Statistical **inference** is the process of leveraging a mathematical modeling apparatus to make deductions about quantities estimated from data;

- about performing the calculations required to make "good" estimates;
- understanding their properties, and how "good" they are relative to alternatives;
- and in particular understanding how those estimated quantities could have differed if you saw a different sample of data
*from the same population*.

Modeling and inference involve

- equations,
- probability distributions,
- and unknown parameters to those equations and distributions which can be estimated from data.