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# Bayes' Theorem Essay Example

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## Bayes' Theorem

On the other hand, Bayesian approach makes use of only one theorem i. The fact remains as that Bayesian approach can be used in different situations where most of the tools of frequentist statistics fall short.In the Bayesian theorem, the conditional probability occur on the bases of unconditional probabilities that are derived using a multiplication rules, that is (Prior x Likelihood) that are further divided by the sum of the possible parameters. Posterior in Bayesian theorem can be identified as conditional probability of the random event or uncertain proposition. It occurs when there is assigned or relevant evidence or background is considered (Jackman, 2009). Posterior is a random variable or conditional that is based on the evidence that is obtained from the experiment. In Bayer’s theorem the relevant case evidence are considered for a particular case.Likelihood can be defined as a conditional probability or the unobserved events of B and A has occurred based on given B. Likelihood is given by P (A I). It shall be noted that the likelihood is a function that is dependent or defined on the events of B and the likelihood is the weight that is given to the events of B depending upon the occurrence of A.The subjective probability mainly the assumption or the summary of believes that are observed to occur. In Bayesian statistic, subjective are collection of the sum possible parameters that are considered before the data. These predictions or beliefs are often said as Prior subjective that provides the occurrence of event between the possible parameters, through providing possible values to the data. However, there are mainly two probability concepts that are applied in different ways in Bayes’ theorem that are objective probabilities and subjective probabilities. Jackman (2009) illustrates the application of subjective probability as ‘probability that corresponds to personal beliefs that are rational and have coherences constrains with respect to probabilities.The probability are based on the parameters of beliefs, therefore it is essential that the parameters should be defined or calculated on the bases of its degree of belief due to which it important that the parameters should be subjective, in order to revise our beliefs about the parameter in the given data. In addition, the beliefs that shall be considered among the parameters of probability should be based on previous events or

References

Bolstad, W.M., 2004. Introduction to Bayesian Statistics. 1st ed. New York: John Wiley & Sons.

Haug, A.J., 2012. Bayesian Estimation and Tracking: A Practical Guide. 1st ed. New York: John Wiley & Sons.

Jackman, S., 2009. Bayesian Analysis for the Socia Sciences. New Jersey: John Wiley & Sons.

Leonard, T. & Hsu, J.S.J., 1999. Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers. 3rd ed. New York : Cambridge University Press.

Savchuk, V. & Tsokos, C.P., 2011. Bayesian Theory and Methods with Applications. 1st ed. New York: Springer Science & Business Media.

Stauffer, H.B., 2007. Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists. 1st ed. New York: John Wiley & Sons.

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