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Nathan Simpson authored Apr 4, 2022
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## currently implemented:
- **basic operations**:
- [`relaxed.hist`](src/relaxed/ops/histograms.py): histograms via kernel density estimation (tunable bandwidth)
- [`relaxed.cut`](src/relaxed/ops/cuts.py): approximates a hard cut with a sigmoid function (tunable slope)
- [`relaxed.hist`](src/relaxed/ops/histograms.py): histograms via kernel density estimation (tunable bandwidth).
- [`relaxed.cut`](src/relaxed/ops/cuts.py): approximates a hard cut with a sigmoid function (tunable slope).
- **fitting routines**:
- [`relaxed.mle.fit`](src/relaxed/mle/global_fit.py): global MLE fit
- [`relaxed.mle.fixed_poi_fit`](src/relaxed/infer/hypothesis_test.py): constrained fit given a value of a parameter of interest
- [`relaxed.mle.fit`](src/relaxed/mle/global_fit.py): global MLE fit.
- [`relaxed.mle.fixed_poi_fit`](src/relaxed/infer/hypothesis_test.py): constrained fit given a value of a parameter of interest.
- **inference**:
- [`relaxed.infer.hypotest`](src/relaxed/infer/hypothesis_test.py): hypothesis test using the profile likelihood as a test statistic
- [`relaxed.fisher_info`](src/relaxed/ops/fisher_information.py): the fisher information matrix (of a `pyhf`-type model)
- [`relaxed.cramer_rao_uncert`](src/relaxed/ops/fisher_information.py): inverts the fisher information matrix to provide uncertainties valid through the [Cramér-Rao bound](https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound)
- [`relaxed.infer.hypotest`](src/relaxed/infer/hypothesis_test.py): hypothesis test based on the profile likelihood. Supports test statistics for both limit setting (`q`) and discovery (`q_0`).
- [`relaxed.fisher_info`](src/relaxed/ops/fisher_information.py): the fisher information matrix (of a `pyhf`-type model).
- [`relaxed.cramer_rao_uncert`](src/relaxed/ops/fisher_information.py): inverts the fisher information matrix to provide uncertainties valid through the [Cramér-Rao bound](https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound).
- **metrics**:
- [`relaxed.metrics.gaussianity`](src/relaxed/metrics/likelihood_gaussianity.py): an experimental metric that quantifies the mean-squared difference of a likelihood function with respect to its gaussian approximation (covariance calculated using the Cramér-Rao bound above)
- [`relaxed.metrics.gaussianity`](src/relaxed/metrics/likelihood_gaussianity.py): an experimental metric that quantifies the mean-squared difference of a likelihood function with respect to its gaussian approximation (covariance calculated using the Cramér-Rao bound above).
- [`relaxed.metrics.asimov_sig`](src/relaxed/metrics/significance.py): easy access to the (single- and multi-bin) stat-only expected significance.

We're maintaining a list of desired differentiable operations in [`list_of_operations.md`](list_of_operations.md) (thanks to [@cranmer](http://github.com/cranmer)) -- feel free to take inspiration or contribute with a PR if there's one you can handle :)
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