Abstract
The theory behind Bayesian Belief Networks (BBN) and Bayes’ theorem is becoming increasingly applicable in economic decision-making in today’s human capital and economic markets across all business, government, and commercial segments in the new global economy. The economic end state of these markets is clearly to maximize stakeholder wealth effectively and efficiently. The question remains, are we? To respond to this question, this chapter provides a discussion of quintessential Bayes’, scope, motivation, intent, utility of the theorem and BBN. Then an introduction to Bayes’ Theorem and BBN and a discussion of inductive versus deductive logic, Popper’s logic of scientific discovery, frequentist versus Bayesian (subjective) views and philosophy, the identification of the truth, finally a classic illustration of the Monty Hall Game Show Paradox.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The basis for the data consist of a 10,000 rows of randomly generated data from a Monte Carlo experiment to build up to and including a four node BBN.
- 2.
E. T. Jaynes, in his book, Probability Theory: The Logic of Science (Jaynes, 1995) suggests the concept of plausible reasoning is a limited form of deductive logic and “The theory of plausible reasoning” …“is not a weakened form of logic; it is an extension of logic with new content not present at all in conventional deductive logic” (p. 8).
- 3.
In the BBN literature, researchers refer to this knowledge as subjective and originates from a priori (prior) probabilities.
- 4.
We computed the (marginal) probability of event A using the law of total probability as: P(A) = P(A, B)+P(A, B ′) = P(A | B)∗ P(B)+P(A | B ′)∗ P(B ′) = 95. 0 % ∗1. 0 %+5. 0 % ∗99. 0 % = 0. 95 %+4. 95 % = 5. 9 %.
- 5.
We computed this as: 490. 1 % = (95 % − 16. 1 %)∕16. 1 %.
- 6.
This term is not statistical but practical in nature.
- 7.
Parameters are statistical reference points such as means and standard deviations, etc.
- 8.
We conducted this search on January 1, 2016. When I first published Strategic Economic Decision-Making: Using Bayesian Belief Networks to Solve Complex Problems (Grover, 2013), there were only 4,000,000 hits.
- 9.
In Bayesian epistemology, P(B | A) is a hypothesis of our initial beliefs. This states that the probability of event B given A is conditioned on a form of evidence, A. (See http://plato.stanford.edu/entries/epistemology-bayesian/ (14 September 2016) for a thorough conversation of this topic.)
- 10.
This means it is occurring at the same time and on the same trial of the experiment.
- 11.
Often we gather these starting points, from observable data. It turns out that this is acceptable, due to the learning that occurs by the algorithm, when we add multiple observable events to the BBN.
- 12.
For Door 1, we compute this as: P(Car Door1 | Contestant Door1, Host Door2) = P(Car Door1, Contestant Door1, Host Door2)∕P(Contestant Door1, Host Door2) = 0. 333333 = 0. 055556∕(0. 055556 + 0. 000000 + 0. 111111).
- 13.
For Door 1, we compute this as: P(Car Door1 | Contestant Door1, Host Door3) = P(Car Door1, Contestant Door1, Host Door3)∕P(Contestant Door1, Host Door3) = 0. 333333 = 0. 055556∕(0. 055556 + 0. 111111 + 0. 000000).
- 14.
For Door 2, we compute this as: P(Car Door2 | Contestant Door2, Host Door1) = P(Car Door2, Contestant Door2, Host Door1)∕P(Contestant Door2, Host Door1) = 0. 333333 = 0. 055556∕(0. 000000 + 0. 055556 + 0. 111111).
- 15.
For Door 1, we compute this as: P(Car Door1 | Contestant Door2, Host Door3) = P(Car Door1, Contestant Door2, Host Door3)∕P(Contestant Door2, Host Door3) = 0. 666667 = 0. 111111∕(0. 111111 + 0. 055556 + 0. 000000).
- 16.
For Door 2, we compute this as: P(Car Door2 | Contestant Door3, Host Door1) = P(Car Door2, Contestant Door3, Host Door1)∕P(Contestant Door3, Host Door1) = 0. 666667 = 0. 111111∕(0. 000000 + 0. 111111 + 0. 055556).
- 17.
For Door 1, we compute this as: P(Car Door1 | Contestant Door3, Host Door2) = P(Car Door1, Contestant Door3, Host Door2)∕P(Contestant Door3, Host Door2) = 0. 666667 = 0. 111111∕(0. 111111 + 0. 000000 + 0. 055556).
- 18.
Ruling out rows 1, 5, and 9 are key to solving this problem.
References
Bolstad, W. M. (2007). Introduction to Bayesian statistics (2nd ed.). Hoboken, NJ: Wiley.
Cox, R. T. (1946). Probability, frequency, and reasonable expectation. American Journal of Physics, 14, 1–13.
Fine, T. L. (2004). The “only acceptable approach” to probabilistic reasoning. In E. T. Jaynes (Ed.), Probability theory: The logic of science. Cambridge: Cambridge University Press; (2003). SIAM News, 37(2), 758.
Grover, J. (2013) Strategic economic decision-making: Using Bayesian belief networks to solve complex problems. SpringerBriefs in Statistics (Vol. 9). New York: Springer Science+Business Media. doi:10.1007/978-1-4614-6040-4_1.
Jaynes, E. T. (1995). Probability theory: The logic of science. http://shawnslayton.com/open/Probability%2520book/book.pdf. Accessed 26 June 2012.
Joyce, J. (2008). In E. N. Zalta (Ed.),“Bayes’ theorem”. The Stanford encyclopedia of philosophy (Fall 2008 ed.). http://plato.stanford.edu/archives/fall2008/entries/bayes-theorem/. Accessed 1 July 2012.
Kendall, M. G. (1949). On the reconciliation of theories of probability. Biometrika (Biometrika Trust), 36(1/2), 101–116. doi:10.1093/biomet/36.1-2.101.
Keynes, J. M. (1921). A treatise on probability: Macmillan and Co. Universal digital library. Collection: Universallibrary. Retrieved from http://archive.org/details/treatiseonprobab007528mbp. Accessed 15 June 2012.
Krauss, S., & Wang, X. T. (2003). The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser. Journal of Experimental Psychology: General, 132(1), 3–22. doi:10.1037/0096-3445.132.1.3. Retrieved 14 September 2016 from http://usd-apps.usd.edu/xtwanglab/Papers/MontyHallPaper.pdf
Monty Hall problem (2015, August 28). Retrieved September 4, 2015 from http://en.wikipedia.org/wiki/Monty_Hall_problem
Mueser, P. R., & Granberg, D. (1999). The Monty Hall Dilemma revisited: Understanding the interaction of problem definition and decision making. Working Paper 99–06, University of Missouri. Retrieved 6 November 2016 from http://econpapers.repec.org/paper/wpawuwpex/9906001.htm
New International Version. Biblica, 2011. Bible Gateway. Web 14 Sep. 2016.
Peterson, E. H. The Message. Bible Gateway. Web. 14 Sep. 2016.
Selvin, S. (1975a, February). A problem in probability (letter to the editor). American Statistician, 29 (1), 67. JSTOR 2683689.
Selvin, S. (1975b, August). On the Monty Hall problem (letter to the editor). American Statistician, 29(3), 134. JSTOR 2683443.
vos Savant, M. (1990a, September 9). Ask Marilyn. Parade Magazine: 16.
vos Savant, M. (1991a, February 17). Ask Marilyn. Parade Magazine: 12.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this chapter
Cite this chapter
Grover, J. (2016). Introduction. In: The Manual of Strategic Economic Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-319-48414-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-48414-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48413-6
Online ISBN: 978-3-319-48414-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)