Essay Sample on Bayes' Theorem

Bayes theorem is a probability theory describing an event's probability on the basis of previous knowledge related to the event. The probability paradigm is relevant in predicting concepts using two variables. The theory, developed by Thomas Bayes, focuses on solving various mathematical problems. It is critical to assess the relevant historical aspects revolving around the development of the theory. Besides, understanding the various principles surrounding Bayes' theorem helps in assessing the need of the paradigm. The concepts of this theorem in various theories help in understanding its application in historic times and in current mathematical calculations.

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

Order now

Influential World Events

The main world event that was critical in the 18th century was the struggle by countries to improve scientific discoveries. The scientific revolution was a prominent concept across the globe, as scholars embarked on finding solutions to major global challenges such as astronomy, wars, and other geographical concepts. Economic development also required mathematical concepts. Governments, especially European nations, emphasized on the role of mathematical inventions in calculating principles of geophysics. Scholars were involved in developing various theories regarding geographical phenomena. During the age of Enlightenment, the British and French governments aimed at establishing academic institutions that helped in advancing science. For instance, the French academy was significant in establishing scientific studies which would help find solutions to natural practices. Besides, the Royal Society was significant in providing necessary resources for finding mathematical solutions in exploring

Thomas Bayes Born in 1701, Reverend Thomas Bayes was a preacher in London. Raised in a religious family setup, the Reverend mainly engaged in ministerial activities while schooling. He was also a mathematical scholar who focused on the concept of probability (Streiner 13323). Bayes focused on probability concepts surrounding the prediction of events. While conducting his research, he realized that the previous events had an impact in predicting the future (Brown 69-70). When he died, he had not published the theory. His close friend and minister, Richard Price, was involved in publishing the work. Bayes, however, made other publications, including a theological concept and another mathematical article.

Royal Society: Publication of Bayes Theorem

Bayes theorem was first presented to the Royal Society by Robert Price. The Royal Society is a scientific institution based in the United Kingdom but focused on proving publications across the world. At the time, the Royal Society was the most credible organization that would allow research publications in various subjects, including mathematics, philosophy and other sciences. The society focused on providing support to scientists for their outstanding discoveries, recognising the scientific excellence, and promoting science in real life situations. For Bayes theorem to be presented in the Royal Society, it must have created a serious discussion on probability.

Results of Bayes Theorem

Bayes Theorem was less significant during the time of its discovery. When Bayes died, Robert Price took the responsibility of publishing Bayes' work. When he re-edited the principle, he published it. However, Bayes theorem was irrelevant until the times of Pierre-Simon Laplace, who independently proved the theory. Laplace later met Bayes and the probability theory affirmed the importance of the theory. However, the theory was critical in solving various mathematical problems at the time.

Bayes theorem was used in collecting statistics on various population issues by the government. For instance, the theory was applied in understanding statistics on cholera victims. This was critical since cholera was a ravaging disease that the government took interest in. The concept was applicable in various clinical medicinal aspects, with much focus being the establishment of treatment formulas. Medical researchers undertook the probability concepts in predicting various medical problems and drugs.

Besides, the results were critical in later years. Alan Turing became popular due to the development of the German Enigma. He utilized the Bayes theorem to decode the German program by applying probability in various situations. Through his interpretation of the theory, he helped his country and the Allies from a World War defeat. Later, the United States was involved in using the probability concept in undertaking a search on the missing H-bomb.

Applying Bayes Theorem in Current World

In current times, the Bayes theorem has been influential in finding solutions to challenges regarding probability concepts. One specific issue is the probability of knowing the number of patients suffering from a disease such as cancer. Considering that a person has a certain symptom that the total number of cancer patients exhibits; this concept does not mean that the person must suffer from cancer. Using the probability theory by Bayes, the chances of having cancer with a particular symptom is 0.09 while 0.91 may express a false point.

Revision of the Bayes Theorem

Bayes theorem was conceptualized in various mathematical theories. The first theory applying Bayes's theorem was Laplace's Central limit theorem. Laplace has significantly explored the importance of the theorem in addressing various probability challenges. Laplace's invention allowed him to handle all types of data. He underscored the relevance of Bayes theorem in dealing with large amounts of data. He utilized the frequentist and Bayesian ideologies to ensure they produced similar results.

The Bayesian inference was influential in measuring the level at which people can believe in a particular concept (Jafarian). Bayes' paradigm is critical in advancing the Bayesian inference. The theorem connects this level of belief in situations before and after a person accounts for evidence.

The frequentist interpretation is another concept of the Bayes principle. In this aspect, the probability equation is involved in finding the outcome proportions. The frequentist interpretation is significant in underscoring the importance of balancing proportions of chances. The outcome proportions will help in predicting the number of times an option may produce an outcome pattern. Bayes theorem is applicable in this principle through the development of tree diagrams. The probability tree diagrams are relevant in explaining the chances of outcomes taking place. Besides, through frequentist interpretation, a person may utilize the principles to calculate inverse probabilities.

Conclusion

Baye's Theorem is critical in understanding probability principles. The application of the principle helps in underscoring the relevant concepts of probability in real-life situations. Bayes theorem was developed in the 18th Century by Thomas Bayes, although his principles were published posthumously. While assessing the importance of the theorem, other scholars such as Laplace designed theories such as the central limit theory. Other theories include the Bayesian inference and frequetnist interpretation. The advancement of the theorem helps in understanding the mathematical challenges that require probability, including statistics, algebra and other relevant mathematical concepts.

Work Cited

Brown, Roger J. "And the Winner is... After 250 years the Rev. Bayes finally finds Redemption." (2018). 69

Jafarian, Amirhossein, et al. "Structure learning in coupled dynamical systems and dynamic causal modelling." Philosophical Transactions of the Royal Society A 377.2160 (2019): 20190048.

Streiner, David L. "Clinical medicine and the legacy of the Reverend Bayes." International journal of clinical practice 73.4 (2019): e13323.