changed ar1 logp to use ar1 precision instead of innovation precision (#3899)

* changed ar1 logp to use ar1 precision instead of innovation precision

* fixed tests for AR1

* making AR1 scipy test behave like pymc3 version

* Update pymc3/distributions/timeseries.py

Co-authored-by: Thomas Wiecki <[email protected]>

* Update pymc3/distributions/timeseries.py

Co-authored-by: Thomas Wiecki <[email protected]>

* updated AR notebook to use new AR1 model

* Fixed release notes

* Black

* Updated AR NB

* Blackified AR NB

Co-authored-by: Thomas Wiecki <[email protected]>
Co-authored-by: AlexAndorra <[email protected]>

Author: 3 people

Diff for: RELEASE-NOTES.md

@@ -34,6 +34,7 @@
 - End of sampling report now uses `arviz.InferenceData` internally and avoids storing
   pointwise log likelihood (see [#3883](https://github.com/pymc-devs/pymc3/pull/3883)).
 - The multiprocessing start method on MacOS is now set to "forkserver", to avoid crashes (see issue [#3849](https://github.com/pymc-devs/pymc3/issues/3849), solved by [#3919](https://github.com/pymc-devs/pymc3/pull/3919)).
+- The AR1 logp now uses the precision of the whole AR1 process instead of just the innovation precision (see issue [#3892](https://github.com/pymc-devs/pymc3/issues/3892), fixed by [#3899](https://github.com/pymc-devs/pymc3/pull/3899)).
 - Forced the `Beta` distribution's `random` method to generate samples that are in the open interval $(0, 1)$, i.e. no value can be equal to zero or equal to one (issue [#3898](https://github.com/pymc-devs/pymc3/issues/3898) fixed by [#3924](https://github.com/pymc-devs/pymc3/pull/3924)).
 - Fixed an issue that happened on Windows, that was introduced by the clipped beta distribution rvs function ([#3924](https://github.com/pymc-devs/pymc3/pull/3924)). Windows does not support the `float128` dtype, but we had assumed that it had to be available. The solution was to only support `float128` on Linux and Darwin systems (see issue [#3929](https://github.com/pymc-devs/pymc3/issues/3849) fixed by [#3930](https://github.com/pymc-devs/pymc3/pull/3930)).