Likelihood based theory for applicatoins

统计理论有两种主要的方法来分析带有数据的统计模型：默认贝叶斯方法和频率法；这两种方法可能会给出截然不同的答案，但存在明显的严重风险。两者都把可能性作为主要因素，但在其他方面有所不同。离散数据代表了一个非常大的领域，需要超越仅仅使用可能性的方法论。这项研究继续目前的工作，证明了似然梯度或平均似然梯度可以给出将感兴趣参数与讨厌参数分开所需的附加物质，然后给出感兴趣参数的高精度p值。该方法涵盖连续参数背景，但它对离散数据和联想表背景的发展表明，迫切需要更大的应用领域。

Statistical theory has two primary methodologies for analyzing a statistical model with data, the default Bayesian and the frequentist; and these can give widely different answers with demonstrably serious risks. Both take likelihood as their primary ingredient but differ on other input. Discrete data represent a very large area of need for methodology that goes beyond the use of just likelihood. This research continues present work that demonstrates that likelihood gradient or mean likelihood gradient can give the additional substance needed to separate an interest parameter from nuisance parameters and then give highly accurate p-values for the interest parameter. The methodology covers the continous parameter context but its development for the discrete data and the contingency table context represents an urgent need for large areas of application.