Update the beta distribution parameters in the `_select_variation_i…

…ndex` method (#647)

Update the beta distribution parameters in the `_select_variation_index` method to avoid bias towards lower success probability.

The current specification of the beta distribution:

```
theta = np.random.beta(conversions + 1, exposures + 1)
``` 
treats every exposure as a failure, that is overstates the failures thus undervalues the success probabilities of the variations. The effect is pronounced for variations with very high baseline conversion rates but less severe for variations with extremely low conversion rates. 

#643

Co-authored-by: James Jory <[email protected]>

src/recommendations/src/recommendations-service/experimentation/experiment_mab.py

@@ -99,7 +99,7 @@ def _select_variation_index(self):
 
         # Sample from posterior (this is the Thompson Sampling approach)
         # This leads to more exploration because variations with > uncertainty can then be selected
-        theta = np.random.beta(conversions + 1, exposures + 1)
+        theta = np.random.beta(conversions + 1, exposures - conversions + 1)
 
         # Select variation index with highest posterior p of converting
         return np.argmax(theta)