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We are now ready to train an amortized posterior approximator. For instance,
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- Radev, S. T., Mertens, U. K., Voss, A., Ardizzone, L., & Köthe, U. (2020).
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BayesFlow: Learning complex stochastic models with invertible neural networks.
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<em>IEEE Transactions on Neural Networks and Learning Systems</em>, available
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for free at: https://arxiv.org/abs/2003.06281.
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<em>IEEE Transactions on Neural Networks and Learning Systems, 33(4)</em>, 1452-1466.
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- Radev, S. T., Graw, F., Chen, S., Mutters, N. T., Eichel, V. M., Bärnighausen, T., & Köthe, U. (2021).
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OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany. <em>PLoS computational biology</em>, 17(10), e1009472.
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OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany. <em>PLoS computational biology, 17(10)</em>, e1009472.
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- Bieringer, S., Butter, A., Heimel, T., Höche, S., Köthe, U., Plehn, T., & Radev, S. T. (2021).
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Measuring QCD splittings with invertible networks. <em>SciPost Physics</em>, 10(6), 126.
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Measuring QCD splittings with invertible networks. <em>SciPost Physics, 10(6)</em>, 126.
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- von Krause, M., Radev, S. T., & Voss, A. (2022).
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Mental speed is high until age 60 as revealed by analysis of over a million participants.
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<em>Nature Human Behaviour</em>, 6(5), 700-708.
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<em>Nature Human Behaviour, 6(5)</em>, 700-708.
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## Model Misspecification
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@@ -174,7 +174,7 @@ The amortizer knows how to combine its losses and you can inspect the summary sp
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### References and Further Reading
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- Schmitt, M., Bürkner P. C., Köthe U., & Radev S. T. (2021). Detecting Model
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- Schmitt, M., Bürkner P. C., Köthe U., & Radev S. T. (2022). Detecting Model
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Misspecification in Amortized Bayesian Inference with Neural Networks. <em>ArXiv
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preprint</em>, available for free at: https://arxiv.org/abs/2112.08866
For the vast majority of simulated data sets, the "true" data-generating model is correctly identified. With these diagnostic results backing us up, we can proceed and apply our trained network to empirical data.
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BayesFlow is also able to conduct model comparison for hierarchical models. See this [tutorial notebook](docs/source/tutorial_notebooks/Hierarchical_Model_Comparison_MPT.ipynb) for an introduction to the associated workflow.
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BayesFlow is also able to conduct model comparison for hierarchical models. See this [tutorial notebook](examples/Hierarchical_Model_Comparison_MPT.ipynb) for an introduction to the associated workflow.
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### References and Further Reading
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### References and Further Reading
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Radev, S. T., Schmitt, M., Pratz, V., Picchini, U., Köthe, U., & Bürkner, P. C. (2023).
This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy -– EXC-2181 - 390900948 (the Heidelberg Cluster of Excellence STRUCTURES) and -- EXC-2075 - 390740016 (the Stuttgart Cluster of Excellence SimTech), the Informatics for Life initiative funded by the Klaus Tschira Foundation, and Google Cloud through the Academic Research Grants program.
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## Citing BayesFlow
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You can cite BayesFlow along the lines of:
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- We approximated the posterior with neural posterior estimation and learned summary statistics (NPE; Radev et al., 2020), as implemented in the BayesFlow software for amortized Bayesian workflows (Radev et al., 2023b).
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- We approximated the likelihood with neural likelihood estimation (NLE; Papamakarios et al., 2019) without hand-cafted summary statistics, as implemented in the BayesFlow software for amortized Bayesian workflows (Radev et al., 2023b).
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- We performed simultaneous posterior and likelihood estimation with jointly amortized neural approximation (JANA; Radev et al., 2023a), as implemented in the BayesFlow software for amortized Bayesian workflows (Radev et al., 2023b).
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1. Radev, S. T., Schmitt, M., Schumacher, L., Elsemüller, L., Pratz, V., Schälte, Y., Köthe, U., & Bürkner, P.-C. (2023). BayesFlow: Amortized Bayesian workflows with neural networks. *arXiv:2306.16015*. ([arXiv](https://arxiv.org/abs/2306.16015))
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2. Radev, S. T., Mertens, U. K., Voss, A., Ardizzone, L., Köthe, U. (2020). BayesFlow: Learning complex stochastic models with invertible neural networks. *IEEE Transactions on Neural Networks and Learning Systems, 33(4)*, 1452-1466. ([arXiv](https://arxiv.org/abs/2003.06281))([IEEE TNNLS](https://ieeexplore.ieee.org/document/9298920))
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3. Radev, S. T., Schmitt, M., Pratz, V., Picchini, U., Köthe, U., & Bürkner, P.-C. (2023). JANA: Jointly amortized neural approximation of complex Bayesian models. *Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, 216*, 1695-1706. ([arXiv](https://arxiv.org/abs/2302.09125))([PLMR](https://proceedings.mlr.press/v216/radev23a.html))
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**BibTeX:**
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```
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@misc{radev2023bayesflow,
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title = {{BayesFlow}: Amortized Bayesian workflows with neural networks},
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author = {Stefan T Radev and Marvin Schmitt and Lukas Schumacher and Lasse Elsem\"{u}ller and Valentin Pratz and Yannik Sch\"{a}lte and Ullrich K\"{o}the and Paul-Christian B\"{u}rkner},
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year = {2023},
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publisher= {arXiv},
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url={https://arxiv.org/abs/2306.16015}
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}
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@article{radev2020bayesflow,
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title={{BayesFlow}: Learning complex stochastic models with invertible neural networks},
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author={Radev, Stefan T. and Mertens, Ulf K. and Voss, Andreas and Ardizzone, Lynton and K{\"o}the, Ullrich},
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journal={IEEE transactions on neural networks and learning systems},
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volume={33},
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number={4},
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pages={1452--1466},
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year={2020},
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publisher={IEEE}
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}
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@inproceedings{pmlr-v216-radev23a,
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title = {{JANA}: Jointly amortized neural approximation of complex {B}ayesian models},
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author = {Radev, Stefan T. and Schmitt, Marvin and Pratz, Valentin and Picchini, Umberto and K\"othe, Ullrich and B\"urkner, Paul-Christian},
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booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
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pages = {1695--1706},
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year = {2023},
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volume = {216},
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series = {Proceedings of Machine Learning Research},
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