Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

Journal of Hydrology

Volumn 536, Issue , 2016, Pages 255-272

  Rajabi, Mohammad Mahdi ^a   Ataie Ashtiani, Behzad ^a,b  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^b FLINDERS UNIVERSITY   (Australia)

Author keywords

Expert knowledge; Fuzzy Bayes; Groundwater modeling; Markov chain Monte Carlo; Polymorphic uncertainty; Polynomial chaos expansions

Indexed keywords

ALGORITHMS; AQUIFERS; BAYESIAN NETWORKS; FUZZY INFERENCE; GROUNDWATER; GROUNDWATER GEOCHEMISTRY; GROUNDWATER RESOURCES; MARKOV PROCESSES; NUMERICAL MODELS; PARAMETER ESTIMATION; STATISTICAL TESTS; UNCERTAINTY ANALYSIS;

EXPERT KNOWLEDGE; FUZZY-BAYES; GROUNDWATER MODELING; MARKOV CHAIN MONTE-CARLO; POLYMORPHIC UNCERTAINTY; POLYNOMIAL CHAOS EXPANSION;

INFERENCE ENGINES;

ALGORITHM; BAYESIAN ANALYSIS; COASTAL AQUIFER; COMPUTER SIMULATION; FUZZY MATHEMATICS; GROUNDWATER; HYDROLOGICAL MODELING; KNOWLEDGE; MARKOV CHAIN; MONTE CARLO ANALYSIS; NUMERICAL METHOD; SALINE INTRUSION; UNCERTAINTY ANALYSIS;

ARABIAN SEA; HORMOZGAN; INDIAN OCEAN; IRAN; KISH ISLAND; PERSIAN GULF;

EID: 84960392704     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2016.02.029     Document Type: Article

References (77)

1. Ataie-Ashtiani B., Rajabi M.M., Ketabchi H. Inverse modelling for freshwater lens in small islands: Kish Island, Persian Gulf. Hydrol. Process. 2013, 27(19):2759-2773.
2. Ataie-Ashtiani B., Ketabchi H., Rajabi M.M. Optimal management of a freshwater lens in a small island using surrogate models and evolutionary algorithms. J. Hydrol. Eng. 2013, 19(2):339-354.
3. Askey, R., Wilson, J., 1985, Some Basic Hypergeometric Polynomials that Generalize Jacobi Polynomials, Memoirs of the American Mathematical Society. AMS, Providence, RI, pp. 319.
4. Beal M.J. Variational Algorithms for Approximate Bayesian Inference 2003, University of London.
5. Bear J. Seawater Intrusion in Coastal Aquifers 1999, Springer Science & Business Media.
6. Beer M., Ferson S., Kreinovich V. Imprecise probabilities in engineering analyses. Mech. Syst. Signal Process. 2013, 37(1):4-29.
7. Berger J.O. Robust Bayesian analysis: sensitivity to the prior. J. Stat. Plan. Inferen. 1990, 25(3):303-328.
8. Berger J.O. An overview of robust Bayesian analysis. Test 1994, 3:5-124.
9. Carrera J., Alcolea A., Medina A., Hidalgo J., Slooten L.J. Inverse problem in hydrogeology. Hydrogeol. J. 2005, 13(1):206-222.
10. Carrera J., Hidalgo J.J., Slooten L.J., Vázquez-Suñé E. Computational and conceptual issues in the calibration of seawater intrusion models. Hydrogeol. J. 2010, 18(1):131-145.
11. Choy S.L., O'Leary R., Mengersen K. Elicitation by design in ecology: using expert opinion to inform priors for Bayesian statistical models. Ecology 2009, 90(1):265-277.
12. Coolen F.P.A., Newby M.J. Bayesian reliability analysis with imprecise prior probabilities. Reliab. Eng. Syst. Safety 1994, 43(1):75-85.
13. Cui T., Fox C., O'Sullivan M.J. Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm. Water Resour. Res. 2011, 47(10).
14. Destercke S., Dubois D., Chojnacki E. Unifying practical uncertainty representations - I: generalized p-boxes. Int. J. Approximate Reasoning 2008, 49(3):649-663.
15. Dong W., Shah H.C. Vertex method for computing functions of fuzzy variables. Fuzzy Sets Syst. 1987, 24(1):65-78.
16. Dubois D., Prade H. A review of fuzzy set aggregation connectives. Inf. Sci. 1985, 36(1):85-121.
17. Elsheikh A.H., Hoteit I., Wheeler M.F. Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates. Comput. Methods Appl. Mech. Eng. 2014, 269:515-537.
18. Ferson S., Hajagos J.G. Arithmetic with uncertain numbers: rigorous and (often) best possible answers. Reliab. Eng. Syst. Safety 2004, 85(1):135-152.
19. Frühwirth-Schnatter S. On fuzzy Bayesian inference. Fuzzy Sets Syst. 1993, 60(1):41-58.
20. Gelman A.G., Rubin D.B. Inference from iterative simulation using multiple sequences. Stat. Sci. 1992, 7:457-472.
21. Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Statistics 4 1992, 169-193. Oxford University Press, Oxford, U.K. J.M. Bernardo, J. Berger, A.P. Dawid, A.F.M. Smith (Eds.).
22. Ghanem R. Probabilistic characterization of transport in heterogeneous media. Comput. Methods Appl. Mech. Eng. 1998, 158(3):199-220.
23. Graf W., Götz M., Kaliske M. Analysis of dynamical processes under consideration of polymorphic uncertainty. Struct. Saf. 2015, 52:194-201.
24. Haario H., Saksman E., Tamminen J. An adaptive Metropolis algorithm. Bernoulli 2001, 223-242.
25. Haario H., Laine M., Mira A., Saksman E. DRAM: efficient adaptive MCMC. Stat. Comput. 2006, 16(4):339-354.
26. Hassan A.E., Bekhit H.M., Chapman J.B. Uncertainty assessment of a stochastic groundwater flow model using GLUE analysis. J. Hydrol. 2008, 362(1):89-109.
27. Hassan A.E., Bekhit H.M., Chapman J.B. Using Markov Chain Monte Carlo to quantify parameter uncertainty and its effect on predictions of a groundwater flow model. Environ. Modell. Softw. 2009, 24(6):749-763.
28. Huber P.J. The use of Choquet capacities in statistics. Bull. Internat. Stat. Inst. 1973, 45(4):181-191.
29. Journel A.G. Constrained interpolation and qualitative information-the soft kriging approach. Math. Geol. 1986, 18(3):269-286.
30. Kaliske M., Serafinska A., Zopf C. Optimized and robust design of tires based on numerical simulation. Tire Sci. Technol. 2013, 41(1):21-39.
31. Karagiannis G., Lin G. Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic input. J. Comput. Phys. 2014, 259:114-134.
32. Ketabchi H., Ataie-Ashtiani B. Assessment of a parallel evolutionary optimization approach for efficient management of coastal aquifers. Environ. Modell. Softw. 2015, 74:21-38.
33. Ketabchi H., Ataie-Ashtiani B. Review: coastal groundwater optimization-advances, challenges, and practical solutions. Hydrogeol. J. 2015, 23(6):1129-1154.
34. Khaleghi B., Khamis A., Karray F.O., Razavi S.N. Multisensor data fusion: a review of the state-of-the-art. Inform. Fusion 2013, 14(1):28-44.
35. Klir G.J. Uncertainty and Information: Foundations of Generalized Information Theory 2005, John Wiley & Sons.
36. Krueger T., Page T., Hubacek K., Smith L., Hiscock K. The role of expert opinion in environmental modelling. Environ. Modell. Softw. 2012, 36:4-18.
37. Kuhnert P.M., Martin T.G., Griffiths S.P. A guide to eliciting and using expert knowledge in Bayesian ecological models. Ecol. Lett. 2010, 13(7):900-914.
38. Laloy E., Rogiers B., Vrugt J.A., Mallants D., Jacques D. Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion. Water Resour. Res. 2013, 49(5):2664-2682.
39. Lavine M. An approach to robust Bayesian analysis for multidimensional parameter spaces. J. Am. Stat. Assoc. 1991, 86(414):400-403.
40. Lavine M. Sensitivity in Bayesian statistics: the prior and the likelihood. J. Am. Stat. Assoc. 1991, 86(414):396-399.
41. Lele S.R., Allen K.L. On using expert opinion in ecological analyses: a frequentist approach. Environmetrics 2006, 17(7):683-704.
42. Lele S.R., Das A. Elicited data and incorporation of expert opinion for statistical inference in spatial studies. Math. Geol. 2000, 32(4):465-487.
43. Levenberg K. A method for the solution of certain non-linear problems in least squares. Quart. Appl. Math. 1944, 2:164-168.
44. Li H., Zhang D. Probabilistic collocation method for flow in porous media: comparisons with other stochastic methods. Water Resour. Res. 2007, 43(9):W09409.
45. Li Y., Chen J., Feng L. Dealing with uncertainty: a survey of theories and practices. Knowl. Data Eng, IEEE Transact. 2013, 25(11):2463-2482.
46. Mahmoodzadeh D., Ketabchi H., Ataie-Ashtiani B., Simmons C.T. Conceptualization of a fresh groundwater lens influenced by climate change: a modeling study of an arid-region island in the Persian Gulf, Iran. J. Hydrol. 2014, 519:399-413.
47. Malinverno A., Briggs V.A. Expanded uncertainty quantification in inverse problems: hierarchical Bayes and empirical Bayes. Geophysics 2004, 69(4):1005-1016.
48. Marshall L., Nott D., Sharma A. A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling. Water Resour. Res. 2004, 40:W02501.
49. Marzouk Y.M., Najm H.N. Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems. J. Comput. Phys. 2009, 228(6):1862-1902.
50. Marzouk Y.M., Xiu D.B. A stochastic collocation approach to Bayesian inference in inverse problems. Commun. Comput. Phys. 2009, 6:826-847.
51. Möller B., Beer M. Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics 2004, Springer Science & Business Media.
52. O'Hagan A., Oakley J.E. Probability is perfect, but we can't elicit it perfectly. Reliab. Eng. Syst. Saf. 2004, 85(1):239-248.
53. O'Hagan A. Probabilistic uncertainty specification: overview, elaboration techniques and their application to a mechanistic model of carbon flux. Environ. Modell. Softw. 2012, 36:35-48.
54. Page T., Heathwaite A.L., Thompson L.J., Pope L., Willows R. Eliciting fuzzy distributions from experts for ranking conceptual risk model components. Environ. Modell. Softw. 2012, 36:19-34.
55. Rajabi M.M., Ataie-Ashtiani B. Sampling efficiency in Monte Carlo based uncertainty propagation strategies: application in seawater intrusion simulations. Adv. Water Resour. 2014, 67:46-64.
56. Rajabi M.M., Ataie-Ashtiani B., Simmons C.T. Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations. J. Hydrol. 2015, 520:101-122.
57. Rajabi M.M., Ataie-Ashtiani B., Janssen H. Efficiency enhancement of optimized Latin hypercube sampling strategies: application to Monte Carlo uncertainty analysis and meta-modeling. Adv. Water Resour. 2015, 76:127-139.
58. Rinderknecht S.L., Borsuk M.E., Reichert P. Bridging uncertain and ambiguous knowledge with imprecise probabilities. Environ. Modell. Softw. 2012, 36:122-130.
59. Rinderknecht S.L., Albert C., Borsuk M.E., Schuwirth N., Künsch H.R., Reichert P. The effect of ambiguous prior knowledge on Bayesian model parameter inference and prediction. Environ. Modell. Softw. 2014, 62:300-315.
60. Ríos Insua D., Ruggeri F. Robust Bayesian Analysis 2000, Springer, New York.
61. Ross J., Ozbek M., Pinder G.F. Hydraulic conductivity estimation via fuzzy analysis of grain size data. Math. Geol. 2007, 39(8):765-780.
62. Ross J., Ozbek M., Pinder G.F. Aleatoric and epistemic uncertainty in groundwater flow and transport simulation. Water Resour. Res. 2009, 45:12.
63. Royall R.M. Statistical Evidence: A Likelihood Primer 1997, Chapman & Hall, London, UK.
64. Sadegh M., Vrugt J.A. Approximate bayesian computation using Markov chain Monte Carlo simulation: DREAM (ABC). Water Resour. Res. 2014, 50(8):6767-6787.
65. Sandri S., Dubois D., Kalfsbeek H.W. Elicitation, assessment, and pooling of expert judgments using possibility theory. Fuzzy Syst., IEEE Transact. 1995, 3(3):313-335.
66. Scholten L., Scheidegger A., Reichert P., Maurer M. Combining expert knowledge and local data for improved service life modeling of water supply networks. Environ. Modell. Softw. 2013, 42:1-16.
67. Schoups G., Vrugt J.A. A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors. Water Resour. Res. 2010, 46(10).
68. Stein M., Beer M., Kreinovich V. Bayesian approach for inconsistent information. Inf. Sci. 2013, 245:96-111.
69. Viertl R. Is it necessary to develop a fuzzy Bayesian inference?. Probability and Bayesian Statistics 1987, 471-475. Springer, US.
70. Viertl R., Hule H. On Bayes' theorem for fuzzy data. Stat. Pap. 1991, 32(1):115-122.
71. Viertl R., Hareter D. Generalized Bayes' theorem for non-precise a-priori distribution. Metrika 2004, 59(3):263-273.
72. Viertl R. Fuzzy Bayesian Inference 2008, Springer, Berlin, Heidelberg, pp. 10-15.
73. Viertl R. Statistical Methods for Fuzzy Data 2011, John Wiley & Sons.
74. Voss, C.I., Provost, A.M., 2010. SUTRA, a model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. U.S. Geological Survey, Water-Resources Investigations, Open-File Report 02-4231.
75. Werner A.D., Bakker M., Post V.E., Vandenbohede A., Lu C., Ataie-Ashtiani B., Simmons C.T., Barry D.A. Seawater intrusion processes, investigation and management: recent advances and future challenges. Adv. Water Resour. 2013, 51:3-26.
76. Woodbury A.D., Ulrych T.J. A full-Bayesian approach to the groundwater inverse problem for steady state flow. Water Resour. Res. 2000, 36(8):2081-2093.
77. Zadeh L.A. The concept of a linguistic variable and its application to approximate reasoning I, II, III. Inform. Sci. 1975, 8(3). pp. 199-249, 301-357, 9, 43-80.