Abstract
Bayes’ rule is universally applied in artificial intelligence and especially in Bayes reasoning, Bayes networks, in decision–making, in generating rules for probabilistic knowledge bases. However, its application requires knowledge about a priori distribution of probability or probability density that frequently is not given. Then, to find at least an approximate solution to a problem, the uniform a priori distribution is used. Do we always have to use this distribution? The paper shows that it is not true. The uniform prior should only be used if there is no knowledge about the real distribution. If however, we possess certain qualitative knowledge, e.g. that the real distribution is the unimodal one, or that its expected value is less than 0.5, then we can use this knowledge and apply a priori distribution being the average distribution of all possible unimodal distributions, instead of the uniform distribution. As a result we will usually get better approximation of the problem solution and will avoid large approximation errors. The paper explains the concept of average distributions and shows how they can be determined with a special method of granulation diminution of elementary events and probability.
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References
Burdzy, K.: The search for certainty. World Scientific, New Jersey (2009)
Frieden, B.R.: Probability, statistical optics, and data testing, 3rd edn. Springer, Heidelberg (2001)
O’Hagan, A., et al.: Uncertain judgement, eliciting experts’ probabilities. Willey, Chichester (2006)
Huber, F., Schmidt-Petri, C.: Degrees of belief. Springer, Science+Business Media B.V. (2009)
Principle of Indifference, http://en.wikipedia.org/wiki/principleofindifference (Cited May 12, 2010)
Bayes’ theorem, http://en.wikipedia.org/wiki/Bayestheorem (Cited May 12, 2010)
Skewness, http://en.wikipedia.org/wiki/Skewness (Cited May 12, 2010)
Keynes, J.K.: A treatise of probability. Macmillan, London (1921)
Li, D., Du, Y.: Artificial intelligence with uncertainty. Chapman & Hall/CRC, Boca Raton (2008)
Paris, J.: The uncertain reasoners companion - a mathematical perspective. Cambridge Tracts in Theoretical Computer Science, vol. 39. Cambridge University Press, Cambridge (1994)
Piegat, A., Landowski, M.: Surmounting information gaps - safe distributions of probability density. In: Metody Informatyki Stosowanej, Komisja Informatyki Polskiej Akademii Nauk Oddzial w Gdansku, Szczecin, Poland, vol. 2(12), pp. 113–126 (2007) (in Polish)
Pouret, O., Naim, P., Marcot, B.: Bayesian networks. In: A practical guide to applications, John Willey & Sons LTD., Chichester (2008)
Russel, R., Norvig, P.: Artificial intelligence - a modern approach, 2nd edn. Prentice Hall, Upper Saddle River (2003)
Yakov, B.H.: Info-gap decision theory - decisions under severe uncertainty, 2nd edn. Academic Press, London (2006)
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Piegat, A., Landowski, M. (2010). Average Prior Distribution of All Possible Probability Density Distributions. In: Nguyen, N.T., Zgrzywa, A., Czyżewski, A. (eds) Advances in Multimedia and Network Information System Technologies. Advances in Intelligent and Soft Computing, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14989-4_18
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DOI: https://doi.org/10.1007/978-3-642-14989-4_18
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