# The value of information in spatial decision making

## Abstract

Experiments performed over spatially correlated domains, if poorly chosen, may not be worth their cost of acquisition. In this paper, we integrate the decision-analytic notion of value of information with spatial statistical models. We formulate methods to evaluate monetary values associated with experiments performed in the spatial decision making context, including the prior value, the value of perfect information, and the value of the experiment, providing imperfect information. The prior for the spatial distinction of interest is assumed to be a categorical Markov random field whereas the likelihood distribution can take any form depending on the experiment under consideration. We demonstrate how to efficiently compute the value of an experiment for Markov random fields of moderate size, with the aid of two examples. The first is a motivating example with presence-absence data, while the second application is inspired by seismic exploration in the petroleum industry. We discuss insights from the two examples, relating the value of an experiment with its accuracy, the cost and revenue from downstream decisions, and the design of the experiment. © International Association for Mathematical Geosciences 2009.