Maximum Likelihood Estimation—A Reliable Statistical Method for Hydrate Nucleation Data Analysis

Analyses on hydrate nucleation and nucleation processes in general are assumed to require a large number of parallels due to the stochastic nature of the process. Stochastic processes are described by an exponential probability distribution. The present work adopts the Maximum Likelihood Estimation (MLE) with penalized estimators for data analysis in gas hydrate nucleation studies. Key parameters analyzed and discussed are nucleation rate and lag time during formation of critical size nuclei. The MLE technique is commonly used in analysis of other types of stochastic processes, but it has not, to our knowledge, previously been applied to hydrate nucleation. A total of six data sets, three on methane–propane hydrate nucleation from the present work, and three on general crystal nucleation extracted from the literature, were analyzed using the MLE. The MLE analysis was compared with a conventional method fitting the Experimental Probability Array to the exponential Probability Distribution Function (EPA-PDF). The results indicated that the MLE method outperforms the EPA-PDF method for data analysis of stochastic nucleation processes, in both consistency and reliability. The dependence on the number of parallels to produce reliable nucleation rate estimates was examined. Permutation tests were incorporated to ensure unbiased comparison from a statistical point of view. The MLE method proved to be consistent and robust, and less dependent on a large number of parallels for reliable estimation of nucleation rates. MLE analysis of the present hydrate nucleation data indicated that 20 parallels is most probably sufficient for this method to maintain reliable estimation of hydrate nucleation rate with statistical consistency. Literature data on other crystallization processes supported a range of 20 to 25 parallels as sufficient.