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HSSM (Hierarchical Sequential Sampling Modeling) is a modern Python toolbox that provides state-of-the-art likelihood approximation methods within the Python Bayesian ecosystem. It facilitates hierarchical model building and inference via fast and robust MCMC samplers. User-friendly, extensible, and flexible, HSSM can rigorously estimate the impact of neural and other trial-by-trial covariates through parameter-wise mixed-effects models for a large variety of cognitive process models.

HSSM is a BRAINSTORM project in collaboration with the Center for Computation and Visualization (CCV) and the Center for Computational Brain Science within the Carney Institute at Brown University.


  • Allows approximate hierarchical Bayesian inference via various likelihood approximators.
  • Estimate impact of neural and other trial-by-trial covariates via native hierarchical mixed-regression support.
  • Extensible for users to add novel models with corresponding likelihoods.
  • Built on PyMC with support from the Python Bayesian ecosystem at large.
  • Incorporates Bambi's intuitive lmer-like regression parameter specification for within- and between-subject effects.
  • Native ArviZ support for plotting and other convenience functions to aid the Bayesian workflow.
  • Utilizes the ONNX format for translation of differentiable likelihood approximators across backends.


hssm is available through PyPI. You can install it with pip via:

pip install hssm

You can also install the bleeding edge version of hssm directly from this repo:

pip install git+

For more detailed guidance, please check out our installation guide.


Possible solutions to any issues with installations with hssm can be located here. We recommend leveraging an environment manager with Python 3.10~3.11 to prevent any problems with dependencies during the installation process. Please note that hssm is tested for python 3.10, 3.11. As of HSSM v0.2.0, support for Python 3.9 is dropped. Use other python versions with caution.

Setting global float type

Using the analytical DDM (Drift Diffusion Model) likelihood in PyMC without forcing float type to "float32" in PyTensor may result in warning messages during sampling, which is a known bug in PyMC v5.6.0 and earlier versions. We can use hssm.set_floatX("float32") to get around this for now.



Here is a simple example of how to use HSSM:

import hssm

# Set float type to float32 to avoid a current bug in PyMC mentioned above
# This will not be necessary in the future

# Load a package-supplied dataset
cav_data = hssm.load_data('cavanagh_theta')

# Define a basic hierarchical model with trial-level covariates
model = hssm.HSSM(
            "name": "v",
            "prior": {
                "Intercept": {"name": "Normal", "mu": 0.0, "sigma": 1.0},
                "theta": {"name": "Normal", "mu": 0.0, "sigma": 1.0},
            "formula": "v ~ (1|participant_id) + theta",
            "link": "identity",

# Sample from the posterior for this model

To quickly get started with HSSM, please follow this tutorial. For a deeper dive into HSSM, please follow our main tutorial.


HSSM is licensed under Copyright 2023, Brown University, Providence, RI


For questions, please feel free to open a discussion.

For bug reports and feature requests, please feel free to open an issue using the corresponding template.


If you want to contribute to this project, please follow our contribution guidelines.