Likelihood based theory for applicatoins

统计理论有两种主要的方法来分析一个有数据的统计模型，默认贝叶斯和频率论;这两种方法可以给出非常不同的答案，并具有明显的严重风险。两者都将可能性作为主要成分，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，超越了使用的只是可能性。这项研究继续目前的工作，表明似然梯度或平均似然梯度可以给额外的物质需要分离的兴趣参数的滋扰参数，然后给出高度准确的p值的兴趣参数。该方法涵盖了连续参数的背景下，但它的离散数据和列联表背景下的发展代表了一个迫切需要大面积的应用。

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.