Monte Carlo Simulations explained courtesy of Brian Schnick

Monte Carlo Simulations explained courtesy of Brian Schnick

I chose to look at one of the above topics that we did not cover in depth, Monte Carlo Simulations. The Cartoon Guide mentions that probability theory is based on gambling, and also that observed data approaches probability models with increasing numbers of trials. There is also a brief mention of bootstrapping, but the idea is not developed. The McGrew text does not mention Monte Carlo Simulations. An Introduction to Scientific Research Methods in Geography describes Monte Carlo as a method of computational modeling as a form of stochastic data collection.

A brief outline from internet pages follows:
Monte Carlo Simulations

1. 
   Definition: algorithms that use repeated random sampling, alternately ‘all it means is to simulate the process inside the computer, and see what happens’ –Dr. Mitteldorf
   
2. 
   History: developed during Manhattan project to determine radiation shield thickness.
   
3. 
   Use: Simulating physical or mathematical systems with a non-deterministic (not infallibly predictable) formula – systems with uncertain inputs.
   
   1. 
      Business risk, fluids, cellular structures.
      
   2. 
      Multidimensional integrals.
      
4. 
   General method
   
   1. 
      Define inputs
      
   2. 
      Generate inputs randomly
      
   3. 
      Perform deterministic computation
      
   4. 
      Aggregate results
      

The Monte Carlo method can be illustrated as a game of Battleship. First a player makes some random shots. Next the player applies algorithms (i.e. a battleship is four dots in the vertical or horizontal direction). Finally based on the outcome of the random sampling and the algorithm the player can determine the likely locations of the other player's ships.
http://en.wikipedia.org/wiki/Monte_Carlo_method
- YouTube resources: Monte Carlo Simulation 1.
- JMP Help has entries when ‘Monte Carlo’ is searched for, but the explanations are deemed Advanced by the software creators.
- The ESRI Guide to GIS Analysis, Vol. 1 & 2 did not mention Monte Carlo Simulation.
-The embedded ArcMap Help has a single, extensive entry for ‘monte carlo simulation models’. The online version has several entries under ‘Advanced modeling through simulations’, each of which requires prior knowledge of ArcMap modeling (something I still need exposure to):


The online help also links to:
Monte Carlo Simulation Basics.
http://www.vertex42.com/ExcelArticles/mc/MonteCarloSimulation.html

The Basics of Monte Carlo Simulations.

http://www.chem.unl.edu/zeng/joy/mclab/mcintro.html

What is Monte Carlo Simulation?

http://www.decisioneering.com/monte-carlo-simulation.html ; updated link: http://www.oracle.com/appserver/business-intelligence/crystalball/index.html . Note: Oracle Crystal Ball is an Excel extension, and is available in an academic version for $99.

Abbaspour, R. A., M. R. Delavar, and R. Batouli (2003). The Issue of Uncertainty Propagation in Spatial Decision Making. http://www.scangis.org/scangis2003/papers/13.pdf.

-The embedded Excel Help does not contain an entry for ‘monte carlo’, but the online version (http://office.microsoft.com/en-us/excel/HA102827771033.aspx?pid=CH100645001033 ) has one that includes demonstrations, as well as information about 3^rd party extensions to Excel that automate Monte Carlo simulations. The non-geographic problems at the end could be modified to make them relevant to this class. For example, a cell phone company is considering moving into a new market area. Based on their other markets, they believe that the number of required cell towers is normally distributed, with a mean of 20 and a standard deviation of 5. Half of the required towers can be leased for $25,000 a year and half will need to be built for $40,000. Would 16, 18, 20, or 22 towers be the best option for one year’s operations?
A lead-in problem could be the one presented at the Dr. Mitteldorf link above regarding the probability of rolling a die a number of times.