.. tinyDA documentation master file, created by sphinx-quickstart on Thu Sep 2 12:44:08 2021. You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. tinyDA ====== tinyDA is a Delayed Acceptance MCMC sampler with finite-length subchain sampling and adaptive error modelling. This is intended as a simple, lightweight implementation, with minimal dependencies, i.e. nothing beyond the SciPy stack. It is fully imperative and easy to use! Features -------- **Proposals** - Random Walk Metropolis Hastings (RWMH) - preconditioned Crank-Nicolson (pCN) - Adaptive Metropolis (AM) - Operator-weighted pCN - Metropolis Adjusted Langevin Algorithm (MALA) - DREAM(Z) - Multiple-Try Metropolis (MTM) **Adaptive Error Models** - State independent - State dependent **Diagnostics** - ArviZ compatibility Documentation ------------- .. toctree:: :maxdepth: 1 modules/sampler modules/posterior modules/proposals modules/distributions modules/diagnostics modules/chains modules/utils Examples -------- Please refer to the `Jupyter Notebooks`_ in the `GitHub repository`_. .. _`Jupyter Notebooks`: https://github.com/mikkelbue/tinyDA/tree/main/examples .. _`GitHub repository`: https://github.com/mikkelbue/tinyDA Installation ------------ Install tinyDA by running: ``pip install tinyDA`` **Dependencies:** - NumPy - SciPy - ArviZ - tqdm - Ray (multiprocessing, optional) Contribute ---------- - `GitHub repository`_ - `Issue tracker`_ .. _`GitHub Repository`: https://github.com/mikkelbue/tinyDA .. _`Issue Tracker`: https://github.com/mikkelbue/tinyDA/issues License ------- The project is licensed under the MIT_ license. .. _MIT: https://github.com/mikkelbue/tinyDA/blob/main/LICENSE References ---------- - Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics, 21(6), 1087–1092. https://doi.org/10.1063/1.1699114 - Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 13. - Liu, J. S., Liang, F., & Wong, W. H. (2000). The Multiple-Try Method and Local Optimization in Metropolis Sampling. Journal of the American Statistical Association, 95(449), 121–134. https://doi.org/10.1080/01621459.2000.10473908 - Haario, H., Saksman, E., & Tamminen, J. (2001). An Adaptive Metropolis Algorithm. Bernoulli, 7(2), 223. https://doi.org/10.2307/3318737 - Cotter, S. L., Roberts, G. O., Stuart, A. M., & White, D. (2013). MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster. Statistical Science, 28(3), 424–446. https://doi.org/10.1214/13-STS421 - Law, K. J. H. (2014). Proposals which speed-up function-space MCMC. Journal of Computational and Applied Mathematics, 262, 127–138. https://doi.org/10.1016/j.cam.2013.07.026 - Vrugt, J. A. (2016). Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation. Environmental Modelling & Software, 75, 273–316. https://doi.org/10.1016/j.envsoft.2015.08.013 - Cui, T., Fox, C., & O’Sullivan, M. J. (2018). A posteriori stochastic correction of reduced models in delayed acceptance MCMC, with application to multiphase subsurface inverse problems. http://arxiv.org/abs/1809.03176 - Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C. (2020). Rank-normalization, folding, and localization: An improved R for assessing convergence of MCMC. https://doi.org/10.1214/20-BA1221 - Lykkegaard, M. B., Dodwell, T. J., & Moxey, D. (2020). Accelerating Uncertainty Quantification of Groundwater Flow Modelling Using Deep Neural Networks. http://arxiv.org/abs/2007.00400 - Lykkegaard, M. B., Mingas, G., Scheichl, R., Fox, C., & Dodwell, T. J. (2020). Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3. - Lykkegaard, M. B., Dodwell, T. J., Fox, C., Mingas, G., & Scheichl, R. (2023). Multilevel Delayed Acceptance MCMC. SIAM/ASA Journal on Uncertainty Quantification, 11(1), 1–30. https://doi.org/10.1137/22M1476770