Bayes theorem

This study discusses the “Bayes theorem” which is a mathematical formula made by a British mathematician to interpret probability. This study also discusses the formula of this “Bayes’ theorem” and some examples of the formula. There are some important uses of this formula in real life that helps to interpret the solution of critical conditions. This theory has some advantages and disadvantages which are also discussed in Thai study briefly. This study is also discussed “Bayes theorem probability” which helps to interpreted probability.  This study discusses the effective role of this formula which is named “Bayes’ theorem” in everyday life. The calculation of the “Bayes theorem” is completed with the determination of “statements, formula, and derivation” of the given data. 

Bayes theorem and its Use and example

The “Bayes theorem” is defined as “is a mathematical formula for determining conditional probability.” “Conditional probability” is based on the outcome which is found in previous times in the same type of situation. This Bayes theorem is held to find a solution in critical situations with the help of additional or new evidence.  Bayes theorem helps to find the risk of any investment and identify the potential borrowers. The theorem is also defined as the test which relies on the incorporation of “Prior probability” and distributed to generate “Posterior probabilities”. “Prior probability” is the statistical inference that helps to interpret the probability by collecting data. 

An example of the Bayes theorem is if an age-related disease is seen and needs to find the probable result of the disease then this theory is used. The age of the person is used to determine the probability of the disease in the person. This example helps to understand the use of the Bayes theorem in real life as that is used in the “Medical science” to interpret the probability of the disease. The Bayes theorem is also used in the “machine learning” process as this helps to calculate the probability of the hypothesis of the given data. This method is used to find the “Unknown parameter” of the “Fixed constant” and this helps to interpret probability by relative frequency. 

Bayes theorem formula and Probability  

In the “Probability theory” Bayes theorem is a mathematical formula that helps to determine the “Conditional probability” of the situation. This method describes the “probability” of a situation based on the “Prior probability” of the situation. The formula which is used for “Bayes theorem” is described below; 

“P* (A/B) = P(B/A)* P(A) / P* (B)”

In this formula;

“P*(A/B)” stands for “the probability of event A occurring, given event B has occurred”.

“P(B|A)” stands for “the probability of event B occurring, given event A has occurred”.

“P(A)” stands for “the probability of event A”.

“P*(B)” stands for “the probability of event B”.  This formula is applicable when “A” and “B” are “Independent events”. In another case where “A” is a “Binary variable” then another formula is followed; 

 “P(B|A–)” stands for “the chance of event B happening given that event A– has occurred”.

“P(B|A+)” stands for “the probability of event B occurring given that event A+ has occurred“. In those cases, A- and A+ are the exclusive outcome of “Event A”. 

Advantages and disadvantages of Bayes theorem 

The Bayes method has some advantages and has some disadvantage switch are described below; 

Advantages:

• The method provides a principled and natural way in the estimation of the probability. 
• The method is very much Flexible and prior data which are used in this method is realistic. 
• This process is to recover the whole area of the problems rather than the estimation of confidential estimation. 
• This method is following the principle of likelihood which is helpful for the estimation of probability. 
• Bayes’ theorem is interpreted probability with the help of mathematical formula. 

Disadvantages:

• The method does not have any correct or particular way which helps to choose the prior. 
• This method produces the posterior distribution by the influence of the prior information. 
• Sometimes there needs to be a high compilation cost to complete the method when there are a large number of parameters or areas.

Conclusion 

It is concluded that this study is discussing Bayes theorem and its formula and use in everyday life. In the study, this is seen: “Bayes theorem” is a mathematical method that helps to interpret the future situation with the help of “Posterior and Prior probability”. Identification of “probability” helps people to complete any task with a clear idea of the situation. This is very applicable in real life and for this reason; this is used to interpret the condition of patients who suffer from rare diseases. This theory is help to interpreted the “Probability” of one situation by analyzing condition. Therefore it is concluded, besides various disadvantages, the Bayes theorem is very much useful for the estimation of conditional probability.