[ENH] Conjugate bayes for proportion

Reference Issues/PRs

This relates to the WIP of design of Bayesian blueprint #35

What does this implement/fix? Explain your changes.

This PR implements the BayesianProportionEstimator, a new estimator for estimating proportions using Bayesian inference with a Beta prior. It includes a notebook demonstrating how to use the estimator with a coin toss example, showing how to update prior beliefs with observed data and visualize the posterior distribution.

Does your contribution introduce a new dependency? If yes, which one?

Yes, matplotlib (for plotting).

What should a reviewer concentrate their feedback on?

Certainly! Here’s the improved version of the text:

The implementation of the BayesianProportionEstimator class should be reviewed for its alignment with the WIP Bayesian blueprint #35. Additionally, please evaluate the clarity and completeness of the accompanying notebook example.

It is important to note that the BayesianProportionEstimator is not a traditional regressor. Instead, during fitting, it takes as input an array of Booleans or 1's and 0's representing the success of a series of experiments.

Due to its specialized nature, the estimator is not suitable for tests designed to validate regression functionality, and it may fail such tests.

Maybe we should put this estimator in its own folder.

Did you add any tests for the change?

Any other comments?

PR checklist

For all contributions

[x] I've added myself to the list of contributors with any new badges I've earned :-) How to: add yourself to the all-contributors file in the skpro root directory (not the CONTRIBUTORS.md). Common badges: code - fixing a bug, or adding code logic. doc - writing or improving documentation or docstrings. bug - reporting or diagnosing a bug (get this plus code if you also fixed the bug in the PR).maintenance - CI, test framework, release. See here for full badge reference
[x] The PR title starts with either [ENH], [MNT], [DOC], or [BUG]. [BUG] - bugfix, [MNT] - CI, test framework, [ENH] - adding or improving code, [DOC] - writing or improving documentation or docstrings.

For new estimators

[ ] I've added the estimator to the API reference - in docs/source/api_reference/taskname.rst, follow the pattern.
[x] I've added one or more illustrative usage examples to the docstring, in a pydocstyle compliant Examples section.
[ ] If the estimator relies on a soft dependency, I've set the python_dependencies tag and ensured dependency isolation, see the estimator dependencies guide.

sktime / skpro