Quasi-Monte Carlo Methods: Combating Complexity in Cost Risk Analysis
Cost analyses rely on probabilistic numerical methods to estimate the impact of risk and uncertainty associated with systems technical definitions and cost estimating methodologies. Such methods involve modeling risk and uncertainty as probabilistic distributions, applying iterative sampling techniques using Monte Carlo (MC) methods, and deriving risk and uncertainty adjusted statistical measures; however, the accuracy of statistical measures resulting from probabilistic analyses is directly dependent on the number of samples considered. Therefore, in probabilistic numerical methods, a trade-off exits between accuracy of results and computational complexity.
To combat increasing computational complexity in probabilistic numerical models, Quasi-Monte Carlo (QMC) sampling techniques employ systematic approaches to random sampling with the goal of achieving accurate statistical measures while using fewer samples than traditional MC methods. In this paper, two QMC sampling techniques are investigated within the framework of cost risk analysis: Sobol Sequences and Latin Hypercube Hammersley Sequences (LHHS). Sobol Sequences are widely deployed in QMC simulation, but are not a standard sampling option in COTS risk analysis software commonly used in cost analysis. LHHS is a relatively new sampling method which is a hybrid of the well established methods: Latin-Hypercube Sampling and Hammersley Sequences. The efficiency of the sampling techniques is tested within the framework of cost risk analysis through the implementation of probabilistic distributions common to the field and through the development of code in VBA and VC++ which enables the techniques to be called from Microsoft Excel.
Booz Allen Hamilton
Blake Boswell is a Consultant for Booz Allen Hamilton’s Business Analytics Team. He is a firm subject matter expert in the areas of quantitative risk analysis and Microsoft Excel development. Blake currently supports a variety of cost estimating projects for the USMC. He is the lead developer for multiple cost and risk estimating tools and is involved with efforts to advance the application of numerical methods to risk analysis. Blake’s research interests include applied probability, computational mathematics, and math modeling and simulation. He presented on the topic of risk analysis at the 2010 SCEA conference, and is a published author in the field of economics with papers involving computation of equilibriums in industrial organization models. Blake received a B.S. in mathematics with concentrations in statistics and economics from Auburn University Montgomery and is currently pursuing a master’s degree in applied economics at Johns Hopkins University.