Statistical Inference Utilizing Agent Based Models

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 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), atomospheric

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 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 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 application models 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

will 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 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.