This paper tries to highlight the benefits that are derived by studying the topic of probability. More emphasis is put on the prior probability and the Bayes theorem. The application of Bayes’ theorem in everyday’s life and in school can never be underestimated. The lesson has brought insight into different applications of probability in real-life situations and in academics; I am capable of applying the lessons learned in different fields and using them in solving problems. In this paper, I have given examples of applications and cited a number of situations where the theorem is applicable. Finally, due to my applications, I have identified areas that still need more advancement to perfect my understanding and application of probability. The theorem can also be when these factors are taken into account. These are discussed below.
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Prior probability is defined as the probability approximated before a real survey. Organisations often conduct activities that rely on probability and mutually related events. By using Bayes Theorem, a statistician articulates the fact that we can reconcile hypothetical inference to actual information illuminated by new evidence. The theorem states that the posterior probability of each hypothesis is directly proportional to its prior probability and the probability of obtaining its evidence (Karl, 20). This is represented by this rule that the epitomised updated opinion likelihood × starting opinion (40). We can further represent this figuratively as:
- is the posterior probability and
- is the prior probability of obtaining the evidence (E). It is also the same as the likelihood of Hypothesis H. The evidence (E) is expected to prove that the hypothesis (denoted as H) is true. The prior probability of the Hypothesis (H) is denoted as
- . The inspiration to accept Bayes’ Theorem is deeply engrained in the failures of the maximum likelihood criterion, which lays more emphasis on the most probable events.
Requirements for Continuous Improvement
There is a need to have more research on the part of students to help us in understanding the probability and Bayes’ theorem application perfectly. In order to optimise the efficiency of Bayes’ Theorem, it is necessary to exhaust all possibilities during surveys so that the posterior probability is as accurate as possible. Wuensch reinstates that; this would reduce the variation between the prior probability and the posterior probability. One of the options would be to set standard weights to prior probabilities and their related parameters to ensure homogeneity. Another requirement would be to execute several tests to evidence while maintaining the standpoint of the hypothesis (86). The hypothesis needs not to have been entirely independent, based on total ignorance and not influenced by contemporaries. Bayers’ theorem can be continuously improved to generate the best values by integrating it in statistical packages to a standard with the implementation of new technologies. The goal is to find the best possible solution for the evidence.
Relevance of the course
This course has provided me with a more precise understanding of the concept of Bayer’s Theorem as well as the significance of its implementation. It justifies the criticism against the maximum likelihood criterion. It also meets the course objectives by exposing the sensitivity of prior probability with respect to the randomly distributed dataset. Understanding the theorem has been an issue amongst students. Through this course, I am able to appreciate the application of probability in risk assessment and predictions. It has also opened a new way of argument and how to improve on its application. Indeed, I am capable of deriving different applications using the Bayes theorem.
Smith, George. Expressing Prior Ignorance of a Probability Parameter. Missouri, Columbia: Division of Biological Sciences, 2003. Print.
Wuensch, Karl. A Brief Introduction to Bayesian Statistics. USA: MV, DFA, 2007. Print.
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