For our example we will use the data below to find out how a stock market index will react to a rise in interest rates.

Here: P(SI) = the probability of the stock index increasing P(SD) = the probability of the stock index decreasing P(ID) = the probability of interest rates decreasing P(II) = the probability of interest rates increasing So the equation will be: Thus with our example plugging in our number we get: In the table you can see that out of 2000 observations, 1150 instances showed the stock index decreased.

This is how Bayes' theorem uniquely allows us to update our previous beliefs with new information.

baysian updating-85baysian updating-7

P(A|B) is the conditional probability of A given that B occurs.

This is the posterior probability due to its variable dependency on B. P(B|A) is the conditional probability of B given that A occurs. If we are interested in the probability of an event of which we have prior observations; we call this the prior probability.

In probabilistic notation this is P(A|B), and is known as posterior probability or revised probability.

This is because it has occurred after original event, hence the post in posterior.

An Example Let's say we want to know how a change in interest rates would affect the value of a stock market index.

All major stock market indexes have a plethora of historical data available so you should have no problem finding the outcomes for these events with a little bit of research.

This particular rule is most often used to calculate what is called the posterior probability.

The posterior probability is the conditional probability of a future uncertain event that is based upon relevant evidence relating to it historically.

(Learn how to analyze the balance sheet in our article, .) So what if one does not know the exact probabilities but has only estimates?

This is where the subjectivists' view comes strongly into play.

(See to read about the effects of a bad forecast.) Now that we have learned how to correctly compute Bayes' Theorem, we can now learn just where it can be applied in financial modeling.