bayes_drt2

This maintained fork is published as the eisyfit-bayes-drt2 distribution for use by EIS Fitting. The Python import name remains bayes_drt2.

Changes in this maintained fork

The only functional source-code change from the upstream project is replacing NumPy's removed trapz function with trapezoid, which is required for NumPy 2.x. The other fork changes only add distribution metadata, preserve the Stan model files in built wheels, and provide PyPI release automation.

bayes_drt2 is a re-implementation of bayes_drt using the cmdstan interface to Stan instead of pystan. This addresses some issues with installation and the removal of optimization functionality in current versions of pystan. The functionality and structure of bayes_drt2 is virtually identical to that of bayes_drt. If you are using bayes_drt without issue, there is no reason to switch to bayes_drt2. See the tutorials for bayes_drt for tutorials on how to use this package (the API is the same).

bayes_drt2 is a Python package for inverting electrochemical impedance spectroscopy (EIS) data to obtain the distribution of relaxation times (DRT) and/or distribution of diffusion times (DDT).

bayes_drt2 implements a hierarchical Bayesian model to provide well-calibrated estimates of the DRT or DDT without ad-hoc tuning. The package offers two methods for solving the model:

• Hamiltonian Monte Carlo (HMC) sampling to estimate the posterior distribution, providing both a point estimate of the distribution and a credible interval
• L-BFGS optimization to maximize the posterior probability, providing a maximum a posteriori (MAP) point estimate of the distribution

It is also possible to perform multi-distribution inversions, e.g. to simultaneously fit both a DRT and a DDT, with these methods. This is an experimental feature and requires some manual tuning. See the tutorials for an example.

The package also provides ordinary and hyperparametric ridge regression methods, which may be useful for comparison or for obtaining initial estimates of the distribution. The hyperparametric ridge regression method is an implementation of the method developed by Ciucci and Chen (https://doi.org/10.1016/j.electacta.2015.03.123) and expanded by Effat and Ciucci (https://doi.org/10.1016/j.electacta.2017.07.050).

Electrochimica Acta article

The methods implemented in bayes_drt2 are the subject of an article in Electrochimica Acta (https://doi.org/10.1016/j.electacta.2020.137493). The theory behind the model is described in detail in the journal article.

Installation

See the installation.txt file for installation instructions.

Dependencies

bayes_drt2 requires:

• numpy
• scipy
• matplotlib
• pandas
• cvxopt
• cmdstan

Issues?

If you run into any issues using the package, please feel free to raise an issue, and I will do my best to help you solve it. Additionally, if you would like to apply the method for more complex analyses, please reach out - I would be happy to help get an appropriate model set up for your use case.

Citing bayes_drt2

If you use bayes_drt2 for published work, please consider citing the following paper:

• Huang, J., Papac, M., and O'Hayre, R. (2020). Towards robust autonomous impedance spectroscopy analysis: a calibrated hierarchical Bayesian approach for electrochemical impedance spectroscopy (EIS) inversion. Electrochimica Acta, 367, 137493. https://doi.org/10.1016/j.electacta.2020.137493

Additionally, if you use the ridge_fit method with hyper_lambda=True or hyper_w=True, please cite the corresponding work below:

• hyper_lambda=True: Ciucci, F., & Chen, C. (2015). Analysis of electrochemical impedance spectroscopy data using the distribution of relaxation times: A Bayesian and hierarchical Bayesian approach. Electrochimica Acta, 167, 439–454. https://doi.org/10.1016/j.electacta.2015.03.123
• hyper_w=True: Effat, M. B., & Ciucci, F. (2017). Bayesian and Hierarchical Bayesian Based Regularization for Deconvolving the Distribution of Relaxation Times from Electrochemical Impedance Spectroscopy Data. Electrochimica Acta, 247, 1117–1129. https://doi.org/10.1016/J.ELECTACTA.2017.07.050