Sequential information gathering schemes for spatial risk and decision analysis applications

  • Jo Eidsvik
  • Gabriele Martinelli
  • Debarun Bhattacharjya
Original Paper
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Abstract

Several risk and decision analysis applications are characterized by spatial elements: there are spatially dependent uncertain variables of interest, decisions are made at spatial locations, and there are opportunities for spatial data acquisition. Spatial dependence implies that the data gathered at one coordinate could inform and assist a decision maker at other locations as well, and one should account for this learning effect when analyzing and comparing information gathering schemes. In this paper, we present concepts and methods for evaluating sequential information gathering schemes in spatial decision situations. Static and sequential information gathering schemes are outlined using the decision theoretic notion of value of information, and we use heuristics for approximating the value of sequential information in large-size spatial applications. We illustrate the concepts using a Bayesian network example motivated from risks associated with CO2 sequestration. We present a case study from mining where there are risks of rock hazard in the tunnels, and information about the spatial distribution of joints in the rocks may lead to a better allocation of resources for choosing rock reinforcement locations. In this application, the spatial variables are modeled by a Gaussian process. In both examples there can be large values associated with adaptive information gathering.

Keywords

Value of information Spatial risk analysis Spatial statistics Sequential information Adaptive testing Bayesian networks Gaussian processes 
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References

  1. Azzimonti D, Bect J, Chevalier C, Ginsbourger D (2016) Quantifying uncertainties on excursion sets under a Gaussian random field prior. SIAM/ASA J Uncertain Quant 4:850–874CrossRefGoogle Scholar
  2. Baio G (2012) Bayesian methods in health economics. CRC Press, Boca RatonCrossRefGoogle Scholar
  3. Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis of spatial data, 2nd edn. CRC Press, Boca RatonGoogle Scholar
  4. Bellman RE (1957) Dynamic Programming. Princeton University Press, PrincetonGoogle Scholar
  5. Bhattacharjya D, Eidsvik J, Mukerji T (2010) The value of information in spatial decision making. Math Geosci 42:141–163CrossRefGoogle Scholar
  6. Bhattacharjya D, Eidsvik J, Mukerji T (2013) The value of information in portfolio problems with dependent projects. Decis Anal 10:341–351CrossRefGoogle Scholar
  7. Bonneau M, Gaba S, Peyrard N, Sabbadin R (2014) Reinforcement learning-based design of sampling policies under cost constraints in Markov random fields: application to weed map reconstruction. Comput Stat Data Anal 72:30–44CrossRefGoogle Scholar
  8. Bratvold RB, Bickel JE, Lohne HP (2009) Value of information in the oil and gas industry: past, present, and future. SPE: Reserv Eval Eng 12:630–638Google Scholar
  9. Brown DB, Smith JE (2013) Optimal sequential exploration: Bandits, clairvoyants, and wildcats. Operat Res 60:262–274Google Scholar
  10. Chen Y, Javdani S, Karbasi A, Bagnell JA, Srinivasa S, Krause A (2015) Submodular surrogates for value of information. In: Proceedings of the 29th AAAI conference on Artif Intel pp 3511–3518Google Scholar
  11. Chiles JP, Delfiner P (2012) Geostatistics: modeling spatial uncertainty, 2nd edn. Wiley, HobokenCrossRefGoogle Scholar
  12. Convertino M, Munoz-Carpena R, Kiker GA, Perz SG (2015) Design of optimal ecosystem monitoring networks: hotspot detection and biodiversity patterns. Stoch Environ Res Risk Assess 29:1085–1101CrossRefGoogle Scholar
  13. Cressie N (1993) Statistics for spatial data. Wiley, HobokenGoogle Scholar
  14. Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, HobokenGoogle Scholar
  15. Dobbie MJ, Henderson BL, Stevens DL (2008) Sparse sampling: spatial design for monitoring stream networks. Stat Surv 2:113–153CrossRefGoogle Scholar
  16. Dyer JS, Sarin R (1979) Measurable multiattribute value functions. Operat Res 27:810–822CrossRefGoogle Scholar
  17. Eidsvik J, Bhattacharjya D, Mukerji T (2008) Value of information of seismic amplitude and CSEM resistivity. Geophysics 73:R59–R69CrossRefGoogle Scholar
  18. Eidsvik J, Mukerji T, Bhattacharjya D (2015) Value of information in the earth sciences. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  19. Ellefmo SL, Eidsvik J (2009) Local and spatial joint frequency uncertainty and its application to rock mass characterization. Rock Mech Rock Eng 42:667–688CrossRefGoogle Scholar
  20. Evangelou E, Eidsvik J (2017) The value of information for correlated GLMs. J Stat Plan Inference 180:30–48CrossRefGoogle Scholar
  21. Golovin D, Krause A (2011) Adaptive submodularity: theory and applications in active learning and stochastic optimization. J Artif Intel Res 42:427–486Google Scholar
  22. Goodson JC, Thomas BW, Ohlmann JW (2017) A rollout algorithm framework for heuristic solutions to finite horizon stochastic dynamic programs. Eur J Operat Res 258:216–229CrossRefGoogle Scholar
  23. Howard R (1966) Information value theory. IEEE Trans Sys Sci Cybern 2:22–26CrossRefGoogle Scholar
  24. Howard R, Abbas A (2015) Foundations of decision analysis. Prentice Hall, Upper Saddle RiverGoogle Scholar
  25. Karam KS, Karam JS, Einstein HH (2007) Decision analysis applied to tunnel exploration planning I: principles and case study. J Constr Eng Manag 133:344–353CrossRefGoogle Scholar
  26. Keisler JM, Collier Z, Chu E, Sinatra N, Linkov I (2014) Value of information analysis: the state of application. Environ Syst Decis 34:3–23CrossRefGoogle Scholar
  27. Krause A, Guestrin C (2009) Optimal value of information in graphical models. J Artif Intel Res 35:557–591Google Scholar
  28. Le ND, Zidek JV (2006) Statistical analysis of environmental space-time processes. Springer, BerlinGoogle Scholar
  29. Lilleborge M, Hauge R, Eidsvik J (2016) Information gathering in Bayesian networks applied to petroleum prospecting. Math Geosci 48:233–257CrossRefGoogle Scholar
  30. Malczewski J (2006) GIS-based multicriteria decision analysis: a survey of the literature. Int J Geogr Inf Sci 20:703–726CrossRefGoogle Scholar
  31. Martinelli G, Eidsvik J, Hauge R, Forland MD (2011) Bayesian networks for prospect analysis in the North Sea. AAPG Bull 95:1423–1442CrossRefGoogle Scholar
  32. Martinelli G, Eidsvik J, Hauge R (2013a) Dynamic decision making for graphical models applied to oil exploration. Eur J Operat Res 230:688–702CrossRefGoogle Scholar
  33. Martinelli G, Eidsvik J, Sinding-Larsen R, Rekstad S, Mukerji T (2013b) Building Bayesian networks from basin modeling scenarios for improved geological decision making. Pet Geosci 19:289–304CrossRefGoogle Scholar
  34. Martinelli G, Eidsvik J (2014) Dynamic exploration designs for graphical models using clustering with applications to petroleum exploration. Knowl Based Syst 58:113–126CrossRefGoogle Scholar
  35. Matheson J, Howard R (1968) An introduction to decision analysis. In Howard R, Matheson J (eds) The principles and applications of decision analysis, vol. I. Strat Dec Group, Menlo Park, California, USA, pp 17–55Google Scholar
  36. Mathieson A, Midgely J, Wright I, Saoula N, Ringrose P (2011) In Salah CO2 storage JIP: CO2 sequestration monitoring and verification technologies applied at Krechba, Algeria. Energy Proc 4:3596–3603CrossRefGoogle Scholar
  37. Miller AC (1975) The value of sequential information. Manag Sci 22:1–11CrossRefGoogle Scholar
  38. Muller W (2007) Collecting spatial data. Springer, BerlinGoogle Scholar
  39. Powell WB (2011) Approximate dynamic programming: solving the curses of dimensionality, 2nd edn. Wiley, HobokenCrossRefGoogle Scholar
  40. Puterman ML (2005) Markov decision processes: discrete stochastic dynamic programming. Wiley, HobokenGoogle Scholar
  41. Raiffa H (1968) Decision analysis: introductory lectures on choices under uncertainty. Addison-Wesley, BostonGoogle Scholar
  42. Rasmussen CE, Williams C (2006) Gaussian processes for machine learning. MIT Press, CambridgeGoogle Scholar
  43. Simon J, Kirkwood CW, Keller LR (2014) Decision analysis with geographically varying outcomes: Preference models and illustrative applications. Operat Res 62:182–194CrossRefGoogle Scholar
  44. Srinivas N, Krause A, Kakade S, Seeger M (2010) Gaussian process optimization in the bandit setting: No regret and experimental design. In: Proceedings of the 27th international conference on machine learningGoogle Scholar
  45. Wang H, Harrison KW (2013) Bayesian approach to contaminant source characterization in water distribution systems: adaptive sampling framework. Stoch Environ Res Risk Assess 27:1921–1928CrossRefGoogle Scholar
  46. Yokota F, Thompson K (2004a) Value of information literature analysis: a review of applications in health risk management. Med Dec Mak 24:287–298CrossRefGoogle Scholar
  47. Yokota F, Thompson K (2004b) Value of information analysis in environmental health risk management decisions: past, present, and future. Risk Anal 24:635–650CrossRefGoogle Scholar
  48. Zetterlund M, Norberg T, Ericsson LO, Rosen L (2011) Framework for value of information analysis in rock mass characterization for grouting purposes. J Construct Eng Manag 137:486–497CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Jo Eidsvik
    • 1
  • Gabriele Martinelli
    • 2
  • Debarun Bhattacharjya
    • 3
  1. 1.Department of Mathematical SciencesNTNUTrondheimNorway
  2. 2.Thomson ReutersOsloNorway
  3. 3.IBM T.J. Watson Research CenterYorktown HeightsUSA

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