Decision Trees, Evaluation with Monte Carlo

Monte Carlo simulations are based on Monte Carlo methods. Monte Carlo method refers to a method of solving sets of equations using an algorithm dependent on repeated random sampling. The Monte Carlo method is used in the process of simulating (approximating) a system. Monte Carlo methods are computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo simulation involves repeated random sampling from input distributions and subsequent calculation of a set of sample values for the output distributions with the repeating of the process over several iterations.

The term Monte Carlo method was used in the 1940s in the more rapid solving of equations and algorithms possible on the first electronic digital computer, the ENIAC computer. The term was used by Nicholas Metropolis and Stanislaw Ulam in 1949. Metropolis attributed the initial insights on the use of the method to Enrico Fermi. The reference to the gaming tables of Monte Carlo, Monaco, shows the importance of randomness and chance events in the entities that are being simulated.

Today, the major uses of the Monte Carlo method involve examining real-life phenomena that need to be approximated or simulated rather than tested in the sense of real-world testing of scientific hypotheses. In testing, for example, in research on humans, there would be the tasks of developing scientific protocols, collecting data in trials, and conducting research on humans that in turn would need to be derived in conjunction with existing federal laws and approved by an institutional review board. If alternative strategies can be effectively modeled, sparing humans lives and costs, then real-world testing may not be needed as extensively as it is needed today.

Use of Monte Carlo simulation has expanded exponentially into many areas where random behavior, uncertainty, and chance events characterize the system being simulated in a diverse range of real-world endeavors: economics; finance (interest rates and stock prices); business (inventory, staffing needs, and office tasks); the sciences; and medical decision making with economic implications (e.g., impact of colonoscopic referral for small and diminutive polyps detected on CT colonography screening).