An article on - Bayes Theorem application and usage

 

Bayes Theorem application and usage

 

Instance and example of usage of Bayes Theorem in Maths and Statistics :

 

P(B|E) = P(E|B)*P(B) / P(E)

 

If one reads the formula , then one will come across the following terms within the instance which can be elaborated with the help of an instance in the following manner :

 

* P( B | E ) - The probability of a belief(B) given a set of evidence(E) is called over here as Posterior Probability . Here , this statement tries to convey the underlying first condition that would be evaluated for going forth over to the next condition for sequential execution . In the given case , the hypothesis that is presented to the reader is whether a person is a female and given the length of her hair is sufficiently long , the subject in concern must be a girl

 

* P( E | B ) - In this conditional form of probability expression , it is expressed that one could be a female given the condition that the subject has sufficiently long hair . In this case , the equation translates to a form of conditional probability .

 

* P ( B ) - Here , the case B stands for the general probaility of being a female with a priori probability of the belief . In the given case , the probability is around 50 percent which could be also translated to a likelihood of occurrence of around 0.5 likelihood

 

 

* P(E) - This is the case of calculating the general probability of having long hair . As per general belief , in a conditional probability equation this term should be also treated as a case of priori probability which means the value for its probability estimate is available well in advance and therefore , the value is pivotal for formulation of the posterior probability

If one would be able to solve the previous problem using the Bayes Formula , then all the constituent values would be put in the given equation which would fill in the given values of the equation .

The same type of analogy is also required for estimation of a certain disease among a certain set of population where one would very likely take to calculate the presence of any particular disease within a given population . For this one needs to undergo a certain type of test which would result in producing a viable or a positive result .

 

Generally , it is perceived that most of the medical tests are not completely accurate and the laboratory would tell for the presence of a certain malignancy within a test which would convey a condensed result about the condition of within a test which would convey a condensed result about the condition of illness of the concerned case .

 

For the case , when one would like to see the number of people showing a positive response from a test is as follows :

1) Case -1 : Who is ill and who gets the correct answer from the test .

This is normally used for the case of estimation of true positives which amounts to 99 percent of the 1 percent of the population who get the illness

2) Case-2 : Who is not ill and who gets the wrong diagnosis result from the test . This group consists of 1 percent of the 99 percent of the population who would get a positive response , even though the illness hasn't been completely discovered or ascertained in the given cases . Again , this is a multiplication of 99 percent and 1 percent ; this group would correspond to the discovery of false positive cases among the given sample . In simple words , this category of grouping takes into its ambit , those patients who are actually not ill (may be fit and fine ) , but due to some aberrations or mistakes in the report which might be under the case of mis-diagnosis of a patient that , the patient is discovered

as a ill person . Under such circumstances, untoward cases of administration of wrong medicines might happen , which rather than curing the person of the given illness might inflict aggravations over the person rendering him more vulnerable to hazards , catastrophies and probably untimely death

 

* So going through the given cases of estimation of correct cases of Classification for a certain disease or illness could help in proper medicine administration which could help in recovery of the patient owing to right Classification of the case ; and if not then the patient would be wrongly classified in a wrong category and probably wrong medicines could get administered to the patient seeking medical assistance for his illness .

 

( I hope , there is some understanding clarity in the cases where the role of Bayesian Probability estimations could be put to use . As mentioned , the usage of this algorithm takes place in a wide-manner for the case of proper treatment and classification of illnesses and patients ; classification of fraudulent cases or credit card / debt card utilisation , productivity of employees at a given organisation by the management after evaluation of certain metrices :P ...... I shall try to extend the use case and applications of this theorem in later blogs and articles )