Some illustrative examples in nonlinear statistics
Lecture plan
Previous lecture we provides that we will continue now with the following topics:
- Probability Primer (Chapter 2) and
- Conditional Independence (Chapter 4)
Some probability and a bit of stats
Topics:
- discrete probability distributions: basic notation.
- The model of independence.
- Limiting distributions - see section 2.3 and 2.5 in the book.
Lecture on board.
Topics covered in lecture 2:
- discrete and continuous random variables
- definition of a statistical model, including parameter space,
implicit/explicit(parametric) description of the same model
- two views of the same object.
- probability simplex, dimensions of the space we live in (the number of stats of discrete random varaibles dictates everything, doesn’t it?:)
- review of conditional probability, independent events, independent random variables
- Examples: the Bernoulli model, the independence model for two random
variables, the model for a count of the number of heads in two coin
tosses
- explicit computation of joint probabilities,
- a peek into implicit description - lead-in to homework 1 questions 2&3,
- a hint as to how this might generalize to other (higher-dimensional) models.
Actual lecture notes:
I do not have these typed up. I hope to be able to share them soon.
License
This document is created for Math/Stat 561, Spring 2023, at Illinois Tech.
While the course materials are generally not to be distributed outside the course without permission of the instructor, all materials posted on this page are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.