Statistics With Both Hands
Statistics is another passion of mine. I somehow managed not to take any statistics courses when I was an undergrad, and I had to make up for it later. Turns out I have a knack for stats. Strange. I am currently refreshing my statistics knowledge, which could be fairly described as "experienced amateur."
I happened upon a paper by James Franklin about logical probability. This really sparked my interest. There are competing schools of thought as to what the nature of probability is. Who knew? The predominant school of thought is known as frequentist, or classical. This is the school of thought that informs standard textbooks. This school considers probability to be the limit of the relative observed frequencies of an event occurring, given an infinite number of trials. The next most common is subjective Bayesian, which holds that probability is a given subject's degree of belief in a proposition. This position is in the minority, but still has a respectable number of scholars behind it. The last, and least, is logical probability, or objective Bayesian. This position hold that probability is a real, logical relationship between different propositions.
This latter position is generally regarded to have been conclusively refuted by the impossibility of determining a prior distribution. Plainly stated, how do you decide on purely logical grounds the weight to give to a given proposition in the initial absence of evidence? This is required under the Bayesian approach, which takes a prior distribution, and modifies it in light of later evidence. The subjective school sidesteps this problem by locating probability in the mind of the individual. There is no mystery that people have different takes on the same idea, so no objective answer is necessary. The frequentists deny any such thing as logical probability, the only kind they recognize is factual probability that has been measured by some experiment.
Despite the difficulties, I find logical probability a more satisfying explanation, and I believe that the prior distribution argument can be answered. I hope to document some of my learnings here.
Elementary Statistics Guide
I have uploaded an early fruit of my statistical education, my Elementary Statistics Guide. For reference purposes only!
Statistics for Experimenters, 1st edition
by Box, Hunter, and Hunter. ISBN 0-471-09315-7
This is a classic work for industrial statistics. I have copied a number of datasets from the book for educational purposes. These are freely available, but no warranty of accuracy is expressed or implied.
Breaking the Law of Averages
By William M. Briggs, ISBN 978-0-557-01990-8
Breaking the Law of Averages is a new take on the introductory statistics class. Briggs focuses on modern techniques and the use of logical probability to simplify the presentation.
A repository of R code used in examples on this website can be found here.