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.(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.Other, and much more inherently complicated business specific, full-scale examples will not be provided, but situations of where and how to use Bayes' Theorem will.
If there is a second event that affects P(A), which we'll call event B, then we want to know what the probability of A is given B has occurred.
Many people put a lot of faith into the estimates and simplified probabilities given by experts in their field; this also gives us the great ability to confidently produce new estimates for new and more complicated questions introduced by those inevitable roadblocks in financial forecasting.
Instead of guessing or using simple probability trees to overcome these road blocks, we can now use Bayes' Theorem if we possess the right information with which to start.
Lawsuits, changes in the prices of raw materials, and many other things can heavily influence the value of a company's net income.
By using probability estimates relating to these factors, we can apply Bayes' Theorem to figure out what is important to us.
In other words, if you gain new information or evidence and you need to update the probability of an event occurring, you can use Baye's Theorem to estimate this new probability.