×

Compatibility of partial or complete conditional probability specifications. (English) Zbl 1138.62311

Summary: The paper deals with the problem of deciding whether or not a set of conditional probabilities are compatible, and if they are, obtaining all the associated compatible joint probabilities. A technique which is called ”rank one extension” is shown to be particularly convenient for identifying all possible compatible distributions corresponding to both complete and partial conditional specifications including the case with zeros. Monitoring the sequential assessment of compatible conditional probabilities and the extension to higher dimensions are also dealt with. The proposed methods are illustrated with several examples.

MSC:

62E99 Statistical distribution theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arnold, B. C.; Gokhale, D. V., On uniform marginal representations of contingency tables, Statist. Probab. Lett., 21, 311-316 (1994) · Zbl 0805.62063
[2] Arnold, B. C.; Gokhale, D. V., Distributions of the most nearly compatible with given families of conditional distributions, The finite discrete case. Test, 7, 377-390 (1998) · Zbl 0955.62053
[3] Arnold, B. C.; Press, S. J., Compatible conditional distributions, J. Amer. Statist. Assoc., 84, 152-156 (1989) · Zbl 0676.62011
[4] Arnold, B. C.; Castillo, E.; Sarabia, J. M., Conditional Specification of Statistical Models, Springer Series in Statistics (1999), Springer: Springer New York · Zbl 0932.62001
[5] Arnold, B. C.; Castillo, E.; Sarabia, J. M., Quantification of incompatibility of conditional and marginal information, Comm. Statist. Theory Methods, 30, 381-395 (2001) · Zbl 1016.60014
[6] Castillo, E.; Gutiérrez, J. M.; Hadi, A. S., Expert Systems and Probabilistic Network Models (1997), Springer: Springer New York
[7] Castillo, E.; Cobo, A.; Jubete, F.; Pruneda, R. E., Orthogonal Sets and Polar Methods in Linear Algebra: Applications to Matrix Calculations, Systems of Equations and Inequalities, and Linear Programming (1999), Wiley: Wiley New York · Zbl 0916.15001
[8] Dawid, A., Conditional independence in statistical theory, J. Roy. Statist. Soc. Ser. B, 41, 1-33 (1979) · Zbl 0408.62004
[9] Dawid, A., Conditional independence for statistical operations, Ann. Statist., 8, 598-617 (1980) · Zbl 0434.62006
[10] Gelman, A.; Speed, T. P., Characterizing a joint probability distribution by conditionals, J. Roy. Statist. Soc. Ser. B, 55, 185-188 (1993) · Zbl 0780.62013
[11] Gelman, A.; Speed, T. P., Corrigendumcharacterizing a joint probability distribution by conditionals, J. Roy. Statist. Soc. Ser. B, 61, 483 (1999)
[12] Lauritzen, S. L.; Spiegelhalter, D. J., Local computations with probabilities on graphical structures and their application to expert systems, J. Roy. Statist. Soc. Ser. B, 50, 157-224 (1988) · Zbl 0684.68106
[13] Pearl, J., Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA
[14] Pérez-Villalta, R., Variables finitas condicionalmente especificadas, Questioó, 24, 425-448 (2000) · Zbl 1138.60304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.