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Probability, Conditional Probability, and Bayes’ Rule

Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

If statistics can be defined as the science that studies uncertainty, then probability is the branch of mathematics that quantifies it. One’s intuition of chance and probability develops at a very early age (Piaget and Inhelder, 1976). However, the formal, precise definition of probability is elusive. There are several competing definitions for the probability of an event, but the most practical one uses its relative frequency in a potentially infinite series of experiments.

Keywords

Conditional Probability Bayesian Network Dose Limit Toxicity Sample Space Venn Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Chapter References

  1. Adel, A. L., Dorr, R. T., Liddil, J. D. (1993). The effect of anticancer drug sequence in experimental combination chemotherapy. Cancer Invest., 11, 1, 15–24.CrossRefGoogle Scholar
  2. Barbeau, E. (1993). The problem of the car and goats. College Math. J., 24, 2, 149–154.Google Scholar
  3. Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond., 53, 370–418.CrossRefGoogle Scholar
  4. Bonferroni, C. E. (1937). Teoria statistica delle classi e calcolo delle probabilita. In Volume in Onore di Ricarrdo dalla Volta, Universita di Firenza, 1–62.Google Scholar
  5. Casscells, W., Schoenberger, A., and Grayboys, T. (1978). Interpretation by physicians of clinical laboratory results. New Engl. J. Med., 299, 999–1000.CrossRefGoogle Scholar
  6. Gillman, L. (1992). The car and the goats, Am. Math. Mon., 99, 1, 3–7.MATHCrossRefMathSciNetGoogle Scholar
  7. Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, Berlin.Google Scholar
  8. Laplace P. S. (1774). Mémoire sur la probabilité des causes par les évenements. Mém. De l’Ac. R. des Sciences de Paris, 6, 621–656.Google Scholar
  9. Lauritzen, S. L. and Spiegelhalter, D. L. (1988). Local computations with probabilities on graphical structures and their application to expert systems. J. R. Stat. Soc. B, 50, 157–194.MATHMathSciNetGoogle Scholar
  10. Piaget, J. and Inhelder B. (1976). The Origin of the Idea of Chance in Children. W.W. Norton & Comp., NY, 276 pp.Google Scholar
  11. Ross, S. (2009). A First Course in Probability, 8th Edition. Prentice Hall.Google Scholar
  12. Selvin, S. (1975). A Problem in Probability. Am. Stat., 29, 1, 67.Google Scholar
  13. Venn, J. (1880). On the employment of geometrical diagrams for the sensible representation of logical propositions. Proc. Cambridge Philos. Soc., 4, 47–59.Google Scholar
  14. Wong, S. K. N., O’Connell, M., Wisdom, J. A., and Dai, H. (2005). Carbon nanotubes as multifunctional biological transporters and near-infrared agents for selective cancer cell destruction. Proc. Natl. Acad. Sci., 102, 11600–11605.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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