Optimal Decision Strategies for Large Spatio-Temporal Decision Problems

North Carolina State University, Raleigh NC

Investigators

Abstract

A number of current public health, ecological, and environmental crises can be conceptualized as spatio-temporal decision problems wherein a harmful replicating agent is spreading across space and, simultaneously, a decision maker must select when, where, and how to allocate limited resources targeted at controlling the spread of the agent. Examples include the spread of an infectious disease across people in a social network, the spread of a computer virus across machines in a network, and the spread of an invasive species across an ecological landscape. The costs of these epidemics are enormous. For example, 32% of global deaths are attributed to infectious diseases, the cost of computer viruses to U.S. businesses is estimated to exceed 60 billion dollars per year, and the cost of invasive species is estimated to exceed 100 billion dollars per year and to affect 100 million acres of land. Thus, improvements to spatio-temporal decision making could have tremendous benefits to all sectors of society. Technological advances have made it increasingly easy to collect, store, and manipulate large amounts of data. This research project takes first steps toward methods that use accumulating data on the spread of a replicating agent to inform resource allocation over time. The methodology adjusts for non-stationary agent dynamics, changing availability of resources, and uncertain or incomplete measurements. A key component of controlling the spread of a replicating agent over space and time is deciding where, when, and how to apply interventions. This control process is formalized as an allocation strategy which comprises a sequence of functions, one per time point, that map up-to-date information on the spread of the agent to a distribution over subsets of locations to receive an intervention. The project formally defines an optimal allocation strategy using potential outcomes, and demonstrates that spatial proximity induces causal interference among locations, thereby preventing direct application of existing methods for sequential treatment assignment. A parametric estimator of the optimal strategy within a pre-specified class of allocation strategies using a systems dynamics model and simulation-optimization is developed. This estimator has low variance and can be applied in a data-impoverished setting, however it may suffer from high bias if the systems dynamics model is misspecified. A semi-parametric estimator of the optimal allocation strategy which does not require correct specification of a systems dynamics model is also developed. Because the semi-parametric estimator relies on fewer assumptions about the underlying systems dynamics, it is potentially robust to model misspecification but may have high variance. To balance bias and variance, and optimize finite sample performance, shrinkage of the semi-parametric estimator toward the parametric estimator will be investigated. The methodologies will be illustrated with an application to the spread of white-nose syndrome in bats.