Bayes' Theorem
I first became interested in Bayes' Theorem after reading Blind Man's Bluff, Sontag (1998). The book made mention how Bayes' Theorem was used to locate a missing thermonuclear bomb in Spain in 1966. Furthermore, it was again used by the military to locate the missing submarine USS Scorpion (Sontag, pg. 97) that had imploded when it sank several years later. I was intrigued by the nature of the theory and wanted to know more about it. When I was reading our textbook for the class, I came across Bayes' Theorem again, and found an avenue to do more research.
There has been much study and many, many articles, papers and books devoted to Bayesian thought and statistics. My research involved literary search at the University of Memphis through Lexis-Nexis, ABI and many other electronic sources available at the University. I read many peer reviewed papers and reviewed several books about Bayed Theorem. I searched the Internet using several search engines and found much of the same literature found through the more conventional methods at the university. Additionally, as part of my research, I conducted an in depth telephone interview with the historian at the Atomic Museum in Albuquerque N.M..
I researched the development of the theorem and its criticism, and included my findings in this paper. Probably the most useful text in understanding the Theorem, and a definitive work supporting its use, is John Earman's work, Bayes or Bust?: A Critical Examination of Bayesian Confirmation. This book examined the relevant literature and the development of Bayesian statistics as well as defended it from its critics.
LIST OF EQUATIONS AND ILLUSTRATIONS
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Equation 1: Bayes Theorem A1
Equation 2: B...
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... T. (1979, November). Why I am not an Objective Bayesian: Some Reflections Prompted by Rosenkranz. Theory and Decision pp.413-440.
Smith, A.F.M. (1986). Why isn't Everyone a Bayesian? Comment American Statistician 40(number 1):10.
Smith, C. (1997). Theory and the Art of Communications Design. Seattle, State of the University Press.
Sontag, S and Drew, C. (1998). Blind Man's Bluff. New York; HarperCollins
Spielman, S. (1977). Physical Probability and Bayesian Statistics. Synthese 36:235-269.
APPENDIX
Equation 1
Equation 2
Equation 3
Equation 4
ILLUSTRATIONS
Illustration 1
A B52 Stratofortress owned by the National Atomic Museum, similar to the one that crash off the coast of Spain in 1966.
Illustration 2
One of the three Atomic bombs found on the coast of Palmares Spain, in 1966.
I believe this essay created an inductive argument, since the Daly provided evidence that helped support the conclusion by making it probab...
Epstein, Richard A. The Theory of Gambling and Statistical Logic. New York: Academic, 1977. Print.
Saltus, Richard. "DNA Fingerprinting: Its A Chance Of Probabilties." The Boston Globe 22 August 1994: 25.
On April 11, 1950, at 9:38 PM, a B-29 took off from Kirtland Air Force Base (AFB) in Albuquerque, New Mexico. The aircraft was on a mission to deliver a Mark 4 nuclear weapon to the 509th Bomb Wing at Walker AFB in Roswell. The aircraft and its crew of 13 were only in flight for approximately three minutes when the plane crashed into a mountain on Monzano Base, Kirtland AFB. All 13 personnel were killed in the crash. Neither the bomb, nor the high explosive material, exploded from the impact. Some of the explosive material was scattered and burned in the gasoline fire that resulted from the impact. The bomb cas...
Dan O'Hair, Mary Wiemann, Dorothy Imrich Mullen, Jason J. Taven. (2012). Dan O'Hair, Mary Wiemann, Dorothy Imrich Mullen, Jason J. Taven. In M. W. Dan O'Hair, Real Communication: An Introduction (pp. 35-64). Boston, New York: Bedford / St. Martin's.
Reliabilism, an epistemological theory created to combat skepticism, claims that a person knows that p if and only if (1) p is true, (2) this person believes that p is true, and that (3) this person has come to the conclusion p via a reliable belief-forming process. A “reliable belief-forming process” could simply be a perceptive act, since reliabilism entails externalism. Externalism claims that you can have knowledge despite not knowing how you came about it (knowing the evidence), exactly. For example, imagine a boy sitting on the beach. He sees a woman walking past him no more than twenty feet away and forms the belief that there is a woman walking past him. Now, he many not exactly understand how he reached that belief, especially when it comes to cognitive processes involved, but nevertheless the fact that his perceptual processes worked reliably justifies his belief. Reliabilism’s analysis is also consistent with fallibilism, which claims that people can be incorrect in their beliefs and still be justified in their beliefs. Once again, consider the boy on the beach. His perceptual processes have consistently served him correctly; for these processes to fail and deceive him would be extremely unlikely, rendering his belief justified even if he were somehow wrong in his belief.
All of these probability laws were utilized by Xenakis in Metastasis. I will now show the correlation of the mathematical version and the musically notated version of the glissadi in Metastasis. Figure 8 is the first page of the score to Metstasis, and Figure 9 is a graphic score of bars 309-314 of Metastasis.
Pierre Simon Laplace on Probability and Statistics . (n.d.). In cerebro.xu.edu. Retrieved March 24, 2014, from http://cerebro.xu.edu/math/Sources/Laplace/
Bennett, J., Briggs, W., & Triola, M. (2014). Statistical reasoning: For everyday life (14th ed.). Boston: Pearson Education, Inc.
I want to commence with a brief, terminological point. Mill uses the term "judgement" interchangeably with the term "proposition," both of which can be defined provisionally as the bearers of truth or falsity. In most of his discussion, however, he uses the language of "propositions;" consequently, I do the same in this paper.
Joseph STRAUBHAAR and Robert LaROSE (2001). Media Now. Communications Media in the Information Age. 3rd Edition. Belmont, Wadsworth/Thompson Learning.
...ss is “made-up” to achieve the desired results. How is one supposed to know which process to use in assessing a belief for reliability and justification if there might be an infinite amount of different processes to choose from? This is a major issue for reliabilists and there is no solution to this problem.
Ever since the original study by Tversky and Kahnerman in 1983, it has been assumed that human reasoning prefers association of terms in lieu of mathematical probabilities in these situations. There is debate, however, as to whether this is a fallacy i...
Joseph STRAUBHAAR and Robert LaROSE (2002). Media Now. Communications Media in the Information Age, 3rd edition. Belmont, Wadsworth/Thompson Learning.
For an example, consider two alternative belief systems A and B consisting of beliefs A1, A2 and B1, B2 respectively. There are two beliefs in each system none of which can justify themselves alone. If A1 → A2 and A2 → A1, then there are 2 inferential connections in A and a high inferential density. Bonjour says this makes A likely. However, if only B1 → B2 and not vice versa, then there is only 1 non-mutual inferential connection in B and thus a low inferential density. Bonjour suggests that lack of mutual justification makes the whole system of B unjustified since B1 must act foundationally.