PEPSDI (Particles Engine for Population Stochastic DynamIcs) is a Bayesian inference framework for dynamic state space mixed effects models (SSMEM). A SSMEM is a powerful tool for modelling multi-individual data since it can account for intrinsic (intra-individual), extrinsic (inter-individual) and residual (measurement-error) variability. Overall, this makes SSMEM:s suitable for, and not limited to, problems in pharmacology [1] and cellular biology [2].
In contrast to non-linear mixed effects frameworks, such as Monolix [3], PEPSDI assumes an underlaying stochastic dynamic model. PEPSDI currently supports stochastic differential equations (SDE:s). For chemical reaction networks (e.g a cellular pathway) PEPSDI further supports the SSA (Gillespie) [4], Extrande [5], and tau-leaping [6] simulators.
By levering Hamiltonian-Monte-Carlo sampling via the Turing-library PEPSDI is flexible regarding the probability distribution of the random-effects. Currently, the random effects can be modelled via a log-normal distribution with either full, or diagonal, covariance matrix. However, additional parameterisations (distributions) can be implemented.
PEPSDI is introduced, and described, in the manuscript add. To get started with PEPSDI the examples in the manuscript are available as notebooks under Code/Examples. This folder also contains notebooks on how to leverage the underlaying algorithms in PEPSDI to perform single-individual inference. An extensive tutorial is further available under the examples-folder. The results presented in the manuscript were produced by the scripts in Code/Result_paper-folder.
This repository is a first (pre-alpha) version of PEPSDI. If wanting to use PEPSDI, and need help, the corresponding author in the manuscript can be contacted.
If you use PEPSDI in your scientific work, please cite: S. Persson, N. Welkenhuysen, S. Shashkova, S. Wiqvist, P. Reith, G. Schmidt, U. Picchini, M. Cvijovic Scalable and flexible inference framework for stochastic dynamic single-cell models. (2022) PLoS Comput Biol 18(5): e1010082. https://doi.org/10.1371/journal.pcbi.1010082
PEPSDI performs full Bayesian inference for SSMEM. This means that PEPSDI infers individual parameters ci, between individual constant parameters ĸ, strength of measurement error ξ and population parameters η; ci ~ π(ci | η). This is achieved by using a Gibbs-sampler to target the full-posterior. Some Gibbs-steps have a tractable likelihood and are thus sampled via HMC, while the remaining Gibbs-step have an intractable likelihood. These are sampled via pseduo-marginal inference [7] where particle-filters are employed to obtain an unbiased likelihood estimate [8]. To properly tune the particles filters, as shown in the example notebooks, a pilot run is required. Furthermore, for computational efficiency we employ, when possible, correlated-particle filters [9], and tune the parameters proposal distributions using adaptive algorithms [10].
PEPSDI can be run with two options. We recommend the second (default in notebooks) where constant parameters (ĸ, ξ) are allowed to vary weakly between cells. This can speed up inference by more than a factor 30.
PEPSDI was developed using Julia 1.5.2 on Linux (has been successfully run on both Fedora and Ubunutu). PEPSDI should work with newer versions off Julia, especially if the toml-file is used to create an environment with all correct dependencies.
Since PEPSDI was developed on Linux, there might be problems with the file-path on Windows. One way to potentially resolve this for a Windows user might be (I have not tested this) to download the Ubuntu-terminal for Windows
PEPSDI SOFTWARE LICENSE TERMS
1 GENERAL
1.1 PEPSDI (Particles Engine for Population Stochastic DynamIcs) is a Bayesian inference framework for single-cell stochastic dynamic models. The PEPSDI software is developed by Sebastian Persson, Umberto Picchini and Marija Cvijovic (the “Licensors”, “we” or “us”) and related contributors as further set forth on the PEPSDI website located at https://github.com/cvijoviclab/PEPSDI. By installing and using PEPSDI, you and your organisation is granted a license to use PEPSDI subject to these terms. If you do not accept these terms, please do not install and do not use PEPSDI.
1.2 PEPSDI is provided together with its source code and intended to be viewed and used as open source. The intent is that you shall be able to freely use and develop PEPSDI for your research, development and educational purposes. However, as much as we encourage use and development of PEPSDI, we want to restrict redistribution and commercial sublicensing, which means that there are some restrictions to your use set forth in Section 2.4.
2 INTELLECTUAL PROPERTY RIGHTS AND LICENSE
2.1 Any and all intellectual property rights, including without limitation copyright protected materials, source code, database rights, registered and unregistered trade-marks, registered and unregistered design rights, patents and patentable inventions, know how (regardless if patentable or not) and all other rights in or relating to PEPSDI is the exclusive property of the Licensors, or the property of the Licensors’s contributing licensors as applicable.
2.2 You are granted a non-exclusive, royalty-free right and license to use PEPSDI for your internal research and development, including commercial research and development, as well as for educational and academic purposes. The license furthermore includes the right to access and amend the source code of PEPSDI and implement such changes in PEPSDI as you deem fit.
2.3 Any amendments made by you to PEPSDI are your intellectual property that you may use freely as long as such use is not contrary to these terms. We encourage that you share amendments with us, in which case we are given the right (but not the obligation) to include them in future versions of PEPSDI and make them available on these terms or terms materially similar, but you are (i) not required to share such amendments and (ii) your amendments if shared are subject to the same limitations of liability as set forth in clause 3.
2.4 Unless you have our prior written consent (which consent may be subject to further terms), you are expressly not permitted to re-distribute PEPSDI, amended or in its original form, or any part thereof, regardless if such re-distribution is made for free or for a fee. You can however point third parties to download PEPSDI directly from our website or other official sources. Furthermore, you may not integrate PEPSDI or parts thereof into other software regardless if such software is licensed on open source or so called “proprietary” terms. Use contrary to this clause 2.4 shall in addition render your license to use PEPSDI null and void.
3 LIMITATION OF LIABILITY
3.1 PEPSDI IS PROVIDED “AS IS” AND “WHERE IS” WITHOUT ANY WARRANTY OF ANY KIND, INCLUDING WITHOUT LIMITATION ANY IMPLIED, EXPRESS OR STATUTORY WARRANTIES, INCLUDING, BUT NOT LIMITED TO, ANY WARRANTIES OF FUNCTIONALITY, COMPLETENESS OR ACCURACY, FITNESS FOR A PARTICULAR PURPOSE, MERCHANTABILITY, LACK OF VIRUSES OR FREEDOM FROM INFRINGEMENT. FURTHERMORE, YOU ACKNOWLEDGE THAT THE SOFTWARE IS NOT, AND WILL NOT BE, ERROR FREE AND RUN WITHOUT ANY INTERRUPTION.
3.2 We do not accept any liability of any kind, whether direct or indirect, in tort or under any form of contractual liability or other doctrine for any damage or claim that may arise as a result of your use of PEPSDI, regardless if such use is with our version without any amendment to PEPSDI that you may have made. 3.3 Furthermore, if any third party makes a claim against us as a result of your amended or unamended use of PEPSDI, you shall indemnify and hold us harmless from any such claim, including related cost and expense such as legal fees.
4 ATTRIBUTION
When publishing scientific results or research reports where PEPSDI has been used in such research, we encourage and appreciate that you include references to your use of PEPSDI in such research, as well as the scientific publications cited on our website.
5 CHOICE OF LAW, DISPUTES
These terms shall be governed and construed in accordance with the substantive laws of Sweden, without regard to its conflicts of law principles. Any dispute, controversy or claim arising out of or in connection with this Agreement, or the breach, termination or invalidity thereof, shall be settled by the courts of Sweden with the district court of Stockholm as first instance.
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- Deligiannidis G, Doucet A, Pitt MK. The Correlated Pseudo-Marginal Method. Journalof the Royal Statistical Society Series B: Statistical Methodology. 2018 nov;80(5):839–870.
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