Likelihood based theory for applicatoins

统计理论有两种主要的方法来分析有数据的统计模型，默认的贝叶斯和频率论；这些问题可能会给出截然不同的答案，并带来明显的严重风险。两者都以可能性为主要成分，但在其他输入上有所不同。离散数据代表了一个非常大的领域需要的方法，而不仅仅是使用似然。这项研究继续了目前的工作，表明似然梯度或平均似然梯度可以提供将兴趣参数与干扰参数分离所需的额外物质，然后为兴趣参数提供高度精确的p值。该方法涵盖了连续参数上下文，但其在离散数据和列联表上下文中的发展代表了广泛应用的迫切需要。

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.