{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T03:08:16Z","timestamp":1791515296962,"version":"4.3.4"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T00:00:00Z","timestamp":1521504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["LP0990135"],"award-info":[{"award-number":["LP0990135"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The use of expert knowledge to quantify a Bayesian Network (BN) is necessary when data is not available. This however raises questions regarding how opinions from multiple experts can be used in a BN. Linear pooling is a popular method for combining probability assessments from multiple experts. In particular, Prior Linear Pooling (PrLP), which pools opinions and then places them into the BN, is a common method. This paper considers this approach and an alternative pooling method, Posterior Linear Pooling (PoLP). The PoLP method constructs a BN for each expert, and then pools the resulting probabilities at the nodes of interest. The advantages and disadvantages of these two methods are identified and compared and the methods are applied to an existing BN, the Wayfinding Bayesian Network Model, to investigate the behavior of different groups of people and how these different methods may be able to capture such differences. The paper focusses on six nodes Human Factors, Environmental Factors, Wayfinding, Communication, Visual Elements of Communication and Navigation Pathway, and three subgroups Gender (Female, Male), Travel Experience (Experienced, Inexperienced), and Travel Purpose (Business, Personal), and finds that different behaviors can indeed be captured by the different methods.<\/jats:p>","DOI":"10.3390\/e20030209","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T15:59:39Z","timestamp":1521561579000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Prior and Posterior Linear Pooling for Combining Expert Opinions: Uses and Impact on Bayesian Networks\u2014The Case of the Wayfinding Model"],"prefix":"10.3390","volume":"20","author":[{"given":"Charisse","family":"Farr","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD 4000, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7655-6254","authenticated-orcid":false,"given":"Fabrizio","family":"Ruggeri","sequence":"additional","affiliation":[{"name":"Consiglio Nazionale delle Ricerche, Istituto di Matematica Applicata e Tecnologie Informatiche, 20133 Milano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kerrie","family":"Mengersen","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD 4000, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,20]]},"reference":[{"key":"ref_1","unstructured":"Johnson, S. (2009). Integrated Bayesian Network Frameworks for Modelling Complex Ecological Issues. [Ph.D. Thesis, School of Mathematical Sciences, Faculty of Science and Technology, Queensland University of Technology]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.envsoft.2006.03.006","article-title":"Parameterisation and evaluation of a Bayesian network for use in an ecological risk assessment","volume":"22","author":"Pollino","year":"2007","journal-title":"Environ. Model. Softw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1089\/106652700750050961","article-title":"Using Bayesian Networks to Analyze Expression Data","volume":"7","author":"Friedman","year":"2000","journal-title":"J. Comput. Biol."},{"key":"ref_4","unstructured":"Heckerman, D. (1990). Probabilistic Similarity Networks, Stanford University Departments of Computer Science and Medicine. Technical Report STN-CS-1316."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.forsciint.2003.08.004","article-title":"A general approach to Bayesian networks for the interpretation of evidence","volume":"139","author":"Taroni","year":"2004","journal-title":"Forensic Sci. Int."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"O\u2019Hagan, A., Buck, C.E., Daneshkhah, A., Eiser, R., Garthwaite, P., Jenkinson, D., Oakley, J., and Rakow, T. (2006). Uncertain Judgements: Eliciting Experts\u2019 Probabilities, John Wiley & Sons.","DOI":"10.1002\/0470033312"},{"key":"ref_7","first-page":"114","article-title":"Combining probability distributions: A critique and annoted bibliography","volume":"1","author":"Genest","year":"1986","journal-title":"Stat. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1214\/12-BA717","article-title":"Combining Expert Opinions in Prior Elicitation","volume":"7","author":"Albert","year":"2012","journal-title":"Bayesian Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF00140056","article-title":"Aggregating opinions through logarithmic pooling","volume":"17","author":"Genest","year":"1984","journal-title":"Theory Decis."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1002\/for.1071","article-title":"The geometric combination of Bayesian forecasting models","volume":"27","author":"Faria","year":"2008","journal-title":"J. Forecast."},{"key":"ref_11","unstructured":"Farr, A., Mengersen, K., Ruggeri, F., and Simpson, D.P. (2018). Combining Opinions for Use in Bayesian Networks: A Measurement Error Approach, Unpublished work."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"90","DOI":"10.3846\/16484142.2014.898695","article-title":"Investigating effective wayfinding in airports: A Bayesian network approach","volume":"29","author":"Farr","year":"2014","journal-title":"Transport"},{"key":"ref_13","unstructured":"Pearl, J. (1985, January 15\u201317). Bayesian networks: A model of self-activated memory for evidential reasoning. Proceedings of the 7th Conference of the Cognitive Science Society, Irvine, CA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/0004-3702(86)90072-X","article-title":"Fusion, Propagation, and Structuring in Belief Networks","volume":"29","author":"Pearl","year":"1986","journal-title":"Artif. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Korb, K., and Nicholson, A. (2011). Bayesian Artificial Intelligence, CRC Press.","DOI":"10.1201\/b10391"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jensen, F., and Nielsen, T. (2007). Bayesian Networks and Decision Graphs, Information Science and Statistics; Springer. [2nd ed.].","DOI":"10.1007\/978-0-387-68282-2"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1111\/1467-9868.00340","article-title":"Chain Graph Models and Their Causal Interpretation","volume":"64","author":"Lauritzen","year":"2002","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_18","unstructured":"Pearl, J. (1988). Probabilistic Reasoning in Intelligent System, Morgan Kaufmann."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Darwiche, A. (2009). Modeling and Reasoning with Bayesian Networks, Cambridge University Press.","DOI":"10.1017\/CBO9780511811357"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kj\u00e6rulff, U., and Madsen, A.L. (2008). Bayesian Networks and Influence Diagrams\u2014A Guide to Construction and Analysis. Information Science and Statistics, Springer.","DOI":"10.1007\/978-0-387-74101-7"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/j.ecolmodel.2006.11.033","article-title":"Advantages and Challenges of Bayesian Networks in Environmental Modelling","volume":"203","author":"Uusitalo","year":"2007","journal-title":"Ecol. Model."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1890\/ES12-00357.1","article-title":"Modeling the viability of the free-ranging cheetah population in Namibia: An object-oriented Bayesian network approach","volume":"4","author":"Johnson","year":"2013","journal-title":"Ecosphere"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1111\/rssc.12228","article-title":"Dynamic Bayesian network inferencing for non-homogeneous complex systems","volume":"67","author":"Wu","year":"2018","journal-title":"J. R. Stat. Soc. Ser. C"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1080\/01621459.1981.10477661","article-title":"Marginalization and Linear Opinion Pools","volume":"71","author":"McConway","year":"1981","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_25","unstructured":"Kyburg, H.E., and Smokler, H.E. (1964). Foresight: Its Logical Laws, Its Subjective Scores. Studies in Subjective Probability, Wiley."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/0013916584161001","article-title":"Cognitive mapping of large-scale environments the interrelationship of action plans, acquisition, and orientation","volume":"16","author":"Book","year":"1984","journal-title":"Environ. Behav."},{"key":"ref_27","first-page":"129","article-title":"Modeling Spatial Knowledge","volume":"2","author":"Kuipers","year":"1978","journal-title":"Cogn. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0304-4009(81)90018-8","article-title":"Wayfinding: A conceptual framework","volume":"5","author":"Passini","year":"1981","journal-title":"Urban Ecol."},{"key":"ref_29","unstructured":"Passini, R. (1984). Wayfinding in Architecture, Van Nostrand Reinhold Company."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1177\/0013916590225001","article-title":"Finding the building in wayfinding","volume":"25","author":"Peponis","year":"1990","journal-title":"Environ. Behav."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1007\/3-540-55966-3_21","article-title":"A conceptual model of wayfinding using multiple levels of abstraction","volume":"Volume 639","author":"Frank","year":"1992","journal-title":"Theories and Methods of Spatio-Temporal Reasoning in Geographic Space"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1061\/TPEJAN.0000845","article-title":"Human Orientation in Transportation Terminals","volume":"2","author":"Braaksma","year":"1980","journal-title":"Transp. Eng. J. ASCE"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"41","DOI":"10.3141\/1662-05","article-title":"Development of a new orientation index for airport terminals","volume":"1662","author":"Dada","year":"1999","journal-title":"Transp. Res. Rec."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1002\/atr.5670180307","article-title":"Quantitative Evaluation of Passenger Terminal Orientation","volume":"18","author":"Tosic","year":"1984","journal-title":"J. Adv. Transp."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1177\/0013916591235002","article-title":"Effects of Signage and Floor Plan Configuration on Wayfinding Accuracy","volume":"23","year":"1991","journal-title":"Environ. Behav."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1080\/01441647.2012.712555","article-title":"Wayfinding: A simple concept, a complex process","volume":"32","author":"Farr","year":"2012","journal-title":"Transp. Rev."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.eswa.2012.07.026","article-title":"A proposed validation framework for expert elicited Bayesian Networks","volume":"40","author":"Pitchforth","year":"2013","journal-title":"Exp. Syst. 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