Luceños' discretization method and its application in decision making under ambiguity

ISIPTA 2007 - Proceedings of the 5th International Symposium on Imprecise Probability: Theories and Applications

Volumn , Issue , 2007, Pages 327-336

  Obermeier, Michael ^a   Augustin, Thomas ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Decision making under ambiguity; Discretization; Gaussian quadrature; Imprecise probabilities; Interval probability; Linear programming; Luce o; Numerical integration

Indexed keywords

DISCRETIZATIONS; GAUSSIAN QUADRATURES; IMPRECISE PROBABILITIES; INTERVAL PROBABILITY; NUMERICAL INTEGRATIONS;

DECISION MAKING; DISCRETE EVENT SIMULATION; LINEAR PROGRAMMING; PROBABILITY DISTRIBUTIONS; SAMPLING; VOLUME MEASUREMENT;

PROBABILISTIC LOGICS;

EID: 84883221897     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. A. S. Ahmad. Statistical Analysis of Heaping and Rounding Effects. Dissertation. Department of Statistics, Univ. of Munich, 2006.
2. T. Augustin. Expected Utility within a Generalized Concept of Probability - A Comprehensive Framework for Decision Making under Ambiguity. Stat. Pap., 43: 5-22, 2002a.
3. T. Augustin. Neyman-Pearson Testing under Interval Probability by Globally Least Favorable Pairs. Reviewing Huber-Strassen Theory and Extending it to General Interval Probability. J. Stat. Plan. Inf., 105: 149-173, 2002b.
4. F. G. Cozman. Credal Networks. Artif. Intell.. 120: 199-233, 2000.
5. S. Ferson et al. Constructing probability boxes and Dempster-Shafer structures. Technical Report (SAND 2002-4015), Sandia National Laboratories, 2003.
6. W. Gautschi. Algorithm 726: ORTHPOL - A Package of Routines for Generating Orthogonal Polynomials and Gauss-Type Quadrature Rules. ACM Trans. Math. Software, 20: 21- 62, 1994.
7. P. J. Huber and V. Strassen. Minimax Tests and the Neyman-Pearson Lemma for Capacities. Ann. Stat., 1: 251-263, Correction, 2: 223-224, 1973.
8. J. F. Kenney and E. S. Keeping. Mathematics of Statistics, Part 2, 2nd edition, D. Van Nostrand Company, INC, 1951.
9. D. Kikuti, F. G. Cozman and C. P. de Campos. Partially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities, In: R. Brafman, U. Junker (eds.): Multidisciplinary IJCAI-05 Workshop on Advances in Preference Handling, Edinburgh, Scotland, 118-123, 2005. see also http://wikix.ilog.fr/wiki/pub/Preference05/WsProceedings/Pref05.pdf.
10. A. Luceño. Discrete Approximations to Continous Univariate Distributions - An Alternative to Simulation. J. Roy. Stat. Soc., B 61: 345-352, 1999.
11. M. Obermeier. Luceños Diskretisierungstechnik für stetige Verteilungen - Implementierung und Anwendung. Diploma thesis, Dep. of Statistics, Univ. of Munich, 2006.
12. R.A. Sack and A.F. Donavan. An Algorithm for Gaussian Quadrature given Modified Moments. Numer. Math., 18: 465-478, 1971/72.
13. W. F. Sheppard. On the Calculation of the most Probable Values of Frequency Constants for Data Arranged according to Equidistant Division of a Scale. Proc. London Math. Soc., 29: 353-380, 1898.
14. D. Skulj. Jeffrey's Conditioning Rule in Neighbourhood Models. Int. J. Approx. Reasoning, 42: 192-211, 2006.
15. J. Stoer and R. Bulirsch. Numerische Mathematik I. Springer, 1999.
16. M. C. M. Troffaes. Decision Making under Uncertainty using Imprecise Probabilities. Int. J. Approx. Reasoning, in press, 2007.
17. L. V. Utkin and T. Augustin. Powerful algorithms for decision making under partial prior information and general ambiguity attitudes. In: F.G. Cozman, R. Nau and T. Seidenfeld (eds.) Proc. of the 4th Int. Symposium on Imprecise Probabilities and their Applications (ISIPTA '05), 349-358, 2005.
18. S. B. Vardeman. Sheppard's Correction for Variances and the "Quantization Noise Model". IEEE Trans. Instr. Meas., 54: 2117- 2119, 2005.
19. P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, 1991.
20. A. Wallner. Bi-elastic Neighbourhood Models. In: J.-M. Bernard, T. Seidenfeld, and M. Zaffalon (eds) Proc. of the 3rd Int. Symposium on Imprecise Probabilities and their Applications (ISIPTA '03), 593-607, 2003.
21. K. Weichselberger. Elementare Grundbegriffe einer allgemeinen Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als umfassendes Konzept. Physica, 2001.
22. J. C. Wheeler. Rocky Mountain. J. Math., 4: 287-296, 1974.