Bayesian updating formula examples carbon dating errors
As indicated in the diagram, Box 1 has 1 red ball and three white balls and Box 2 has 2 red balls and 2 white balls. In the first step (the green arrow in the above diagram), a box is randomly chosen from two boxes.
In the second step (the blue arrow), a ball is randomly selected from the chosen box.
If you don't know a lot about probability theory, Bayesian methods probably sounds like a scary topic. While any mathematically based topic can be taken to rather complex depths, the use of a basic Bayesian probability model in financial forecasting can help refine probability estimates using an intuitive process.
Bayesian Probability Bayesian probability's application in corporate America is highly dependent on the "degree of belief" rather than historical frequencies of identical or similar events.
Since a box is chosen at random, it is easy to see that . Some of the conditional probabilities are natural and are easy to see. These two conditional probabilities are “forward” conditional probabilities since the events and occur in a natural chronological order.
For example, if the chosen box is Box 1, it is clear that the probability of selecting a red ball is , i.e. What about the reversed conditional probabilities and ?
Bayes' Theorem The particular formula from Bayesian probability we are going to use is called Bayes' Theorem, sometimes called Bayes' formula or Bayes' rule.
We open up a discussion of the Bayes’ formula by going through a basic example.