Daniel P. Heard
Quantitative Risk AnalystUSAA Federal Savings Bank
Statistical Inference Utilizing Agent Based Models
Agent-based models (ABMs) are computational models used to simulate the behaviors, actions and interactions of agents within a system. The individual agents each have their own set of assigned attributes and rules, which determine their behavior within the ABM system. These rules can be deterministic or probabilistic, allowing for a great deal of flexibility. ABMs allow us to observe how the behaviors of the individual agents affect the system as a whole and if any emergent structure develops within the system. Examining rule sets in conjunction with corresponding emergent structure shows how small-scale changes can affect large-scale outcomes within the system. Thus, we can better understand and predict the development and evolution of systems of interest. ABMs have become ubiquitous---they used in business (virtual auctions to select electronic ads for display), atmospheric science (weather forecasting), and public health (to model epidemics). But there is limited understanding of the statistical properties of ABMs. Specifically, there are no formal procedures for calculating confidence intervals on predictions, nor for assessing goodness-of-fit, nor for testing whether a specific parameter (rule) is needed in an ABM. Motivated by important challenges of this sort, this dissertation focuses on developing methodology for uncertainty quantification and statistical inference in a likelihood-free context for 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 focus 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 approximate the ABM. Emulator methods combine observed data with output from ABM simulations, using these to 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 models for the spread of HIV based on detailed data on a social network of men who have sex with men (MSM) in southern India. Use of an ABM allows us to determine which social/economic/policy factors contribute to the transmission of the disease. We aim to estimate the effect that proposed medical interventions will have 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.