Monte Carlo Analysis in Academic Research

Abstract

Monte Carlo analysis is a research strategy that incorporates randomness into the design, implementation or evaluation of theoretical models. It began in the 1940s, when the development of computer hardware and mathematical models made it possible to generate streams of random numbers. These random number streams are combined with mathematical models in order to create models and evaluate theories of random processes. This chapter attempts to tame this diverse, unmanageable collection of concepts and methods by dividing simulation projects into three types. The first, commonly called "Monte Carlo simulation," is used to evaluate statistical estimators. When an estimation procedure is proposed, it is standard procedure to test it against a variety of simulated research problems. A second type of project, referred to as "Markov chain Monte Carlo" (or MCMC), helps researchers to draw conclusions about complicated probability models for which conventional research strategies do not yield insights. The third 1 type of project arises in the study of complex systems, which are characterized by a large number of loosely interconnected, autonomous elements. Commonly known as agent-based models, these simulations have found enthusiastic advocates in environmental and social sciences.Keywords: Monte Carlo, Markov chain Monte Carlo (MCMC), pseudo random number generation (PRNG), Bayesian statistics, agent-based modeling Monte Carlo (MC) analysis is a general term that refers to research that employs random numbers, usually in the form of a computer model (or simulation). Although this research began in the natural sciences, computer science, and mathematics, it is now widely applied in social science as well. This essay attempts to explain the fundamental ideas that spurred the creation of these new procedures as well as their eventual adaptation for use in social science research.This chapter is not a "how to" guide for simulation, but rather it is a "what for" or "why you might want to" guide. Some of the difficulties that arise in MC research projects are considered as well. It begins with some background information on the development of computers and algorithms for random numbers. After that, the chapter takes up applications in the evaluation of proposed statistical estimators, the practice of Bayesian statistics via computer simulation, and investigation of complex systems through agent-based models. Some conclusions about the challenges that face the field are presented, along with a conclusion. A significant part of the presentation is about the exciting developments that have occurred since 1990. Rapid improvements in hardware and software have opened up opportunities for scholars to work with models that were previously prohibited by conceptual and technical barriers. At the current time, we are able to conceptualize and implement models that were simply impossible just 10 years ago. The extremely rapid progress has been driven by a fruitful interaction of substantive researchers in the natural and social science...

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