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.
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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 4:850–874
Baio G (2012) Bayesian methods in health economics. CRC Press, Boca Raton
Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis of spatial data, 2nd edn. CRC Press, Boca Raton
Bellman RE (1957) Dynamic Programming. Princeton University Press, Princeton
Bhattacharjya D, Eidsvik J, Mukerji T (2010) The value of information in spatial decision making. Math Geosci 42:141–163
Bhattacharjya D, Eidsvik J, Mukerji T (2013) The value of information in portfolio problems with dependent projects. Decis Anal 10:341–351
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 72:30–44
Bratvold RB, Bickel JE, Lohne HP (2009) Value of information in the oil and gas industry: past, present, and future. SPE: Reserv Eval Eng 12:630–638
Brown DB, Smith JE (2013) Optimal sequential exploration: Bandits, clairvoyants, and wildcats. Operat Res 60:262–274
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 3511–3518
Chiles JP, Delfiner P (2012) Geostatistics: modeling spatial uncertainty, 2nd edn. Wiley, Hoboken
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 29:1085–1101
Cressie N (1993) Statistics for spatial data. Wiley, Hoboken
Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, Hoboken
Dobbie MJ, Henderson BL, Stevens DL (2008) Sparse sampling: spatial design for monitoring stream networks. Stat Surv 2:113–153
Dyer JS, Sarin R (1979) Measurable multiattribute value functions. Operat Res 27:810–822
Eidsvik J, Bhattacharjya D, Mukerji T (2008) Value of information of seismic amplitude and CSEM resistivity. Geophysics 73:R59–R69
Eidsvik J, Mukerji T, Bhattacharjya D (2015) Value of information in the earth sciences. Cambridge University Press, Cambridge
Ellefmo SL, Eidsvik J (2009) Local and spatial joint frequency uncertainty and its application to rock mass characterization. Rock Mech Rock Eng 42:667–688
Evangelou E, Eidsvik J (2017) The value of information for correlated GLMs. J Stat Plan Inference 180:30–48
Golovin D, Krause A (2011) Adaptive submodularity: theory and applications in active learning and stochastic optimization. J Artif Intel Res 42:427–486
Goodson JC, Thomas BW, Ohlmann JW (2017) A rollout algorithm framework for heuristic solutions to finite horizon stochastic dynamic programs. Eur J Operat Res 258:216–229
Howard R (1966) Information value theory. IEEE Trans Sys Sci Cybern 2:22–26
Howard R, Abbas A (2015) Foundations of decision analysis. Prentice Hall, Upper Saddle River
Karam KS, Karam JS, Einstein HH (2007) Decision analysis applied to tunnel exploration planning I: principles and case study. J Constr Eng Manag 133:344–353
Keisler JM, Collier Z, Chu E, Sinatra N, Linkov I (2014) Value of information analysis: the state of application. Environ Syst Decis 34:3–23
Krause A, Guestrin C (2009) Optimal value of information in graphical models. J Artif Intel Res 35:557–591
Le ND, Zidek JV (2006) Statistical analysis of environmental space-time processes. Springer, Berlin
Lilleborge M, Hauge R, Eidsvik J (2016) Information gathering in Bayesian networks applied to petroleum prospecting. Math Geosci 48:233–257
Malczewski J (2006) GIS-based multicriteria decision analysis: a survey of the literature. Int J Geogr Inf Sci 20:703–726
Martinelli G, Eidsvik J, Hauge R, Forland MD (2011) Bayesian networks for prospect analysis in the North Sea. AAPG Bull 95:1423–1442
Martinelli G, Eidsvik J, Hauge R (2013a) Dynamic decision making for graphical models applied to oil exploration. Eur J Operat Res 230:688–702
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 19:289–304
Martinelli G, Eidsvik J (2014) Dynamic exploration designs for graphical models using clustering with applications to petroleum exploration. Knowl Based Syst 58:113–126
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 17–55
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 4:3596–3603
Miller AC (1975) The value of sequential information. Manag Sci 22:1–11
Muller W (2007) Collecting spatial data. Springer, Berlin
Powell WB (2011) Approximate dynamic programming: solving the curses of dimensionality, 2nd edn. Wiley, Hoboken
Puterman ML (2005) Markov decision processes: discrete stochastic dynamic programming. Wiley, Hoboken
Raiffa H (1968) Decision analysis: introductory lectures on choices under uncertainty. Addison-Wesley, Boston
Rasmussen CE, Williams C (2006) Gaussian processes for machine learning. MIT Press, Cambridge
Simon J, Kirkwood CW, Keller LR (2014) Decision analysis with geographically varying outcomes: Preference models and illustrative applications. Operat Res 62:182–194
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 learning
Wang H, Harrison KW (2013) Bayesian approach to contaminant source characterization in water distribution systems: adaptive sampling framework. Stoch Environ Res Risk Assess 27:1921–1928
Yokota F, Thompson K (2004a) Value of information literature analysis: a review of applications in health risk management. Med Dec Mak 24:287–298
Yokota F, Thompson K (2004b) Value of information analysis in environmental health risk management decisions: past, present, and future. Risk Anal 24:635–650
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 137:486–497
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Eidsvik, J., Martinelli, G. & Bhattacharjya, D. Sequential information gathering schemes for spatial risk and decision analysis applications. Stoch Environ Res Risk Assess 32, 1163–1177 (2018). https://doi.org/10.1007/s00477-017-1476-y
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DOI: https://doi.org/10.1007/s00477-017-1476-y