Talking probabilities: communicating probabilistic information with words and numbers

The number of knowledge-based systems that build on Bayesian belief networks is increasing. The construction of such a network however requires a large number of probabilities in numerical form. This is often considered a major obstacle, one of the reasons being that experts are reluctant to provide numerical probabilities. The use of verbal probability expressions as an additional method of eliciting probabilistic information may to some extent remove this obstacle. In this paper, we review studies that address the communication of probabilities in words and/or numbers. We then describe our own experiments concerning the development of a probability scale that contains words as well as numbers. This scale appears to be an aid for researchers and domain experts during the elicitation phase of building a belief network and might help users understand the output of the network. ” 1999 Elsevier Science Inc. All rights reserved.

[1]  Chris Elsaesser,et al.  Explanation of Probabilistic Inference , 1987, Conference on Uncertainty in Artificial Intelligence.

[2]  Dennis T. Kennedy,et al.  An Applied Study Using the Analytic Hierarchy Process to Translate Common Verbal Phrases to Numerical Probabilities , 1997 .

[3]  A. Gifi,et al.  NONLINEAR MULTIVARIATE ANALYSIS , 1990 .

[4]  Robert M. Hamm,et al.  Selection of verbal probabilities: A solution for some problems of verbal probability expression. , 1991 .

[5]  Marek J. Druzdzel.  Qualitative Verbal Explanations in Bayesian Belief Networks , 1996 .

[6]  Marek J. Druzdzel,et al.  Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information , 1995, UAI.

[7]  Wibecke Brun,et al.  Verbal probabilities: Ambiguous, context-dependent, or both? , 1988 .

[8]  Forrest W. Young,et al.  Introduction to Multidimensional Scaling: Theory, Methods, and Applications , 1981 .

[9]  Michael J. Olson,et al.  Patterns of preference for numerical and verbal probabilities. , 1997 .

[10]  D. Budescu,et al.  Consistency in interpretation of probabilistic phrases , 1985 .

[11]  Elke U. Weber,et al.  Contextual Effects in the Interpretations of Probability Words: Perceived Base Rate and Severity of Events , 1990 .

[12]  S S Mol,et al.  [Is usually more often than frequently; or how often is sometimes?]. , 1992, Nederlands tijdschrift voor geneeskunde.

[13]  David A. Schkade,et al.  Numeric and linguistic information representation in multiattribute choice , 1991 .

[14]  D R Timmermans,et al.  Lost for words: using verbal terms to express probabilities in oral radiology. , 1993, Dento maxillo facial radiology.

[15]  Alf Zimmer,et al.  Verbal Vs. Numerical Processing of Subjective Probabilities , 1983 .

[16]  E Reiss.  In quest of certainty. , 1984, The American journal of medicine.

[17]  P J Lucas,et al.  Converting a rule-based expert system into a belief network. , 1993, Medical informatics = Medecine et informatique.

[18]  How medical professionals evaluate expressions of probability. , 1987, The New England journal of medicine.

[19]  Steen Andreassen,et al.  MUNIN - A Causal Probabilistic Network for Interpretation of Electromyographic Findings , 1987, IJCAI.

[20]  Benjamin Kuipers,et al.  Critical Decisions under Uncertainty: Representation and Structure , 1990, Cogn. Sci..

[21]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[22]  David V. Budescu,et al.  Decisions based on numerically and verbally expressed uncertainties. , 1988 .

[23]  Paul Krause,et al.  Representing Uncertain Knowledge , 1993, Springer Netherlands.

[24]  F. Mosteller,et al.  Quantifying Probabilistic Expressions , 1990 .

[25]  J H Galla,et al.  Properdin deficiency with IgA nephropathy. , 1981, The New England journal of medicine.

[26]  Keung-Chi Ng,et al.  A Sensitivity Analysis of Pathfinder: A Follow-Up Study , 1991, UAI.

[27]  J Kievit,et al.  How do surgeons' probability estimates of operative mortality compare with a decision analytic model? , 1996, Acta psychologica.

[28]  Helmut Jungermann,et al.  Rarely occurring headaches and rarely occurring blindness: Is rarely=rarely? The meaning of verbal frequentistic labels in specific medical contexts. , 1996 .

[29]  Piero P. Bonissone,et al.  Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-off Precision and Complexity , 1985, UAI.

[30]  W O Robertson.  Quantifying the meanings of words. , 1983, JAMA.

[31]  Geoffrey R. Norman,et al.  Expressions of probability: words and numbers. , 1980 .

[32]  Eelko Huizingh,et al.  A comparison of verbal and numerical judgments in the analytic hierarchy process , 1997 .

[33]  S. Schiffman.  Introduction to Multidimensional Scaling , 1981 .

[34]  J. Fox,et al.  Alternatives to Bayes? , 1980, Methods of Information in Medicine.

[35]  Ido Erev,et al.  Revision of opinion with verbally and numerically expressed uncertainties , 1990 .

[36]  P F van der Stelt,et al.  Blind chance? An investigation into the perceived probabilities of phrases used in oral radiology for expressing chance. , 1993, Dento maxillo facial radiology.

[37]  M. Nakao,et al.  Numbers are better than words. Verbal specifications of frequency have no place in medicine. , 1983, The American journal of medicine.

[38]  Robert Ramberg,et al.  Computational advice and explanations - behavioural and computational aspects , 1995, INTERACT.

[39]  R M Kenney,et al.  Between never and always. , 1981, The New England journal of medicine.

[40]  Gregory M. Provan,et al.  The Sensitivity of Belief Networks to Imprecise Probabilities: An Experimental Investigation , 1996, Artif. Intell..

[41]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

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

[43]  Forrest W. Young,et al.  Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features , 1977 .

[44]  Cheryl Frenck-Mestre,et al.  Determinants of numerical versus verbal probabilities , 1993 .

[45]  Silja Renooij,et al.  How to Elicit Many Probabilities , 1999, UAI.

[46]  D. Budescu,et al.  Preferences and reasons for communicating probabilistic information in verbal or numerical terms , 1993 .

[47]  Ruth Beyth-Marom,et al.  How probable is probable? A numerical translation of verbal probability expressions , 1982 .

[48]  L D Cohn,et al.  Adolescents' misinterpretation of health risk probability expressions. , 1995, Pediatrics.

[49]  José Mira Mira,et al.  DIAVAL, a Bayesian expert system for echocardiography , 1997, Artif. Intell. Medicine.

[50]  Rami Zwick,et al.  Comparing the calibration and coherence of numerical and verbal probability judgments , 1993 .

[51]  Marek J Druzdzel,et al.  Verbal Expressions of Probability in Informed Consent Litigation , 1991, Medical decision making : an international journal of the Society for Medical Decision Making.

[52]  I. Erev,et al.  Verbal versus numerical probabilities: Efficiency, biases, and the preference paradox☆ , 1990 .

[53]  Gregory M. Provan,et al.  Why is diagnosis using belief networks insensitive to imprecision in probabilities? , 1996, UAI.

[54]  P. Groenen,et al.  Modern Multidimensional Scaling: Theory and Applications , 1999 .

[55]  G R Norman,et al.  Expressions of probability: words and numbers. , 1980, The New England journal of medicine.

[56]  R. Darlington,et al.  Regression and Linear Models , 1990 .

[57]  A. Tenbrunsel,et al.  Organizational Behavior and Human Decision Processes , 2013 .

[58]  B J O'Brien,et al.  Words or numbers? The evaluation of probability expressions in general practice. , 1989, The Journal of the Royal College of General Practitioners.

[59]  P. Lucas,et al.  Computer-based Decision Support in the Management of Primary Gastric non-Hodgkin Lymphoma , 1998, Methods of Information in Medicine.

[60]  Henrik I. Christensen,et al.  Use of causal probabilistic networks as high-level models in computer vision , 1990 .