Monte Carlo Probability Research Articles

Uncertainty Structure of Dilution with Pipette and Volumetric Flask

Indeterminate error of dilution with pipette and flask is studied based on experiments, statistics, Monte Carlo simulation and probability theory. Equations which describe the error of sample concentration after the dilution are probabilistically derived and verified experimentally and statistically. The uncertainty structure of dilution is shown to be different for the pipette-pipette dilution and the pipette-flask dilution. The theory for dilution error developed here will be a basis to predict the precision of some chemical analyses such as the internal standard method in chromatography.

Search-based importance sampling

Abstract Importance sampling as a special technique in Monte Carlo probability integration has been shown to be a highly efficient and rather unrestricted method. Non-Gaussian and dependent random variables and nonlinear limit functions can be treated relatively easily and with reasonable rates of convergence. A major draw-back, however, is the need to identify so-called “interesting” or “important” regions for integration. Reference to first-order second-moment (FOSM) methods may help, as well as numerical maximization routines applied. Each involves certain difficulties. An alternative procedure, based on directing and correcting the importance sampling function as sampling is carried out, is presented herein. In particular it is possible to have a multi-modal sampling function.