Flavio

This point release fixes a few minor issues and adds or updates the following experimental measurements:

- Missing observables in the 2015 CMS [measurement](https://arxiv.org/abs/1507.08126) of B→K*μ⁺μ⁻
- 2013 CMS [measurement](https://arxiv.org/abs/1308.3409) of B→K*μ⁺μ⁻ (which is statistically independent of the former)
- 2017 LHCb measurement of B_s→μ⁺μ⁻ updated to [published version](https://arxiv.org/abs/1703.05747). Thanks to Marc Olivier Bettler and Flavio Archilli for useful correspondence and for providing the 2D likelihood data.

This minor release fixes some minor bugs, brings one new feature and new measurements.

New feature

When using the `FastFit` class, the computationally expensive Standard Model covariance matrix containing theory uncertainties and their correlations can now be saved to disk using the `save_sm_covariance` method and loaded back using `load_sm_covariance` so it does not have to be recomputed.

New measurements

The new measurements of the B→K*μμ angular analysis by ATLAS and CMS shown at Moriond EW 2017 have been added. Moreover, the corresponding measurements by the Tevatron experiment CDF, that were still missing, are also included now. That's 631 lines of new experimental data!

This is a quick bug fix release correcting a typo in the QCDF corrections to B→Vll decays at low q². The numerical impact of the change on observables is tiny. Thanks a lot to Christoph Langenbruch for reporting this bug.

This minor release brings a few improvements to the handling of experimental measurements and theory parameters as well as some new experimental measurements.

YAML export for parameter constraints and measurements

The values and uncertainties of all parameters are represented in flavio by an instance of the `ParameterConstraints` class. By default, the instance `flavio.default_parameters` is populated from YAML files (see [the documentation](https://flav-io.github.io/docs/customize.html)). Similarly, experimental measurements and their uncertainties are represented by instances of the `Measurement` class, populated from the file `measurements.yaml`. The new feature in this release is that these classes can now also be *exported* to YAML, using the new `get_yaml()` methods. This allows to create or modify measurements or parameter constraints in code and export them to a simple text file for later reuse or for sharing them.

New experimental measurements

- [New LHCb limit](https://arxiv.org/abs/1703.02508) on B_s,d→ττ
- All BaBar and Belle measurements of B→X_sll
- Existing limits on lepton flavour violating B decays
- [BaBar limit](https://arxiv.org/abs/1605.09637) on B→Kττ

Interface changes

- The observable `BR(Bd->mumu)` was renamed to `BR(B0->mumu)` for consistency with other observables
- When specifying multivariate numerical constraints in YAML, the key `distribution: multivariate_numerical` now has to be specified explicitly. Multivariate *normal* constraints can now be specified using the same format.
- Multivariate normal distributions can now alternatively be specified in terms of standard deviations and a correlation matrix instead of a covariance matrix

This release brings a new plot function, parallelization, a few minor new features and bug fixes,
as well as updated experimental data.

New plot function

For Bayesian analyses using Markov chains, smooth 1D and 2D histograms often
have to be generated. This is already possible using the functions
`smooth_histogram` and `density_contour` in `flavio.plots`. The new function
`density_contour_joint` combines these functions by showing the contours of a
2D distribution along with the 1D marginals along the x and y axes.
There is a demo of the new function in the new [notebook in the examples repository](https://github.com/flav-io/flavio-examples/blob/master/Plots_for_Bayesian_analyses.ipynb).

Parallelization

When generating likelihood contour plots from parameter or Wilson coefficient
fits, one faces the often time consuming steps of computing the likelihood in
a 2D plane (using `flavio.plots.likelihood_contour` or
`flavio.plots.likelihood_contour_data`) or of generating the pseudo-measurement
for `FastFit` instances (using the `make_measurement` method).
All of these three functions can now be *parallelized*, leveraging the
power of multi-CPU systems. This works by simply passing the option
`threads=N` with `N` > 1 to these functions.

Treatment of upper limits

For treating upper limits in experimental measurements, e.g. on branching
ratios of unobserved decays, there is a new probability distribution
`GeneralGammaUpperLimit` that is appropriate for low-statistics counting
experiments with an uncertain background. This applies e.g. to the
rare *B* decays with neutrinos in the final state mentioned below.

Other improvements

- For all classes with named instances, e.g. `Observable`, `Measurement`, or `Parameter`, instances can now be accessed with a dictionary-like notation, e.g. `Observable['BR(Bs->mumu)']`, in addition to the old `get_instance` method.
- All 1D probability distributions now have methods `get_error_left`, `get_error_right` with an argument `nsigma` that return the lower and upper error for a given number of sigmas.
- The `FastFit` has gained a new method `best_fit` returning the position and log-likelihood of the best fit point in the space of fit parameters and Wilson coefficients.

Experimental data

- The world average of `BR(B->Xsgamma)` has been updated to use the value of [Misiak and Steinhauser](https://arxiv.org/abs/1702.04571) that includes the recent [Belle measurement](https://arxiv.org/abs/1608.02344)
- All existing limits on decays of the type B→M*νν*, where M is a meson, have been added, including the new [Belle analysis](https://arxiv.org/abs/1702.03224), and using the new generalized treatment of upper limits mentioned above. Thanks to James Kahn for useful discussions.

This release brings major improvements especially in two sectors: the treatment of numerical likelihoods and plotting functions for 1D and 2D likelihoods. Users of `flavio.plots.band_plot` should read on as there have been some interface changes.

Improved treatment of numerical likelihoods
- Measurements of one- or multi-dimensional experimental constraints can now be specified in numerical form directly in YAML files. An example are the correlated measurements of rare leptonic B decays by CMS and LHCb that are now [included by default](https://github.com/flav-io/flavio/blob/dd313fa1060b1ad0491e44ed94059af7d1349f13/flavio/data/measurements.yml#L2671-L2752). See also [the documentation](https://flav-io.github.io/docs/probability.html#arbitrary-numerical-univariate-constraints).

Improvements to plot functions
- The function `flavio.plots.band_plot`, used for 2D likelihood plots given a log-likelihood function (e.g. from a `FastFit` instance) has been superseded by the new function `flavio.plots.likelihood_contour`. The old name still works but might be removed in the near future. `flavio.plots.likelihood_contour` actually calls two functions after one another: `flavio.plots.likelihood_contour_data` computes the numerical values to plot; `flavio.plots.contour` produces the actual plot.
The advantage of this split is that these functions can also be called separately, e.g. to perform the time-consuming calculation only once and be able to make tweaks to the plot style without the need for recomputation.
- The function `flavio.plots.density_contour`, used for density plots e.g. for Bayesian MCMC analyses, has been rewritten from scratch:
- Data production is also separated into `flavio.plots.density_contour_data` and the same function `flavio.plots.contour` as for the likelihood plots is used for presentation
- For the kernel density estimate, a fast fourier transform is used now. For a large number of points, as is typical for MCMC analyses, this leads to an enormous speed-up. Density contours can now be plotted from samples with several million points in a matter of seconds!
- The function `flavio.plots.smooth_histogram`, the 1D analogue of density contour, has also been rewritten from scratch:
- Instead of just interpolating a histogram, it now also uses a Gaussian KDE based on FFT
- The 1 sigma region can now be displayed as a shaded vertical band
- A new function `flavio.plots.pdf_plot` plots 1D likelihoods, e.g. from `FastFit` instances, with the same style as `smooth_histogram`.

All the old and new plot functions are documented in detail in the [API docs](https://flav-io.github.io/apidoc/flavio/plots/plotfunctions.m.html). Example notebooks will follow in due time.

Physics updates

Finally, there have also been some small physics improvements, in addition to the experimental measurements mentioned above.
- Some parameters [updated](https://github.com/flav-io/flavio/commit/77b16517afc8560743ea16b7ac8ed6dacd8f3c97) to HFAG 2016 values
- Mass-eigenstate rate asymmetry in B_s→ll added (`ADeltaGamma(Bs->mumu)` etc.)
- Angular observable S₆^c in B→K*ll added (e.g. `<S6c>(B0->K*mumu)`)