Probabilidade Intervalar e Cadeias de Markov Intervalares no Maple

Authors

  • M.A. CAMPOS
  • G.P. Dimuro
  • A.C.R. COSTA
  • J.F.F. Araújo
  • A.M. DIAS

DOI:

https://doi.org/10.5540/tema.2002.03.02.0053

Abstract

O objetivo deste trabalho é, inicialmente, apresentar uma implementação do cálculo de probabilidades intervalares utilizando o Maple. Foram desenvolvidos duas bibliotecas: Mat-Int, que contempla procedimentos para os operadores intervalares básicos da matemática intervalar, incluindo a álgebra matricial intervalar, e Prob-Int, para a implementação da probabilidade intervalar, contendo procedimentos para o cálculo de probabilidades intervalares para variáveis aleatórias discretas. A seguir, apresenta-se a noção de cadeia de Markov intervalar e sua implementação no Maple. Ao final, descreve-se uma aplicação utilizando os conceitos propostos.

References

[1] J.F.F. Araújo, “Probabilidades Intervalares com Aplicações no Maple”, ESIN/UCPel, Pelotas, RS, 2001. (disponível em http://gmc.ucpel.tche.br/fmc)

H. Bunke e T. Caelli (Eds), Hidden Markov models applied in computer vision, em “Machine Perception and Artificial Intelligence”, World Scientific, Vol. 45, 2001.

M.A. Campos, “Uma Extensão Intervalar para a Probabilidade Real”, Tese de Doutorado, Centro de Informática, UFPE, PE, 1997.

M.A. Campos, Interval probabilities, application to discrete ramdom variables, em “Seleta do XXII CNMAC” (E.X.L. de Andrade, J.M. Balthazar, S.M. Gomes, G.N. Silva, A. Sri Ranga, eds.), Tendências em Matemática Aplicada e Computacional, Vol. 1, No. 2, pp. 333-344, SBMAC, 2000.

A.M. Dias e G.P. Dimuro, “Matemática Intervalar com Aplicações no Maple”, ESIN/UCPel, Pelotas, 2000. (disponível em http://gmc.ucpel.tche.br/mat-int)

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, 23, No. 1 (1991), 5-48.

U.W. Kulisch e W.L. Miranker, “Computer Arithmetic in Theory and Practice”, Academic Press, New York, 1981.

H.E. Kyburg Jr., “Interval-valued Probabilities”, (disponível em http://www.ensmain.rug.ac.be/ ipp, acessado em Maio, 2002).

M.B. Monagan, K.O. Geddes, K.M. Heal, G. Labahn and S.M. Vorkoetter, “Maple V: Program. Guide”, Springer, New York, 1998.

R.E. Moore,“Methods and Applications of Interval Analysis”, SIAM, Philadelphia, 1979.

A. Neumaier, “Interval Methods for Systems of Equations”, Cambridge University Press, Cambridge, 1990.

B. Tessem, Interval probability pPropagation, International Journal of Approximate Reasoning, 7 (1992), 95-120.

K. Weichselberger, Axiomatic foundations of the theory of interval-probability, em “Symposia Gaussiana, Conference B: Statistical Sciences”, pp 47-64, Munich, 1993.

W. Yoselogff, “Finite Mathematics”, Worth Publishing, New York, 1975.

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Published

2002-06-01

How to Cite

CAMPOS, M., Dimuro, G., COSTA, A., Araújo, J., & DIAS, A. (2002). Probabilidade Intervalar e Cadeias de Markov Intervalares no Maple. Trends in Computational and Applied Mathematics, 3(2), 53–62. https://doi.org/10.5540/tema.2002.03.02.0053

Issue

Vol. 3 No. 2 (2002)

Section

Original Article

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