Br J Math Stat Psychol. 2021 Nov 6. doi: 10.1111/bmsp.12257. Online ahead of print.
ABSTRACT
Approximately counting and sampling knowledge states from a knowledge space is a problem that is of interest for both applied and theoretical reasons. However, many knowledge spaces used in practice are far too large for standard statistical counting and estimation techniques to be useful. Thus, in this work we use an alternative technique for counting and sampling knowledge states from a knowledge space. This technique is based on a procedure variously known as subset simulation, the Holmes-Diaconis-Ross method, or multilevel splitting. We make extensive use of Markov chain Monte Carlo methods and, in particular, Gibbs sampling, and we analyse and test the accuracy of our results in numerical experiments.
PMID:34741466 | DOI:10.1111/bmsp.12257
