HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python - Supplemental Material

TLDR: Gelman et al. as discussed by the authors used Markov Chain Monte Carlo (MCMC) sampling method to produce samples from the posterior distribution, where the likelihood of observing the data (in this case choices and RTs) given each parameter value and the prior probability of the parameters.

Abstract: where P (x|θ) is the likelihood of observing the data (in this case choices and RTs) given each parameter value and P (θ) is the prior probability of the parameters. In most cases the computation of the denominator is quite complicated and requires to compute an analytically intractable integral. Sampling methods like Markov-Chain Monte Carlo (MCMC) (Gamerman and Lopes, 2006) circumvent this problem by providing a way to produce samples from the posterior distribution. These methods have been used with great success in many different scenarios (Gelman et al., 2003) and will be discussed in more detail below.