The first items are the handout that Jeff wrote, on R; a chart on "preliminaries," which we did not use, but summarizes the syllabus that was handed out; and a chart set on the introduction to the basics of probability, which will be the next discussion after the introduction to R. This chart set has the fundamental equations we will be using all semester.
The usual frequentist and the Bayesian approaches to statistics differ in the way they use probability theory. The frequentist's main tool is the sampling distribution, that is, the probability distribution of the data, given some hypothesis (e.g., the null hypothesis of no effect, or the hypothesis that a parameter has a particular value). The frequentist looks at what happens if the data space is sampled repeatedly. This leads to notions like p-values, confidence intervals, and the other tools of the frequentist toolkit. The Bayesian approach is different: In Bayesian theory, the data are fixed at the actual value observed, and the probability distribution of interest is the one on the hypotheses. (In frequentist theory, this idea makes no sense, because in this view of statistics, only data, not hypotheses, can have a probability distribution; but the Bayesian viewpoint is different!)
Jeff lectured using his notes on R. We only got to the top of page 3, and the main things mentioned were:
- Your assignment is to install R on your computer (if you have one), and also to install the LearnBayes package that is companion to the Albert book. Google 'r', or click here.
- The R prompt is a "greater than" sign, >
- Get information about an R function by typing >?median , for example
- You can write >x=5, etc., using R as a fancy calculator with named variables.
- Vectors are not matrices. They have a length, but not dimensions. This is an annoying feature (see the top of p. 3 of the handout).
Here is a link to the R reference that Jeff noted on page 1 of the handout.
Good luck, and see you on Thursday!
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