1. Statistics

Statistics is the science of learning from data. It provides the inductive framework for inferring underlying models, estimating unknown parameters, and testing hypotheses about the processes that generated observed outcomes.

1.1 Core Philosophy

Statistics answers the question: "Given observed data, what can we infer about the underlying model or process?"

Starting from samples and observations, we build methods that let us: - Estimate population parameters from finite samples - Quantify uncertainty in our estimates - Test hypotheses about model structure - Compare competing models and select the best fit - Make predictions with measurable confidence

1.2 Topics Covered

• Maximum Likelihood Estimation —

Inductive reasoning from data to models