A distance measure for bounding probabilistic belief change

We propose a distance measure between two probability distributions, which allows one to bound the amount of belief change that occurs when moving from one distribution to another. We contrast the proposed measure with some well known measures, including KL-divergence, showing how they fail to be the basis for bounding belief change as is done using the proposed measure. We then present two practical applications of the proposed distance measure: sensitivity analysis in belief networks and probabilistic belief revision. We show how the distance measure can be easily computed in these applications, and then use it to bound global belief changes that result from either the perturbation of local conditional beliefs or the accommodation of soft evidence. Finally, we show that two well known techniques in sensitivity analysis and belief revision correspond to the minimization of our proposed distance measure and, hence, can be shown to be optimal from that viewpoint.

[1]  Linda C. van der Gaag,et al.  Making Sensitivity Analysis Computationally Efficient , 2000, UAI.

[2]  R. Jeffrey The Logic of Decision , 1984 .

[3]  P. Diaconis,et al.  Updating Subjective Probability , 1982 .

[4]  Enrique F. Castillo,et al.  Sensitivity analysis in discrete Bayesian networks , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[5]  A. A. J. Marley,et al.  The Logic of Decisions. , 1972 .

[6]  Silja Renooij,et al.  Analysing Sensitivity Data from Probabilistic Networks , 2001, UAI.

[7]  R. Jeffrey Probability and the Art of Judgment , 1992 .

[8]  L. C. van der Gaag,et al.  A Computational Architecture for N-Way Sensitivity Analysis of Bayesian Networks , 2000 .

[9]  L. J. Savage,et al.  Probability and the weighing of evidence , 1951 .

[10]  I. Good Good Thinking: The Foundations of Probability and Its Applications , 1983 .

[11]  Huaiyu Zhu On Information and Sufficiency , 1997 .

[12]  Adnan Darwiche,et al.  When do Numbers Really Matter? , 2001, UAI.

[13]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[14]  Adnan Darwiche,et al.  A differential approach to inference in Bayesian networks , 2000, JACM.

[15]  Kathryn B. Laskey Sensitivity analysis for probability assessments in Bayesian networks , 1995, IEEE Trans. Syst. Man Cybern..

[16]  A. Hasman,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[17]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.