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Source: Laboratory of Jonathan Flombaum—Johns Hopkins University

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Updated: Jan 20, 2026

Probability Laws for Inherited Traits

Probability Laws for Inherited Traits

Parallel probability density approximation.

Yi-Shin Lin¹, Andrew Heathcote², William R Holmes³

¹Division of Psychology, School of Medicine, University of Tasmania, Hobart, Tasmania, Australia. yishinlin001@gmail.com.

Behavior Research Methods

|September 1, 2019

Summary

This summary is machine-generated.

Parallel Probability Density Approximation (pPDA) accelerates Bayesian estimation for complex psychological models. This GPU-accelerated method enhances computational efficiency for nonparametric probability density calculations.

Keywords:

Bayesian modeling C++CUDA GPU Kernel density estimate Markov chain Monte Carlo Probability density approximation R

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Linearization and Approximation

Linearization and Approximation

Published on: January 12, 2026

Area of Science:

Cognitive Science
Computational Neuroscience
Psychological Modeling

Background:

Probability Density Approximation (PDA) is a nonparametric technique for calculating probability densities.
PDA enables Bayesian estimation of psychological processes lacking analytic probability functions, broadening quantitative theory testing.
Standard PDA is computationally intensive, demanding extensive Monte Carlo simulations for precision.

Purpose of the Study:

Introduce Parallel PDA (pPDA), an efficient implementation of PDA.
Leverage GPUs for simultaneous, large-scale model simulations.
Provide a practical solution for high-precision, rapid probability density approximation.

Main Methods:

Developed pPDA using Armadillo C++ and CUDA C libraries.
Utilized graphics processing units (GPUs) for massive parallel computation.
Applied pPDA to fit a piecewise linear ballistic accumulator model to empirical data.

Main Results:

Demonstrated pPDA's ability to conduct millions of model simulations concurrently.
Achieved rapid approximation of probability densities with high precision.
Successfully fitted a complex cognitive model to empirical data using pPDA.

Conclusions:

pPDA offers a computationally efficient alternative to traditional PDA for complex cognitive models.
The method significantly reduces the time required for precise probability density approximation.
Simulation studies provide guidelines for applying pPDA to diverse cognitive modeling research.