Bioinformatics/Bayesian Algorithms

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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: . Then a little rearrangement leads to what we want to know: what is the probability of a true i given the data j?