Priors: Silent or Active Partners of Bayesian Inference?

Case Studies in Bayesian Statistical Modelling and Analysis

Volumn , Issue , 2012, Pages 30-65

  Choy, Samantha Low ^a,b  

^a Cooperative Research Centre for National Plant Biosecurity ^*  (Australia)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Bayesian analyses in practice, in problem solving inference; Formulation of priors, within Bayesian cycle of learning; Jeffreys' priors and maximum likelihood; Methodology for prior models, one of two main goals; Modelling informative priors; Multi faceted role of priors, in Bayesian inference; Prior and communication of results, success of Bayesian inference; Prior formulation, from 'objective' to 'subjective'; Prior, conditionally conjugate for a parameter; Priors, silent or active partners of Bayesian inference

Indexed keywords

INFERENCE ENGINES; MAXIMUM LIKELIHOOD; PROBLEM SOLVING;

BAYESIAN; BAYESIAN ANALYSIS; BAYESIAN INFERENCE; INFORMATIVE PRIORS; JEFFREYS; METHODOLOGY FOR PRIOR MODELS, ONE OF TWO MAIN GOALS; PRIOR FORMULATION, FROM 'OBJECTIVE' TO 'SUBJECTIVE; PRIOR, CONDITIONALLY CONJUGATE FOR A PARAMETER;

BAYESIAN NETWORKS;

EID: 84949788261     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118394472.ch3     Document Type: Chapter

References (76)

1. Albert I, Donnet S, Guihenneuc-Jouyaux C, Low Choy S, Mengersen K and Rousseau J In press Combining expert opinions in prior elicitation. Bayesian Analysis.
2. Anderson C, Low Choy S, Dominiak B, Gillespie PS, Davis R, Gambley C, Loecker H, Pheloung P, Smith L, Taylor S and Whittle P accepted Biosecurity surveillance systems, plants. In Biosecurity in Agriculture and the Environment (ed. S McKirdy) CABI, Wallingford.
3. Bayarri MJ and Berger JO 2004 The interplay of Bayesian and Frequentist analysis. Statistical Science 19, 58-80.
4. Bayes T and Price R 1763 An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London 53, 370-418.
5. Bedrick EJ, Christensen R and Johnson W 1996 A new perspective on priors for generalized linear models. Journal of the American Statistical Association 91(436), 1450-1460.
6. Bensmail H, Celeux G, Raftery AE and Robert CP 1997 Inference in model-based cluster analysis. Statistics and Computing 7, 1-10.
7. Berger J 2006 The case for objective Bayesian analysis. Bayesian Analysis 1, 385-402.
8. Berger J and Bernardo JM 1992 On the development of reference priors (with discussion). In Bayesian Statistics 4 (eds JM Bernado et al.), pp. 35-60. Oxford University Press, Oxford.
9. Bernardo J 2006 Objective Bayesian statistics: an introduction to Bayesian reference analysis. Postgraduate Tutorial Seminar, Valencia 8/ISBA 2006World Meeting on Bayesian Statistics, Spain.
10. Bernardo JM 1979 Reference posterior distribution for Bayesian inference (with discussion). Journal of the Royal Statistical Society, Series B 41, 113-147.
11. Box GEP and Tiao GC 1982 Bayesian Inference in Statistical Analysis. John Wiley & Sons, Inc., New York.
12. Branscum AJ, JohnsonWO and Thurmond MC 2007 Bayesian beta regression: applications to household expenditure data and genetic distance between foot-and-mouth disease viruses. Australian and New Zealand Journal of Statistics 49(3), 287-301.
13. Burgman M 2005 Risks and Decisions for Conservation and Environmental Management. Ecology, Biodiversity and Conservation. Cambridge University Press, Cambridge.
14. Chaloner KM and Duncan GT 1983 Assessment of a beta prior distribution: PM elicitation. The Statistician 32(1/2), 174-180.
15. Congdon P 2001 Bayesian Statistical Modelling. John Wiley & Sons, Inc., New York.
16. Cooke RM and Goossens LLHJ 2008 TU Delft expert judgment data base. Reliability Engineering and System Safety 93, 657-674.
17. Dawid AP 2004 Probability, causality and the empiricalworld: a Bayes-de Finetti-Popper-Borel synthesis. Statistical Science 19(1), 44-57.
18. de la Place PS 1774 Mémoire sur la probabilité des causes par les événements. Memoires de Mathematique et de Physique 6, 621-656.
19. Denham R and Mengersen K 2007 Geographically assisted elicitation of expert opinion for regression models. Bayesian Analysis 2(1), 99-136.
20. El-Gamal M and Grether D 1995 Are people Bayesian? Uncovering behavioural strategies. Journal of the American Statistical Association 90(432), 1137-1145.
21. Fienberg SE 2006 When did Bayesian inference become 'Bayesian'?. Bayesian Analysis 1, 1-40.
22. Fisher R, O'Leary RA, Low-Choy S, Mengersen K and Caley MJ 2012 Elicit-n: New method and software for eliciting species richness, Environmental Modelling & Software.
23. French S 1986 Calibration and the expert problem. Management Science 32(3), 315-321.
24. French S 2011 Aggregating expert judgement. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales 105, 181-206.
25. Frühwirth-Schnatter S 2006 Finite Mixture and Markov Switching Models. Springer Series in Statistics. Springer, Berlin.
26. Frühwirth-Schnatter S and Wagner H 2011 Bayesian variable selection for random intercept modelling of Gaussian and non-Gaussian data. In Bayesian Statistics 9, pp. 165-200, Oxford University Press, Oxford.
27. Funtowicz SO and Ravetz JR 1993 Science for the post-normal age. Futures 25, 735-755.
28. Garthwaite PH and O'Hagan A 2000 Quantifying expert opinion in the UK water industry: an experimental study. The Statistician 49, 455-477.
29. Gelman A 2006 Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1(3), 515-533.
30. Gelman A, Carlin JB, SternHSand Rubin DB 2004 Bayesian Data Analysis, 2nd edn. Chapman and Hall/CRC, Boca Raton, FL.
31. Genest C and Zidek JV 1986 Combining probability distributions: a critique and an annotated bibliography. Statistical Science 1(1), 114-135.
32. Ghosh JK, Delampady M and Samanta T 2006 An Introduction to Bayesian Analysis: Theory and Methods. Springer, New York.
33. Gill J andWalker LD 2005 Elicited priors for Bayesian model specifications in political science research. Journal of Politics 67(3), 841-872.
34. Goldstein M 2006 Subjective Bayesian analysis: principles and practice. Bayesian Analysis 1, 403-420.
35. Goldstein M 2011 External Bayesian analysis for computer simulators. In Bayesian Statistics 9 (eds JM Bernardo et al.),pp. 201-228. Oxford University Press, Oxford.
36. Hobbs NT and Hilborn R 2006 Alternatives to statistical hypothesis testing in ecology: a guide to self teaching. Ecological Applications 16, 5-19.
37. Hora SC, Hora JA and Dodd NG 1992 Assessment of probability distributions for continuous random variables: a comparison of the bisection and fixed value methods. Organizational Behaviour and Human Decision Processes 51, 135-155.
38. James A, Low Choy S, Murray J and Mengersen K 2010 Elicitator: an expert elicitation tool for regression in ecology. Environmental Modelling & Software 25(1), 129-145.
39. Johnson S, Low Choy S and Mengersen K 2011 Integrating Bayesian networks and geographic information systems: good practice examples. Integrated Environmental Assessment and Management, published online 19 September, doi: 10.1002/ieam.262.
40. Kadane JB, Dickey JM, Winkler RL, Smith WS and Peters SC 1980 Interactive elicitation of opinion for a normal linear model. Journal of the American Statistical Association 75, 845-854.
41. Kass RE and Greenhouse JB 1989 Comments on the paper by J. H. Ware. Statistical Science 4(4), 310-317.
42. Langhammer PF, Bakarr MI, Bennun LA, Brooks TM, Clay RP, Darwall W, Silva ND, Edgar GJ, Eken G, Fishpool LDC, da Fonseca GAB, Foster MN, Knox DJ, Matiku P, Radford EA, Rodrigues ASL, Salaman P, Sechrest W and Tordoff AW 2007 Identification and gap analysis of key biodiversity areas: targets for comprehensive protected area systems. Best Practice Protected Area Guidelines Series no. 15, IUCN (The World Conservation Union), Gland, Switzerland. ( accessed 9 May 2012).
43. Leal J, Wordsworth S, Legood R and Blair E 2007 Eliciting expert opinion for economic models: an applied example. Value in Health 10(3), 195-203.
44. Lindley D 1983 Reconciliation of probability distributions. Operations Research 31(5), 866-880.
45. Lindley DV 1956 On a measure of the information provided by an experiment. Annals of Mathematical Statistics 27, 986-1005.
46. Lipscomb J, Parmigiani G and Hasselblad V 1998 Combining expert judgment by hierarchical modeling: an application to physician staffing. Management Science 44, 149-161.
47. Low Choy S and Wilson T 2009 How do experts think about statistics? Hints for improving undergraduate and postgraduate training. International Association for Statistics Education Satellite Conference Proceedings, Durban, South Africa. ( accessed 9 May 2012).
48. Low Choy S, James A, Murray J and Mengersen K 2011 Elicitator: a user-friendly, interactive tool to support the elicitation of expert knowledge. In Expert Knowledge and Its Applications in Landscape Ecology (eds AH Perera, CA Drew and CJ Johnson), pp. 39-67. Springer.
49. Low Choy S, Mengersen K and Rousseau J 2008 Encoding expert opinion on skewed nonnegative distributions. Journal of Applied Probability and Statistics 3, 1-21.
50. Low Choy S, Murray J, James A and Mengersen K 2010 Indirect elicitation from ecological experts: from methods and software to habitat modelling and rock-wallabies. In Handbook of Applied Bayesian Analysis (eds A O'Hagan and M West). Oxford University Press, Oxford.
51. MarinJMand Robert CP 2007 Bayesian Core: A practical approach to computational Bayesian statistics. Springer, Berlin.
52. McCarthy M 2007 Bayesian Methods for Ecology. Cambridge University Press, Cambridge.
53. Morgan MG, Pitelka LF and Shevliakova E 2001 Elicitation of expert judgments of climate change impacts on forest ecosystems. Climate Change 49, 279-307.
54. Murray J, Low Choy S, Possingham H and Goldizen A 2008 The importance of ecological scale for wildlife conservation in naturally fragmented environments: a case study of the brush-tailed rock-wallaby (Petrogale penicillata). Biological Conservation 141, 7-22.
55. Murray JV, Goldizen AW, O'Leary RA, McAlpine CA, Possingham H and Low Choy S 2009 How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise?Acase study using brush-tailed rock-wallabies Petrogale penicillata. Journal of Applied Ecology 46, 842-851.
56. Oakley JE and O'Hagan A 2007 Uncertainty in prior elicitations: a nonparametric approach. Biometrika 94, 427-441.
57. Oakley JE and O'Hagan A 2010 SHELF: the Sheffield Elicitation Framework (version 2.0). School of Mathematics and Statistics, University of Sheffield.
58. O'Hagan A, Buck CE, Daneshkhah A, Eiser R, Garthwaite P, Jenkinson D, Oakley J and Rakow T 2006 Uncertain Judgements: Eliciting Experts' Probabilities. John Wiley & Sons, Inc., Hoboken, NJ.
59. O'Leary R, Low Choy S, Murray J, Kynn M, Denham R, Martin T and Mengersen K 2009 Comparison of three elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby Petrogale penicillata. Environmetrics 20, 379-398.
60. O'Leary R, Murray J, Low Choy S and Mengersen K 2008 Expert elicitation for Bayesian classification trees. Journal of Applied Probability and Statistics 3(1), 95-106.
61. Plous S 1993 The Psychology of Judgment and Decision Making. McGraw-Hill, New York.
62. Roback PJ and Givens GH 2001 Supra-Bayesian pooling of priors linked by a deterministic simulation model. Communications in Statistics - Simulation and Computation 30(3), 447-476.
63. Robert CP 1996 Mixtures of distributions: inference and estimation. In Markov Chain Monte Carlo in Practice (eds WR Gilks, S Richardson and DJ Spiegelhalter), pp. 441-464. Chapman & Hall, London.
64. Speirs-Bridge A, Fidler F, McBride M, Flander L, CummingGand Burgman M 2010 Reducing overconfidence in the interval judgments of experts. Risk Analysis 30(3), 512-523.
65. Spetzler CS and Staël von Holstein CAS 1975 Probability encoding in decision analysis. Management Science 22(3), 340-358.
66. Spiegelhalter DJ, Adams KR and Myles JP 2004 Bayesian Approaches to Clinical Trials and Health-Care Evaluation. Statistics in Practice. John Wiley & Sons, Ltd, Chichester.
67. Stephens M 1997 Bayesian methods for mixtures of normal distributions. PhD thesis. Faculty of Mathematical Sciences.
68. Stigler SM 1986 Laplace's 1774 memoir on inverse probability. Statistical Science 1(3), 359-363.
69. Stone M 1961 The opinion pool. Annals of Mathematical Statistics 32(4), 1339-1342.
70. Strauss H and Zeigler L 1975 The Delphi technique and its uses in social science research. Journal of Creative Behaviour 9, 253-259.
71. Tebaldi C, Sanso B and Smith RL 2011 Characterizing uncertainty of future climate change projections using hierarchical Bayesian models. In Bayesian Statistics 9, Proceedings of the Ninth Valencia International Meeting, 3-8 June 2010 (eds JM Bernardo et al.), pp. 639-658. Oxford University Press, Oxford.
72. Tuyl F, Gerlach R and Mengersen K 2008 A comparison of Bayes-Laplace, Jeffreys, and other priors: the case of zero events. The American Statistician 62(1), 40-44.
73. Uusitalo L 2007 Advantages and challenges of Bayesian networks in environmental modelling. Ecological Modelling 203, 312-318.
74. West M 1985 Generalized linear models: scale parameters, outlier accommodation and prior distributions. In Bayesian Statistics 2 (eds JM Bernardo et al.). North-Holland, Amsterdam.
75. Williams K, LowChoy S, Rochester Wand Alston C 2011 Using Bayesian mixture models that combine expert knowledge and GIS data to define ecoregions. In Expert Knowledge and its Application in Landscape Ecology (eds AH Perera, CA Drew and CJ Johnson), pp. 229-251. Springer, New York.
76. Zellner A and Siow A 1980 Posterior Odds Ratios for Selected Regression Hypotheses (with discussion), pp. 585-603. Oxford University Press, Oxford.