ABSTRACT
Quick Study Guide This chapter is given to further advance probabilistic inference to statis-
tical inference. However, this chapter is not to teach you hands-on statistical methodologies, nor are you expected to perform statistical analyses. Instead, we will provide in-depth discussions and critiques on fundamental statistical principles and di¤erent statistical paradigms that are derived from these principles. Each of the principles is appealingly intuitive but the surrounding controversies are extremely complex. We will use paradoxes in numerical forms to e¤ectively explain the abstract concepts and complex issues. Even so, a great patience is required to fully bene…t from this chapter. We will describe the three statistical paradigms frequentism, Bayesian-
ism, and likelihoodism, and the Decision Approach as well. After reviewing the concepts of statistical model, point estimate, con…dence interval, p-value, type-I and type-II errors, and level of signi…cance, we will provide a detailed discussion of …ve essential statistical principles and surrounding controversies: the conditionality principle, the su¢ ciency principle, the likelihood principle, the law of likelihood, and Bayes’law. The discussion of controversies will be broadened to statistical analyses,
including model …tting, data pooling, subgroup analyses, regression to the mean, and the issue of confounding. We put a large e¤ort on the multiplicity issues due. We will make an attempt to unify the statistical paradigms under the
proposed principle of evidential totality and the new concept of causal space. This chapter covers comprehensively and in depth most controversial issues
in statistical inference. To make it e¤ective, I will again borrow from the power of paradoxes.
