Part X — Foundations of Statistics

Data is generated by a random process, and the goal of statistics is to figure out that data-generating process — well enough to make predictions, and to understand what drives it. Where probability derives data from a known model, statistics infers the model from observed data. This part sets up that inversion: populations versus samples, descriptive summaries, sampling distributions, statistical models, and the bias–variance decomposition of estimation error.

Topics

Topic	Focus
Population vs Sample	The gap between the data-generating process and observed data
Descriptive Statistics	Summaries of location, spread, and shape
Sampling Distributions	The distribution of a statistic across repeated samples
Statistical Models	Parametric, nonparametric, and semiparametric models; identifiability
Bias and Variance	The two components of estimation error