Scientific Summary To Bayes Theorem Literature Review Example

‘Bayes Theorem’ was originally stated by Thomas Bayes and is also known as ‘Bayes Law’ or ‘Bayes Rule.’ It is used in the mathematical manipulation of conditional probabilities to clarify the relationship between theory and evidence. A number of probability interpretations may be generated from the probabilities involved in Bayes theorem. Bayes theorem can be applied in a variety of statistical calculations involving probabilities. The Bayesian interpretation of probability expresses how a subjective degree of belief should logically change to account for the evidence.
Mathematically, Bayes theorem is the relationship between probabilities and conditional probabilities. For example, if P(A) and P(B) are the probabilities of events A and B & P(A/B) is the conditional probability when A is given and P(B/A) is the conditional probability when B is given in a particular situation, then, Bayes theorem can be written as:
PAB= PBA.P(A)P(B)
There is another form of Bayes theorem that is useful in inferring causes from their effects as it is easy to determine the probability of an effect when the presence or absence of the cause is known. This form is presented as:
PAB= PBA.P(A)PBA.PA+ PB-A.P(-A)
In this formula, A is our theory or hypothesis (to be tested) and B is evidence that will help us in proving or disproving our hypothesis. P(A) is the probability of theory before we consider the evidence (B) and is known as prior probability of A. Our goal is to discover that what is the probability of A (being true theory/hypothesis) if our evidence (B) is true? This is a conditional probability [P(A/B)], probability that one ‘condition’ is true provided that the other ‘condition’ is true. Hence, P(A/B) represents the probability assigned to A after taking into account the evidence B. To calculate, P(A/B), we need P(A) the prior probability, P(-A) the probability of A being false, P(B/A) and P(B/-A) are the conditional probabilities indicating how probable our evidence is depending on whether our theory is true or untrue.