Gaussian Distribution, Confidence Intervals, Binomial (Wald) Proportion, Wilson Score Interval and Delta Theorem

In this chapter, we describe the basic properties of the Gaussian and skew distributions and present the Central Limit Theorem. We explore the Binomial (Wald) proportion confidence interval and Wilson Score interval as means to obtain the confidence intervals of the parameters on the confusion matrix. We provide the steps to calculate and interpret these confidence intervals, providing numerical examples for clarity. We likewise demonstrate how the Delta theorem can inform the confidence interval around the prevalence threshold. Finally, we describe the analogous concept in Bayesian theory, the credible interval.