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
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
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.
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