Bioinformatics/Bayesian Algorithms

Bayesian algorithms are useful if there exists a limited amount of experimental data and one wants to evaluate a hypothesis which is based on that data. For example, if we pose the question whether i is true given j, we want to know the posterior probability P(i|j) (probability of i if j is already given). But this posterior probability is not directly inferable from the data, so we reverse the statement: If our hypothetical i were true (=given), what is the probability of j? What we can say, is that the probability of a true i with given j times the probability of j is equal to the probability of true j with i given times the probability of i. We can put this into a mathematical form: $$P(i|j)*P(j)=P(j|i)*P(i)$$. Then a little rearrangement leads to what we want to know: what is the probability of a true i given the data j? $$P(i|j)=[P(j|i)*P(i)]/P(j)$$