Parallel probability density approximation
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Parallel probability density approximation Yi-Shin Lin 1 & Andrew Heathcote 1 & William R. Holmes 2
# The Psychonomic Society, Inc. 2019
Abstract Probability density approximation (PDA) is a nonparametric method of calculating probability densities. When integrated into Bayesian estimation, it allows researchers to fit psychological processes for which analytic probability functions are unavailable, significantly expanding the scope of theories that can be quantitatively tested. PDA is, however, computationally intensive, requiring large numbers of Monte Carlo simulations in order to attain good precision. We introduce Parallel PDA (pPDA), a highly efficient implementation of this method utilizing the Armadillo C++ and CUDA C libraries to conduct millions of model simulations simultaneously in graphics processing units (GPUs). This approach provides a practical solution for rapidly approximating probability densities with high precision. In addition to demonstrating this method, we fit a piecewise linear ballistic accumulator model (Holmes, Trueblood, & Heathcote, 2016) to empirical data. Finally, we conducted simulation studies to investigate various issues associated with PDA and provide guidelines for pPDA applications to other complex cognitive models. Keywords R . C++ . CUDA . GPU . Kernel density estimate . Markov chain Monte Carlo . Bayesian modeling . Probability density approximation
With the rapidly increasing capabilities of computer hardware and software in recent years, simulation-based approaches to investigating mathematical models of various phenomena have exploded. In the long history of using cognitive models to test theories, some of the work has been qualitative in nature, seeing whether a theory can predict the observed patterns of data. Other work has been quantitative in nature, determining whether a model/theory can quantitatively match features of the data. The latter approach typically involves fitting a model to data to determine how well the theory encoded in that model matches the observations. Most (though not all) past methods of achieving this have typically been limited to relatively simple models that have tractable likelihood functions. More recently, however, new simulation-based methods have been developed (Palestro, Sederberg, Osth, van Zandt, & Turner, 2018) that utilize modern computational power to significantly expand the scope of models that quantitative fitting
* Yi-Shin Lin [email protected] 1
Division of Psychology, School of Medicine, University of Tasmania, Hobart, Tasmania, Australia
2
Department of Physics and Astronomy & Department of Mathematics, Quantitative Systems Biology Center, Vanderbilt University, Nashville, TN, USA
can be applied to. Here we describe a highly efficient, graphics processing unit (GPU)-enabled parallel implementation of canonical Bayesian Markov chain Monte Carlo (MCMC) methods that utilizes probability density approximation (PDA; Holmes, 2015; Turner & Sederberg, 2014). MCMC methods can be used to preform either Bayesian compu
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