Tuesday, June 28, 2011

Notes on Bayesian Analysis

This afternoon I encountered one of those rare moments when I had little to do since I was waiting on input from a number of collaborators, so I read through half of this site on intuitively understanding Bayes' Theorem. Here are some things that I learned or that were made clearer than my previous understanding:
1. The outcome of Bayesian analysis is a modification of the prior (the probability of an event that is known before the analysis) which produces the posterior (the probability of an event given certain conditions and dependent upon the prior).
2. Bayesian analysis requires three pieces of information: the prior and two conditional probabilities (a true positive and a false positive outcome).
3. If the two conditional probabilities are equal, the prior is unmodified and equals the posterior. This is because the result of the test is uncorrelated with the outcome.
4. The degree to which the prior is modified can be described by the concept of differential pressure, i.e. the relative difference between the two conditional probabilities. The process of changing the prior due to differential pressure is known as selective attrition.
5. People use spatial intuition to grasp numbers. Teachers can use this and the idea of natural frequencies to their advantage to teach difficult concepts.
6. Related to number 5, the way in which given information is presented in a word problem (e.g. percentages vs. ratios) will affect the percentage of correct scores.
Is Bayesian analysis related to Kant's a priori and a posteriori knowledge?