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https://github.com/mathause/dist_cov

conditional distributions with covariates
https://github.com/mathause/dist_cov

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conditional distributions with covariates

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# Distributions with covariates



[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.7922002.svg)](https://doi.org/10.5281/zenodo.7922002)



Authors: Mathias Hauser1, Dominik Schumacher1, Sonia I. Seneviratne1



1Institute for Atmospheric and Climate Science, Department of Environmental Systems Science, ETH Zurich, Zurich, Switzerland



Conditional distributions with covariates



:warning: **Warning**: this package does currently not have any tests.



## Approach



We use distributions where one (or more) parameter is dependent on a covariate - e.g. the global mean temperature ($T_{glob}$). for the normal distribution model the mean ($\mu$) and standard deviation ($\sigma$) as follows:



$\mu' = \beta_0 + \beta_1 * T_{glob}$



$\sigma' = \sigma$



As no such distribution is available in python we adapt distributions in scipy (e.g. [scipy.stats.norm](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html)).



### Markov chain Monte Carlo (MCMC) sampler



The parameter uncertainty is estimated with [emcee](https://emcee.readthedocs.io/en/stable/) - an MCMC sampler - see `dist_cov.sample.run_mcmc`. Also check it's website for a good overview. Of course any other MCMCM sampler can be used as well.



I usually describe this as follows: "We calculate uncertainties in a Bayesian setting and use a Markov Chain MonteCarlo (MCMC) sampler that is affine-transformation invariant (Goodman & Weare, [2010](https://doi.org/10.2140/camcos.2010.5.6); Foreman-Mackey et al., [2013](https://doi.org/10.1086/67006)) to estimate the parameters of the distributions. Starting from non-informative* priors, the converged posterior distributions (50,000** non-independent samples) give an estimate of the parameteruncertainty.



* Not all priors are non-informative (i.e. when setting a `constrain` in `dist_cov.distributions.gev_cov`)!



** This is `n_walker * production` in `dist_cov.sample.run_mcmc`



## Installation



### Dependencies



dist_cov depends on the python packages emcee, numpy, and scipy. To run the examples corner.py, matplotlib, and xarray are required as well.



### Install development version



dist_cov is not available from pypi or conda-forge, therefore it needs to be installed using pip directly from github.



```bash

pip install git+https://github.com/mathause/dist_cov

```



To run the examples also install:



```bash

pip install corner matplotlib xarray

```



### Install latest released version



Go to the [newest release on github](https://github.com/mathause/dist_cov/releases/latest), copy the URL of the `*.tar.gz` source file at the botton and then use pip to install it (i.e., `pip install ...`).



## Documentation



Documentation is sparse, but check the [examples](./examples).



## Citing dist_cov



Please cite Hauser et al. ([2017](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017EF000612)) or [10.5281/zenodo.7922001](https://doi.org/10.5281/zenodo.7922001) if you are using dist_cov.



If you use [emcee](https://emcee.readthedocs.io/en/stable/) also consider citing Foreman-Mackey et al. ([2013](https://doi.org/10.1086/67006)) and/ or Goodman & Weare ([2010](https://doi.org/10.2140/camcos.2010.5.6)).



## History



This code was originally developed for Hauser et al. ([2017](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017EF000612)) based on the approach described in Coles ([2001](https://link.springer.com/book/10.1007/978-1-4471-3675-0); Chapter 3).

It has been employed in several rapid attribution studies under the auspices of the world weather attribution group, namely:

- Siberian heatwave of 2020 (Ciavarella et al., [2020](https://www.worldweatherattribution.org/siberian-heatwave-of-2020-almost-impossible-without-climate-change/) and Ciavarella et al., [2021](https://link.springer.com/article/10.1007/s10584-021-03052-w))

- Western North American heat wave of 2021 (Philip et al., [2021](https://www.worldweatherattribution.org/western-north-american-extreme-heat-virtually-impossible-without-human-caused-climate-change/) and Philip et al., [2022](https://esd.copernicus.org/articles/13/1689/2022/))

- Indian heat wave of 2022 (Zachariah, et al., [2022](https://www.worldweatherattribution.org/climate-change-made-devastating-early-heat-in-india-and-pakistan-30-times-more-likely/) and Zachariah et al., in review)

- UK heatwave of 2022 (Zachariah et al. [2022](https://www.worldweatherattribution.org/without-human-caused-climate-change-temperatures-of-40c-in-the-uk-would-have-been-extremely-unlikely/))

- Northern Hemisphere droughts of 2022 (Schumacher et al., [2022](https://www.worldweatherattribution.org/high-temperatures-exacerbated-by-climate-change-made-2022-northern-hemisphere-droughts-more-likely/) and Schumacher et al., in review)



It further builds the starting point for modelling extremes in MESMER-X (Quilcaille et al., [2022](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022GL099012)).



## Changelog



See [CHANGELOG.md](CHANGELOG.md).



## License



This project is published under a MIT license.



## References



- Ciavarella, A., Cotterill, D., Stott, P., ... Hauser, M., et al. Prolonged Siberian heat of 2020 almost impossible without human influence. Climatic Change 166, 9 (2021). https://doi.org/10.1007/s10584-021-03052-w

- Coles, S. (2001), An Introduction to Statistical Modeling of Extreme Values, vol. 208, Springer, London.

- Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. (2013). emcee: The MCMC hammer.Publications of the Astronomical Society ofthe Pacific,125, 306–312. https://doi.org/10.1086/67006

- Goodman, J., & Weare, J. (2010). Ensemble samplers with affine invariance.Communications in Applied Mathematics and ComputationalScience,5(1), 65–80. https://doi.org/10.2140/camcos.2010.5.6

- Hauser, M., Gudmundsson, L., Orth, R., Jézéquel, A., Haustein, K., Vautard, R., van Oldenborgh, G.J., Wilcox, L. and Seneviratne, S.I. (2017), Methods and Model Dependency of Extreme Event Attribution: The 2015 European Drought. Earth's Future, 5: 1034-1043. https://doi.org/10.1002/2017EF000612

- Philip, S. Y., Kew, S. F., van Oldenborgh, G. J., Anslow, F. S., Seneviratne, S. I., Vautard, R., Coumou, D., Ebi, K. L., Arrighi, J., Singh, R., van Aalst, M., Pereira Marghidan, C., Wehner, M., Yang, W., Li, S., Schumacher, D. L., Hauser, M., Bonnet, R., Luu, L. N., Lehner, F., Gillett, N., Tradowsky, J. S., Vecchi, G. A., Rodell, C., Stull, R. B., Howard, R., and Otto, F. E. L.: Rapid attribution analysis of the extraordinary heat wave on the Pacific coast of the US and Canada in June 2021, Earth Syst. Dynam., 13, 1689–1713, https://doi.org/10.5194/esd-13-1689-2022, 2022.

- Quilcaille, Y., Gudmundsson, L., Beusch, L., Hauser, M., & Seneviratne, S. I. (2022). Showcasing MESMER-X: Spatially resolved emulation of annual maximum temperatures of Earth System Models. Geophysical Research Letters, 49, e2022GL099012. https://doi.org/10.1029/2022GL099012