Statistical Analysis: an Introduction using R/Chapter 5
This chapter contains the most "pure maths" concepts of the book. It is intended to demonstrate 3 main concepts of probability, using two complementary graphical methods. This may make it easier to understand the concepts of likelihood and Bayesian techniques used in the next chapter. However, If you already know some probabiltiy theory, or are willing to accept the 3 probabilty concepts below, then you may wish to move on the Chapter 3.
A link to the wiki prob book
- Mutually exclusive additivity p(a or b) = P(a) + P(b)
- p(a and b),
- concept of independence
- Conditional probability
- Bayes' Theorem
Methods to use
- Probability spaces
- Decision trees
Do this graphically. I have a few ideas of how.
Main text here
a bit about likelihood & models, as intro to Ch 3
R sections: using R as a calculator - or should this go in a later chapter?
Introduce the idea of classifying prob space using a single sample statistic, thus probability distributions, cumulative distributions, quantiles (use graphs).
Introduce binomial distribution. Don't give formula: link to binomial dist on wikipedia. Produce graph. Some sample statistics can be calculated analytically....
Introduce Poisson distribution