I've been working with trying to understand and explain how Naive Bayes classifier works with the adjusted (prior and posterior) probabilities, and wanted to show my example to ensure I'm executing it correctly. Here is the data:
Data
Name | Art Fair | Fishing | Shovel Snow | Wedding
Jon No Yes Yes No
Jane Yes Yes No Yes
Jill Yes Yes Yes Yes
Art Fair (AF) & Wedding (W)
P(both AF & W/just AF) = 2/2 = 100%
P( (total user either-both AF & W)/total) = (2-2)/2 = 0%
Normalize Probability = 100% / (100% + 0%) = 100%
Fishing (F) & Wedding (W)
P(both F & W/just F) = 2/3 = 67%
P( (total user either-both F & W)/total) = (3-2)/3 = 33%
Normalize Probability = 67% / (67% + 33%) = 67%
Shovel Snow (SS) & Wedding (W)
P(both SS & W/just SS) = 1/2 = 50%
P( (total user either-both SS & W)/total) = (3-1)/3 = 66%
Normalize Probability = 50% / (50% + 66%) = 43%
Would it be accurate that based on the data, I'm calculating the posterior probability (normalized probability) correctly?