Implementation of Diffusion decision model with across-trial variability in boundary separation

PyPI Python License: MIT tests

Diffusion decision model with across-trial variability in boundary separation (sa), drift (sv), and non-decision time (st). This codebase presents the DDM-SA as a fully differentiable PyTensor likelihood for gradient-based Bayesian estimation.

The likelihood is analytic (Navarro–Fuss density; drift variability integrated in closed form, uniform variability by Gauss–Legendre quadrature), so NUTS gets exact gradients. It is validated against the Fortran implementation the model was originally developed in; the Fortran programs, the data, and reference results ship in this repository so every validation is reproducible from a clone.

Install

From PyPI:

pip install saddm               # core: numpy, scipy, pytensor
pip install "saddm[sampling]"   # + pymc, arviz, numpyro (pinned jax)
pip install "saddm[hssm]"       # + hssm

From a clone, for development or to run the verification and examples:

pip install -e ".[test]"        # + pytest, numba (reference backend)
pip install -e ".[hssm]"        # everything the examples need

The sampling and hssm extras pin jax==0.5.3 / numpyro==0.19.0 deliberately: newer jax silently freezes numpyro's NUTS at its initial point.

Quickstart

from saddm import make_ddmsa_model, sample_ddmsa, sample_ddmsa_exact

data  = sample_ddmsa_exact(a=1.1, z=0.5, v=1.5, t=0.25,
                           sv=0.8, sa=0.5, st=0.08, n_trials=2000)
idata = sample_ddmsa(make_ddmsa_model(data), backend="numpyro")

saddm.ddmsa_logp(rt, response, a, z, v, t, sv, sa, st, sz) is the per-trial log-likelihood; every parameter may be a scalar or a per-trial vector.

With HSSM, register saddm.ddmsa_logp as a loglik_kind="analytical" likelihood; examples/estimate_HSSM_saddm.py is the minimal adapter.

Layout

path contents
saddm/ ddmsa.py: the likelihood and PyMC glue. core.py/integrator.py/model.py: the Numba reference implementation (reference extra).
tests/ test_ddmsa.py: verification suite — s = 1 closed forms, agreement with the Numba/Fortran reference, finite-difference gradients, corner finiteness, per-trial broadcasting, backend agreement, static-zero collapse (run directly with --sample for an end-to-end NUTS check). Remaining test_*.py cover the Numba reference.
verification/ parameter_recovery.py: 100-config NUTS recovery study. recovery_figure.py, compare_to_fortran.py, likelihood_figure.py: analysis and figures (read results/reference/ by default; set RESULTS for a fresh run).
examples/ HSSM applications: flat fit on cavanagh_theta, the per-subject + k-sweep replication of the Fortran intertemporal-choice analysis, hierarchical variants, and the random-effects figure.
fortran/ The Fortran programs that produced the benchmarks, with build notes.
data/itc_amasino/ Amasino et al. (2019) trials, the Fortran benchmarks, and the exact k-sweep permutation files.
results/reference/ Reference outputs: recovery, ITC, hierarchical, and cavanagh results with figures. Everything else under results/ is gitignored, and every script writes there by default.

Citation

@unpublished{shevlin2026little,
  author = {Shevlin, Blair R. K. and Fernandez, Kiant{\'e} and Ratcliff, Roger and Krajbich, Ian},
  title  = {A little goes a long way: Fitting one-shot decisions with cognitive models},
  note   = {Manuscript in preparation},
  year   = {2026},
}

Blair R. K. Shevlin* and Kianté Fernandez* contributed equally.

:Author: Kianté Fernandez, Blair R K Shevlin, Roger Ratcliff, Ian Krajbich

:Contact: kiante@ucla.edu, blair.shevlin@mssm.edu, ratcliff.22@osu.edu, krajbich@ucla.edu

Project links

Data verified by PyPI on Sep 4, 2026
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Credits

Author: Kianté Fernandez, Blair R K Shevlin, Roger Ratcliff, Ian Krajbich

GitHub Statistics

Data verified by PyPI on Sep 4, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

MIT License (MIT)

Requires

Python >=3.11

Provides Extra

sampling hssm reference test

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