Bootstrap Markov chain Monte Carlo and optimal solutions for the Law of Categorical Judgment (Corrected)

Abstract

A novel procedure is described for accelerating the convergence of Markov chain Monte Carlo computations. The algorithm uses an adaptive bootstrap technique to generate candidate steps in the Markov Chain. It is efficient for symmetric, convex probability distributions, similar to multivariate Gaussians, and it can be used for Bayesian estimation or for obtaining maximum likelihood solutions with confidence limits. As a test case, the Law of Categorical Judgment (Corrected) was fitted with the algorithm to data sets from simulated rating scale experiments. The correct parameters were recovered from practical-sized data sets simulated for Full Signal Detection Theory and its special cases of standard Signal Detection Theory and Complementary Signal Detection Theory.