Bayesian Parameter Inference for Stochastic Models


For a multitude of different field sciences, determining the underlying mechanistic models is important in order to further our understanding. An accurate estimation of the parameters of such mechanistic models through data can be computationally prohibitive. This project exploits neural networks in order to learn minimal and near sufficient summary statistics as latent embeddings on simulated data for multiple stochastic models. This is corroborated with sharp model parameter posteriors observed through approximate Bayesian computation experiments.

Starting Date / Status

April 2018


PI / Partners

Mathematical Methods in Environmental Research (EAWAG)

Biomedical Simulation (ZHAW)

Data Science Lab (USI)

Director of Paul Scherrer Institute (PSI)



Reliably estimating parameters of mechanistic models from data (Bayesian inference) is computationally expensive if (i) the data is big or (ii) the model is stochastic. Stochastic models are needed for reliable predictions.


Advances in algorithms as well as parallel computing infrastructure allow for Bayesian inference to be applied to a large class of stochastic models and to be scaled up to big data. We developed neural network based framework which can learn minimal and near sufficient summary statistics as latent embeddings on simulated data for multiple stochastic models. Experiments with approximate Bayesian computation yield sharp model parameter posteriors. For both stochastic models, developed solution finds near sufficient summary statistics.


The developed methodology can be applied in many fields of science and engineering, wherever system understanding (mechanistic model) needs to be combined with data, for advancing domain knowledge and making more reliable predictions.


  • Stephan Allenspach, Pascal Puphal, Joosep Link, Ivo Heinmaa, Ekaterina Pomjakushina, Cornelius Krellner, Jakob Lass, Gregory S. Tucker, Christof Niedermayer, Shusaku Imajo, Yoshimitsu Kohama, Koichi Kindo, Steffen Krämer, Mladen Horvatić, Marcelo Jaime, Alexander Madsen, Antonietta Mira, Nicolas Laflorencie, Frédéric Mila, Bruce Normand, Christian Rüegg, Raivo Stern, and Franziska Weickert. “Revealing three-dimensional quantum criticality by Sr substitution in Han purple”. Physical Review Research 3.2 (2021): 023177. doi: 10.1103/PhysRevResearch.3.023177

  • David J. Warne, Anthony Ebert, Christopher Drovandi, Wenbiao Hu, Antonietta Mira, and Kerrie Mengersen. “Hindsight is 2020 vision: a characterisation of the global response to the COVID-19 pandemic.” BMC public health 20, no. 1 (2020): 1-14. doi: 10.1186/s12889-020-09972-z

  • Louis Raynal, Sixing Chen, Antonietta Mira, and Jukka-Pekka Onnela. “Scalable Approximate Bayesian Computation for Growing Network Models via Extrapolated and Sampled Summaries.” Bayesian Anal. Advance Publication 1 – 28, 2021. doi: 10.1214/20-BA1248

  • K. Guratinder, M. Schmidt, H. C. Walker, R. Bewley, M. Wörle, D. Cabra, S. A. Osorio, M. Villalba, A. K. Madsen, L. Keller, A. Wildes, P. Puphal, A. Cervellino, Ch. Rüegg, and O. Zaharko. “Magnetic correlations in the triangular antiferromagnet FeGa 2 S 4.” Physical Review B 104.6 (2021): 064412. doi: 10.1103/PhysRevB.104.064412

  • Carlo Albert, Antonio Ferriz-Mas, Filippo Gaia, and Simone Ulzega. “Can Stochastic Resonance explain Recurrence of Grand Minima?”, The Astrophysical Journal Letters 916.2 (2021): L9. doi: 10.3847/2041-8213/ac0fd6

  • Carlo Albert, Simone Ulzega, Firat Ozdemir, Fernando Perez-Cruz, and Antonietta Mira. “Learning Summary Statistics for \\Bayesian Inference with Autoencoders”, submitted.

  • Ward et al., “Ideal Bond Disorder in the Quantum Spin Ladder”, in preparation