A Dasymetric-Based Monte Carlo Simulation Approach to the Probabilistic Analysis of Spatial Variables

Abstract

GIScience 2016 Short Paper Proceedings A Dasymetric-Based Monte Carlo Simulation Approach to the Probabilistic Analysis of Spatial Variables April Morton 1 , Jesse Piburn 1 , Ryan McManamay 1 , Nicholas Nagle 2 , Robert N. Stewart 1 Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831 Email: {mortonam; piburnjo; mcmanamayra; stewartrn}@ornl.gov University of Tennessee, Knoxville, Department of Geography, 1000 Phillip Fulmer Way, Knoxville, TN 37916 Email: nnagle@utk.edu Abstract Monte Carlo simulation is a popular numerical experimentation technique used in a range of scientific fields to obtain the statistics of unknown random output variables. Though Monte Carlo simulation is a powerful technique for the probabilistic understanding of many processes, it can only be applied if it is possible to infer the probability distributions describing the required input variables. This is particularly challenging when the input probability distributions are related to population counts unknown at desired spatial resolutions. To overcome this challenge, we propose a framework that uses a dasymetric model to infer the probability distributions needed for a specific class of Monte Carlo simulations dependent on population counts. 1. Introduction Monte Carlo simulation is a numerical experimentation technique that has been widely used in a variety of scientific domains to obtain the statistics of unknown random output variables by repeatedly sampling values from a set of known input random variables and then feeding them through a computational model (Mahadevan 1997). Dasymetric mapping, on the other hand, has been widely used in the field of areal interpolation to disaggregate coarse resolution population data to a finer resolution through the use of ancillary data (Eicher and Brewer 2001). Though Monte Carlo simulation is a powerful technique for the probabilistic understanding of many processes, it can only be applied if the probability distributions describing the required input variables can be inferred. Unfortunately, conventional inference methods cannot often be used to infer the probability distributions of population counts (i.e. counts of populations with specific characteristics) that are unknown at desired spatial resolutions. Fortunately, recent advancements in dasymetric mapping, which may not be well known to researchers utilizing Monte Carlo simulation in fields other than areal interpolation, provide novel methods for estimating the probability distributions of population counts. To highlight the potential link between dasymetric mapping and Monte Carlo simulation, we propose a framework that uses the penalized maximum entropy dasymetric model (PMEDM) proposed by Nagle et. al (2014) to learn the parameters of multinomial distributions describing population counts needed to complete a specific class of Monte Carlo simulations. 2. Methodology Suppose we’d like to calculate, through Monte Carlo simulation, the sample mean � � and sample standard deviation � � � of an output variable � � = � � ( � � , � � ) for a set of non-overlapping regions � ∈ {1, … , �} where � � = [� �1,…, � �� ] and � � = [� �1,…, � �� ] are vectors of random variables with