Contributions to the adaptive Monte Carlo method

Abstract

The GUM Supplement 1 presented the adaptive Monte Carlo (AMC) method. A basic implementation of an AMC procedure involves carrying out an increasing number of Monte Carlo trials until four parameters have stabilized in a statistical sense. Although the AMC method has been successfully used for uncertainty evaluations, the amount of stored data was seen as significant, and even after achieving stability, it can be lost with the increase in the number of trials. To overcome these problems, two modifications to the AMC method were proposed, implemented and validated. The first is related to data storage, while the second consists of applying an alternative criterion to assess convergence. After modifications, the AMC was named the modified adaptive Monte Carlo (MAMC) method and was applied when estimating the uncertainty of measurements carried out with a micrometer. The MAMC effectiveness was validated through the comparison of the uncertainty values and those from the application of the GUM and AMC methods. Under the evaluated experimental conditions, the MAMC showed greater repeatability when compared to AMC, regarding the number of trials to be carried out. This factor contributes toward the higher reliability of this method. The amount of data to be stored and manipulated through the application of the MAMC method was decreased significantly. This fact may increase the adoption of the AMC method.