在张量库里-韦斯模型中的相互作用顺序估计
1Department of Statistics and Data Science, Faculty of Science, National University of Singapore, Singapore 117546, Singapore.
Entropy (Basel, Switzerland)
|March 28, 2025
概括
在旋转库里-韦斯模型中估计相互作用参数p是不可能的,如果逆温度β是未知的. 只有当 β 已知并且超过与 p 相关的特定值时,才能对 p 进行一致的估计.
科学领域:
- 统计物理学的统计物理.
- 信息理论是信息理论.
- 概率理论的概率理论是什么
背景情况:
- 库里-韦斯模型是统计力学的一个基本模型.
- 估计模型参数对于理解物理系统至关重要.
- 相互作用参数"p"和逆温度"β"是p-旋转库里-韦斯模型的关键特征.
研究的目的:
- 调查从单个观测中估计p-旋转库里-韦斯模型的相互作用参数"p"的可能性.
- 确定参数估计可行的条件.
- 将这些发现扩展到p-spin Erdös-Rényi Ising模型.
主要方法:
- 来自统计推理的连续性论据.
- 在统计模型中分析参数识别能力.
- 磁系统的数学建模.
主要成果:
- "p"和"β"的联合估计是不可能的.
- 当"β"未知时,估计"p"是不可能的.
- 发现了一个日益增长的值函数β*(p).
- 对于β<β*(p) 不可能对"p"进行一致的估计,而当"β"已知时,对于β>β*(p) 是可能的.
结论:
- 复杂的统计模型中的参数估计可能从根本上受到限制.
- 参数之间的关系显著影响它们的可估计性.
- 这些发现为旋转模型中的统计推理提供了理论界限.
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