Assumptions Assumptions come from science or scientific theory Assumptions come from the way in which data was collected Assumptions come from extracting information from data Parameters We are making inferences about parameters Mean, probability, and variance are all parameters for our random variables. Parametric Model We know the $\theta$, we know the joint CDF. The model is that class of CDF. $$F_Y(y|\theta)$$ The pipe symbol can be replaced with a semicolon, up to the editor.
Inference Conditioning is the soul of statistics. Statistics is the soul of science. Probability and Inference Converting from model parameter to data is probability. Converting from data to model parameter is inference. 3 Big Picture Questions What is truth? What is good? Good model? Good method? What is beauty? Beauty is in the eyes of the beholder Beauty is what the editors of the annals of statistics look for.