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