By Jo Eidsvik, Tapan Mukerji, Debarun Bhattacharjya
Amassing the proper and the correct quantity of data is essential for any decision-making approach. This publication provides a unified framework for assessing the worth of capability info collecting schemes by way of integrating spatial modelling and selection research, with a spotlight on the planet sciences. The authors talk about the price of imperfect as opposed to excellent details, and the price of overall as opposed to partial info, the place purely subsets of the information are bought. ideas are illustrated utilizing a set of quantitative instruments from choice research, akin to choice timber and impression diagrams, in addition to versions for non-stop and discrete based spatial variables, together with Bayesian networks, Markov random fields, Gaussian methods, and multiple-point geostatistics. specific in scope, this booklet is of curiosity to scholars, researchers and pros within the Earth and environmental sciences, who use utilized information and determination research concepts, and especially to these operating in petroleum, mining, and environmental geoscience.
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Value of Information in the Earth Sciences: Integrating Spatial Modeling and Decision Analysis
Collecting the proper and the correct amount of knowledge is essential for any decision-making technique. This ebook offers a unified framework for assessing the worth of strength info collecting schemes by way of integrating spatial modelling and determination research, with a spotlight on the planet sciences. The authors talk about the price of imperfect as opposed to excellent details, and the worth of overall as opposed to partial details, the place purely subsets of the information are received.
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Example text
16) p ( x | y) = p ( x, y) p ( y) = p ( x) p ( y | x) p ( y) ∝ p ( x) p ( y | x). 25) Here, the numerator consists of the prior model p ( x ) and the likelihood model p ( y | x ) . 25) to obtain the last expression. In some situations, one may be interested in computing the marginal likelihood in the denominator, which is also sometimes referred to as the pre-posterior model. 26) or using sums for the discrete situation. Pitfalls: likelihood and marginal likelihood Note that the marginal likelihood p( y) is usually more difficult to represent than the likelihood p ( y | x ) .
Geophysicists can use experience to predict the response given the oil content, since there is a physical relation. This can be summarized in the likelihood p ( y | x ) . The interpretation of p( y) is based on marginalizing over all oil saturations. 25) is often referred to as Bayes’ rule. One uses Bayes’ rule to construct the posterior from the prior and the likelihood. , goes forward – from x to y, Bayes’ rule allows for going the opposite way from y to x. This kind of analysis is tagged as Bayesian inversion.
The split in nodes (and sub-nodes) is useful to communicate the model definitions to practitioners. This modular feature of graphs makes it easy to expand on smaller parts of the graph, possibly without changing the entire modeling framework. 14 (bottom) shows a BN for reservoir prospects in a region of the North Sea. The root nodes represent the source rock variable at geological kitchens, while the leaf nodes in the network represent potential drilling locations called prospects and segments.