Dependence of Bayesian Model Selection Criteria and Fisher Information Matrix on Sample Size

Mathematical Geosciences

Volumn 43, Issue 8, 2011, Pages 971-993

  Lu, Dan ^a   Ye, Ming ^a   Neuman, Shlomo P ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ARIZONA   (United States)

Author keywords

Asymptotic analysis; Drift models; Model selection; Model uncertainty; Prior model probability; Variogram models

Indexed keywords

DRIFT MODEL; MODEL SELECTION; MODEL UNCERTAINTY; PRIOR MODEL PROBABILITY; VARIOGRAM MODELS;

ASYMPTOTIC ANALYSIS; BAYESIAN NETWORKS; COVARIANCE MATRIX; FISHER INFORMATION MATRIX; INFORMATION THEORY; MARKOV PROCESSES; MODEL STRUCTURES; MONTE CARLO METHODS; UNCERTAINTY ANALYSIS;

COMPUTER SIMULATION;

AUTOCORRELATION; BAYESIAN ANALYSIS; COMPUTER SIMULATION; GEOSTATISTICS; MODELING; MONTE CARLO ANALYSIS; PROBABILITY; RANKING; UNCERTAINTY ANALYSIS; VARIOGRAM;

EID: 80855141656     PISSN: 18748961     EISSN: 18748953     Source Type: Journal    
DOI: 10.1007/s11004-011-9359-0     Document Type: Article

References (62)

1. Akaike H (1974) New look at statistical model identification. IEEE Trans Autom Control AC-19: 716-722.
2. Berk R (1966) Limiting behavior of posterior distributions when the model is incorrect. Ann Math Stat 37: 51-58.
3. Bernardo JM, Smith AFM (1994) Bayesian theory. Wiley, Chichester.
4. Burnham KP, Anderson DR (2002) Model selection and multiple model inference: a practical information-theoretical approach, 2nd edn. Springer, New York.
5. Burnham KP, Anderson DR (2004) Multimodel inference-understanding AIC and BIC in model selection. Sociol Methods Res 33(2): 261-304 conditions: 3. Application to synthetic and field data. Water Resour Res 22(2): 228-242.
6. Chib S (1995) Marginal likelihood from the Gibbs output. J Am Stat Assoc 90: 1313-1321.
7. Cressie N (1993) Statistics of spatial data. Wiley, New York.
8. Deutsch CV, Journel AG (1998) GSLIB: Geostatistical software library and user's guide, 2nd edn. Oxford Univ Press, New York.
9. Draper D (1995) Assessment and propagation of model uncertainty. J R Stat Soc B 57(1): 45-97.
10. Draper D (2007) Bayesian multilevel analysis and MCMC. In: de Leeuw J (ed) Handbook of Quantitative Multilevel Analysis. Springer, New York, Chapter 3.
11. Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis, 1st edn. Chapman & Hall, USA.
12. Hastings W (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1): 97-109.
13. Hoeksema RJ, Kitanidis PK (1985) Analysis of the spatial structure of properties of selected aquifers. Water Resour Res 21(4): 563-572.
14. Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: A tutorial. Stat Sci 14(4): 382-417.
15. Hurvich CM, Tsai CL (1989) Regression and time series model selection in small sample. Biometrika 76(2): 99-104.
16. Jeffreys H (1961) Theory of probability, 3rd edn. Oxford University Press, Oxford.
17. Journel AG, Rossi ME (1989) When do we need a trend model in kriging? Math Geol 21(7): 715-739.
18. Kashyap RL (1982) Optimal choice of AR and MA parts in autoregressive moving average models. IEEE Trans Pattern Anal Mach Intell 4(2): 99-104.
19. Kass RE, Vaidyanathan SK (1992) Approximate Bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. J R Stat Soc, Ser B, Stat Methodol 54(1): 129-144.
20. Kass RE, Raftery AE (1995) Bayesian factor. J Am Stat Assoc 90: 773-795.
21. Kitanidis PK, Lane RW (1985) Maximum likelihood parameter estimation of hydrologic spatial processes by the Gaussian-Newton method. J Hydrodyn 79: 53-71.
22. Kyriakidis PC, Journel AG (1999) Geostatistical space-time models: a review. Math Geol 31(6): 651-684.
23. Lewis SM, Raftery AE (1997) Estimating Bayes factor via posterior simulation with the Laplace-Metropolis estimator. J Am Stat Assoc 92(438): 648-655.
24. Leuangthong O, Deutsch CV (2004) Transformation of residuals to avoid artifacts in geostatistical modeling with a trend. Math Geol 36(3): 287-305.
25. Marchant BP, Lark RM (2004) Estimating variogram uncertainty. Math Geol 36(8): 867-898.
26. Marchant BP, Lark RM (2007) The Matern variogram model: implications for uncertainty propagation and sampling in geostatistical surveys. Geoderma 140: 337-345.
27. Marshall L, Nott D, Sharma A (2004) A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling. Water Resour Res 40: W02501. doi: 10. 1029/2003WR002378.
28. Marshall L, Nott D, Sharma A (2005) Hydrological model selection: A Bayesian alternative. Water Resour Res 41: W10422. doi: 10. 1029/2004WR003719.
29. Matérn B (1986) Spatial variation. Springer, Berlin.
30. McBratney AB, Webster R (1986) Choosing functions for semi-variogram of soil properties and fitting them to sampling estimates. J Soil Sci 37: 617-639.
31. Mosteller F, Wallace DL (1964) Inference and disputed authorship: the federalist. Addison-Wesley, Reading.
32. Neath AA, Cavanaugh JE (1997) Regression and time series model selection using variants of the Schwarz information criterion. Commun Stat, Theory Methods 26: 559-580.
33. Neuman SP (2003) Maximum likelihood Bayesian averaging of alternative conceptual-mathematical models. Stoch Environ Res Risk Assess 17(5): 291-305.
34. Neuman SP, Xue L, Ye M, Lu D (2011) Bayesian analysis of data-worth considering model and parameter uncertainties. Adv Water Resour doi: 10. 1016/j. advwaters. 2011. 02007.
35. Nowak W (2010) Measures of parameter uncertainty in geostatistical estimation and geostatistical optimal design. Math Geosci 42(2): 199-221.
36. Nowak W, de Barros FPJ, Rubin Y (2010) Bayesian geostatistical design: task-driven optimal site investigation when the geostatistical model is uncertain. Water Resour Res 46: W03535. doi: 10. 1029/2009WR008312.
37. Ortiz CJ, Deutsch CV (2002) Calculation of uncertainty in the variogram. Math Geol 34(2): 169-183.
38. Pardo-Iguzquiza E, Dowd P (2001) Variance-covariance matrix of the experimental variogram: assessing variogram uncertainty. Math Geol 33(4): 397-419.
39. Pardo-Iguzquiza E, Chico-Olmo M, Garcia-Soldado MJ, Luque-Espinar JA (2009) Using semivariogram parameter uncertainty in hydrogeological applications. Ground Water 47(1): 25-34.
40. Poeter EP, Anderson DA (2005) Multimodel ranking and inference in ground water modeling. Ground Water 43(4): 597-605.
41. Poeter EP, Hill MC (2007) MMA, A computer code for multi-model analysis. US Geological Survey Techniques and Methods TM6-E3.
42. Raftery AE (1995) Bayesian model selection in social research. Sociol Method 25: 111-163.
43. Riva M, Willmann M (2009) Impact of log-transmissivity variogram structure on groundwater flow and transport predictions. Adv Water Resour 32: 1311-1322.
44. Riva M, Panzeri M, Guadagnini A, Neuman SP (2011) Role of model selection criteria in geostatistical inverse estimation of statistical data- and model-parameters. Water Resour Res 47: W07502. doi: 10. 1029/2011WR010480.
45. Rissanen J (1978) Modeling by shortest data description. Automatica 14: 465-471.
46. Rojas R, Feyen L, Dassargues A (2008) Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resour Res 44: W12418. doi: 10. 1029/2008WR006908.
47. Rojas R, Batelaan O, Feyen L, Dassargues A (2010a) Assessment of conceptual model uncertainty for the regional aquifer Pampa del Tamarugal-North Chile. Hydrol Earth Syst Sci 14(2): 171-192.
48. Rojas R, Kahunde S, Peeters L, Batelaan O, Feyen L, Dassargues A (2010b) Application of a multimodel approach to account for conceptual model and scenario uncertainties in groundwater modelling. J Hydrol 394(3-4): 416-435.
49. Rojas R, Feyen L, Batelaan O, Dassargues A (2010c) On the value of conditioning data to reduce conceptual model uncertainty in groundwater modeling. Water Resour Res 46: W08520. doi: 10. 1029/2009WR008822.
50. Samper FJ, Neuman SP (1989a) Estimation of spatial covariance structures by adjoint state maximum likelihood cross-validation: 1. Theory. Water Resour Res 25(3): 351-362.
51. Samper FJ, Neuman SP (1989b) Estimation of spatial covariance structures by adjoint state maximum likelihood cross-validation: 2. Synthetic experiments. Water Resour Res 25(3): 363-371.
52. Singh A, Walker DD, Minsker BS, Valocchi AJ (2010) Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework. Stoch Environ Res Risk Assess. doi: 10. 1007/s00477-010-0384-1.
53. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2): 461-464.
54. Tsai FTC, Li X (2010) Reply to comment by Ming Ye et al. on "Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window". Water Resour Res 46: W02802. doi: 10. 1029/2009WR008591.
55. Tsai FTC, Li X (2008a) Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window. Water Resour Res 44: W09434. doi: 10. 1029/2007WR006576.
56. Tsai FTC, Li X (2008b) Multiple parameterization for hydraulic conductivity identification. Ground Water 46(6): 851-864.
57. Ye M, Neuman SP, Meyer PD (2004) Maximum Likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff. Water Resour Res 40: W05113. doi: 10. 1029/2003WR002557.
58. Ye M, Neuman SP, Meyer PD, Pohlmann KF (2005) Sensitivity analysis and assessment of prior model probabilities in MLBMA with application to unsaturated fractured tuff. Water Resour Res 41: W12429. doi: 10. 1029/2005WR004260.
59. Ye M, Meyer PD, Neuman SP (2008a) On model selection criteria in multimodel analysis. Water Resour Res 44: W03428. doi: 10. 1029/2008WR006803.
60. Ye M, Pohlmann KF, Chapman JB (2008b) Expert elicitation of recharge model probabilities for the Death Valley regional flow system. J Hydrol 354: 102-115. doi: 10. 1016/j. jhydrol. 2008. 03. 001.
61. Ye M, Pohlmann KF, Chapman JB, Pohll GM, Reeves DM (2010a) A model-averaging method for assessing groundwater conceptual model uncertainty. Ground Water. doi: 10. 1111/j. 1745-6584. 2009. 00633. x.
62. Ye M, Lu D, Neuman SP, Meyer PD (2010b) Comment on "Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window by Frank T.-C. Tsai and Xiaobao Li. Water Resour Res 46: W02801. doi: 10. 1029/2009WR008501.