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具有欧几里得结构模型中的贝叶斯推断AI 解读

When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be…

具有欧几里得结构的模型中的贝叶斯推断AI 解读

When a parameter space is endowed with a Euclidean structure, there is a Euclidean measure, called the structural (or geometric) prior, which is an obvious candidate to represent ignorance concerning an unknown parameter. The rationale for using this prior is strengthened when the unknown parameter is the canonical parameter of an exponential family. Then the structural prior is the uniform prior for the canonical parameter. It is shown also that Euclidean structures can be…

线性与仿射函数模型中的最大似然及最小二乘估计AI 解读

In a linear (or affine) functional model the principal parameter is a subspace (respectively an affine subspace) in a finite dimensional inner product space, which contains the means of $n$ multivariate normal populations, all having the same covariance matrix. A relatively simple, essentially algebraic derivation of the maximum likelihood estimates is given, when these estimates are based on single observed vectors from each of the $n$ populations and an independent…

内在统计推断（二）AI 解读

According to an invariance principle, for some models having a certain group structure, there is a uniquely defined prior representing ignorance, which is called the inner prior. It is shown that the corresponding posterior probability of a likelihood region has a simple frequency interpretation as a mean conditional confidence level. The central multivariate normal model is considered as an example.

内在统计推断AI 解读

For any linear model there is, according to an invariance argument, a uniquely defined prior representing ignorance, which will be called the inner prior. It is shown that the corresponding posterior probabilities are weighted averages of conditional confidence levels. This frequency interpretation compares favorably with the usual interpretation of confidence levels as unconditional probabilities of coverage. Of particular interest to users of statistical methods is that…