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| 1 | +Entropy Pooling in Python |
| 2 | +========================= |
| 3 | + |
| 4 | +Due to popular demand from developers, this package contains the Entropy Pooling |
| 5 | +implementation from the [fortitudo.tech Python package](https://github.com/fortitudo-tech/fortitudo.tech) |
| 6 | +with a more permissive BSD 3-Clause license. |
| 7 | + |
| 8 | +This package contains only one function called ep and has minimal dependencies |
| 9 | +with just scipy. See [this example](https://github.com/fortitudo-tech/entropy-pooling/blob/main/example/EntropyPooling.ipynb) |
| 10 | +for how you can import and use the ep function. |
| 11 | + |
| 12 | +Installation instructions |
| 13 | +------------------------- |
| 14 | + |
| 15 | +Installation can be done via pip: |
| 16 | + |
| 17 | + pip install entropy-pooling |
| 18 | + |
| 19 | +Theory |
| 20 | +------ |
| 21 | +Entropy Pooling is a powerful method for implementing subjective views and |
| 22 | +performing stress-tests for fully general Monte Carlo distributions. It was first |
| 23 | +introduced by [Meucci (2008)](https://ssrn.com/abstract=1213325) and refined |
| 24 | +with sequential algorithms by [Vorobets (2021)](https://ssrn.com/abstract=3936392). |
| 25 | + |
| 26 | +The original Entropy Pooling approach solves the minimum relative entropy problem |
| 27 | + |
| 28 | +$$q=\text{argmin}\lbrace x'\left(\ln x-\ln p\right)\rbrace$$ |
| 29 | + |
| 30 | +subject to the constraints |
| 31 | + |
| 32 | +$$Ax=b \quad \text{and} \quad Gx\leq h.$$ |
| 33 | + |
| 34 | +The constraints matrices $A$ and $G$ contain transformations of the Monte Carlo |
| 35 | +simulation that allow you to implement subjective views and stress-tests by |
| 36 | +changing the joint scenario probabilities from a prior probability vector $p$ |
| 37 | +to a posterior probability vector $q$. |
| 38 | + |
| 39 | +A useful statistic when working with Entropy Pooling is the effective number of |
| 40 | +scenarios introduced by [Meucci (2012)](https://ssrn.com/abstract=1971808). For |
| 41 | +a causal Bayesian nets overlay on top of Entropy Pooling, see |
| 42 | +[Vorobets (2023)](https://ssrn.com/abstract=4444291). |
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