ABSTRACT
The history and use of probability and statistical methods in the sciences is a long and varied one. Statisticians and researchers applying statistical methods should understand the relevant literatures underlying the scientific interpretation of the models they are helping to develop. In the physical, life and social sciences, statistics is used to help organize, collect and model characteristics and potential associations of interest where measurements are subject to random fluctuation. This chapter discusses how to approach basic model building with simple statistical concepts. By focusing on the need to interpret the likelihood function and the information it provides, the chapter explains that two main statistical approaches, Bayesian and frequentist, can be integrated into practical analyses of many scientific problems. In large sample statistical applications the expected local curvature of the log-likelihood function about its mode, the Fisher information, provides an approximation to the underlying variation in the model.
