Bayesian Inference

Bayesian inference is way of reasoning which integrates uncertainty. It is a statistical approach to reasoning.

Strong syllogisms are statements like:
1. A implies B
2. B implies C
3. A is true, therefore C is true

However most experimental, and almost all daily reasoning works within a much weaker framework

1. D implies E
2. E is true, therefore the existent of D becomes more probable.

Example 1:
(E) It is cloudy, therefore (D) it is more likely to rain later --> Decision: Take an umbrella.

Most practical and scientific reasoning relies on this.

However consider the case of Ireland:

Example 2, Ireland:
(E1) It is sunny now (E2) we are in Ireland (E) it is still likely to rain later --> Decision: Taka an umbrella

Obviously, the fact that you are located in rainy Ireland modifies the reasoning process (in Bayesian language it represents a high prior probability of rain) . Many facts may modify the reasoning process, Bayesian inference provides a simple mathematical framework to perform

I was introduced to these ideas in E.T. Jaynes book, a very readable chatty introduction to probability, http://bayes.wustl.edu/for more infor