用.
结论:
- 逻辑-β过程为建模依赖概率提供了一种灵活且计算效率高的方法.
- 它为在各种领域推进贝叶斯非参数建模提供了有价值的工具.
- 这种方法在模拟和现实应用中都被证明是有效的.
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