Mediation: new example notebook (#158)

* mediation analysis notebook + figure

* pre-commit checks

* fix typos

* xr import not needed, update sampling parameters

* add xarray to watermark

* tweak model definition, add sanity check for total effect

* update likelihood terms + add m, x as pm.Data objects

* update comparison figure + "sanity check" -> "double check"

Co-authored-by: Oriol Abril-Pla <oriol.abril.pla@gmail.com>

Author: drbenvincent

examples/case_studies/mediation.png

@@ -5,6 +5,7 @@ Gallery.contents = {
     "case_studies/rugby_analytics": "Case Studies",
     "case_studies/multilevel_modeling": "Case Studies",
     "case_studies/putting_workflow": "Case Studies",
+    "case_studies/mediation_analysis": "Case Studies",
     "case_studies/bayesian_ab_testing": "Case Studies",
     "diagnostics_and_criticism/Diagnosing_biased_Inference_with_Divergences": "Diagnostics and Model Criticism",
     "diagnostics_and_criticism/model_comparison": "Diagnostics and Model Criticism",