Statistical Inference Utilizing Agent Based Models

Abstract

Agent-based models (ABMs) are computational models used to simulate the behaviors, actionsand interactions of agents within a system. The individual agents each have their own set of assigned attributes and rules, which determinetheir behavior within the ABM system. These rules can bedeterministic or probabilistic, allowing for a great deal offlexibility. ABMs allow us toobserve how the behaviors of the individual agents affect the systemas a whole and if any emergent structure develops within thesystem. Examining rule sets in conjunction with corresponding emergentstructure shows how small-scale changes canaffect large-scale outcomes within the system. Thus, we can betterunderstand and predict the development and evolution of systems ofinterest. ABMs have become ubiquitous---they used in business(virtual auctions to select electronic ads for display), atomosphericscience (weather forecasting), and public health (to model epidemics).But there is limited understanding of the statistical properties ofABMs. Specifically, there are no formal proceduresfor calculating confidence intervals on predictions, nor forassessing goodness-of-fit, nor for testing whether a specificparameter (rule) is needed in an ABM.Motivated by important challenges of this sort, this dissertation focuses on developing methodology for uncertaintyquantification and statistical inference in a likelihood-free contextfor ABMs. Chapter 2 of the thesis develops theory related to ABMs, including procedures for model validation, assessing model equivalence and measuring model complexity. Chapters 3 and 4 of the thesis focuses on two approaches for performing likelihood-free inference involving ABMs, which is necessary because of the intractability of the likelihood function due to the variety of input rules and the complexity of outputs.Chapter 3 explores the use of Gaussian Process emulators in conjunction with ABMs to perform statistical inference. This draws upon a wealth of research on emulators, which find smooth functions on lower-dimensional Euclidean spaces that approximatethe ABM. Emulator methods combine observed data with output from ABMsimulations, using theseto fit and calibrate Gaussian-process approximations. Chapter 4 discusses Approximate Bayesian Computation for ABM inference, the goal of which is to obtain approximation of the posterior distribution of some set of parameters given some observed data. The final chapters of the thesis demonstrates the approaches for inference in two applications. Chapter 5 presents application models the spread of HIV based on detailed data on a social network of men who have sex withmen (MSM) in southern India. Use of an ABMwill allow us to determine which social/economic/policy factors contribute to thetransmission of the disease. We aim to estimate the effect that proposed medical interventions willhave on the spread of HIV in this community. Chapter 6 examines the function of a heroin market in the Denver, Colorado metropolitan area. Extending an ABM developed from ethnographic research, we explore a procedure for reducing the model, as well as estimating posterior distributions of important quantities based on simulations.