Models, Estimators, and Tests
Ery Arias-Castro · Cambridge University Press eBooks · 2022
A prototypical (although somewhat idealized) workflow in any scientific investigation starts with the design of the experiment to probe a question or hypothesis of interest. The experiment is modeled using several plausible mechanisms. The experiment is conducted and the data are collected. These data are finally analyzed to identify the most adequate mechanism, meaning the one among those considered that best explains the data. Although an experiment is supposed to be repeatable, this is not always possible, particularly if the system under study is chaotic or random in nature. When this is the case, the mechanisms above are expressed as probability distributions. We then talk about probabilistic modeling --- albeit with not one but several probability distributions. It is as if we contemplate several probability experiments, and the goal of statistical inference is to decide on the most plausible one in view of the collected data. We introduce core concepts such as estimators, confidence intervals, and tests.