Thresholds of Confidence: An Analysis of Statistical Methods for Composition: Part 2: Applications

This is Part 2 of a two-part analysis of serialism, randomness and statistical feedback. Part 1 developed the theoretical basis, which the present article applies to seven compositional scenarios. Scenarios 1-3 cover discrete distributions in static contexts and deem methods effective when they are able to utilize the least-weighted state at least once. Scenarios 4 and 5 cover continuous distributions, again in static contexts. These scenarios measure effectiveness by comparing the expected mean and variance with the statistics obtained from populations. Scenario 6 covers discrete distributions with evolving weights, with effectiveness being gauged through the number of samples required to establish a trend. Scenario 7 covers conditional distributions through the paradigm of the Markov chain. Here a realization is deemed effective if it represents the least-weighted transition at least once.