Parallel probability density approximation

Probability Density Approximation (PDA) is a non-parametric method of calculating probabilitydensities. When integrated into Bayesian estimation, it allows researchers to fit psychologicalprocesses for which analytic probability functions are unavailable, significantly expanding thescope of theories that can be quantitatively tested. PDA is, however, computationally intensive,requiring large numbers of Monte Carlo simulations to attain good precision. We introduceParallel PDA (pPDA), a highly efficient implementation of this method utilizing Armadillo C++and CUDA C libraries to conduct millions of model simulations simultaneously in graphicsprocessing units (GPUs). This approach provides a practical solution for rapidly approximatingprobability densities with high precision. In addition to demonstrating this method, we fit a Piecewise Linear Ballistic Accumulator model (Holmes, Trueblood & Heathcote, 2016) toempirical data. Finally, we conduct simulation studies to investigate various issues associatedwith the PDA and provide guidelines for pPDA applications to other complex cognitive models