Multiple updates to v5 (pymc-devs#516)

* update notebooks authored by Ben Vincent to v5

Author: drbenvincent

examples/case_studies/mediation_analysis.ipynb

@@ -5,9 +5,9 @@ jupytext:
     format_name: myst
     format_version: 0.13
 kernelspec:
-  display_name: Python 3 (ipykernel)
+  display_name: pymc_env
   language: python
-  name: python3
+  name: pymc_env
 ---
 
 (mediation_analysis)=
@@ -182,7 +182,7 @@ with pm.Model() as total_effect_model:
     c = pm.Normal("c", mu=0, sigma=1)
     σy = pm.HalfCauchy("σy", 1)
     μy = iy + c * _x
-    pm.Normal("yy", mu=μy, sd=σy, observed=y, dims="obs_id")
+    pm.Normal("yy", mu=μy, sigma=σy, observed=y, dims="obs_id")
 ```
 
 ```{code-cell} ipython3

examples/case_studies/mediation_analysis.myst.md

@@ -5,9 +5,9 @@ jupytext:
     format_name: myst
     format_version: 0.13
 kernelspec:
-  display_name: pymc-dev-py39
+  display_name: pymc_env
   language: python
-  name: pymc-dev-py39
+  name: pymc_env
 ---
 
 (moderation_analysis)=
@@ -234,13 +234,13 @@ def model_factory(x, m, y):
         x = pm.ConstantData("x", x)
         m = pm.ConstantData("m", m)
         # priors
-        β0 = pm.Normal("β0", mu=0, sd=10)
-        β1 = pm.Normal("β1", mu=0, sd=10)
-        β2 = pm.Normal("β2", mu=0, sd=10)
-        β3 = pm.Normal("β3", mu=0, sd=10)
+        β0 = pm.Normal("β0", mu=0, sigma=10)
+        β1 = pm.Normal("β1", mu=0, sigma=10)
+        β2 = pm.Normal("β2", mu=0, sigma=10)
+        β3 = pm.Normal("β3", mu=0, sigma=10)
         σ = pm.HalfCauchy("σ", 1)
         # likelihood
-        y = pm.Normal("y", mu=β0 + (β1 * x) + (β2 * x * m) + (β3 * m), sd=σ, observed=y, dims="obs")
+        y = pm.Normal("y", mu=β0 + (β1 * x) + (β2 * x * m) + (β3 * m), sigma=σ, observed=y)
 
     return model
 ```
@@ -361,6 +361,7 @@ But readers are strongly encouraged to read {cite:t}`mcclelland2017multicollinea
 ## Authors
 - Authored by Benjamin T. Vincent in June 2021
 - Updated by Benjamin T. Vincent in March 2022
+- Updated by Benjamin T. Vincent in February 2023 to run on PyMC v5
 
 +++
 

examples/case_studies/moderation_analysis.ipynb

@@ -437,6 +437,7 @@ Of course, when using the difference in differences approach for real applicatio
 
 ## Authors
 - Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in Sept 2022 ([#424](https://github.com/pymc-devs/pymc-examples/pull/424)).
+- Updated by Benjamin T. Vincent in February 2023 to run on PyMC v5
 
 +++
 

examples/case_studies/moderation_analysis.myst.md

@@ -488,6 +488,7 @@ The bad news of course, is that as of the last data point (May 2022) the number
 
 ## Authors
 - Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in July 2022.
+- Updated by Benjamin T. Vincent in February 2023 to run on PyMC v5
 
 +++
 

examples/causal_inference/difference_in_differences.ipynb

@@ -348,6 +348,7 @@ There are of course many ways that the interrupted time series approach could be
 
 ## Authors
 - Authored by [Benjamin T. Vincent](https://github.com/drbenvincent) in October 2022.
+- Updated by Benjamin T. Vincent in February 2023 to run on PyMC v5
 
 +++