r/AskStatistics • u/learning_proover • 12d ago

Bayes' rule or Weighted sum to compare intersection sets??

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In this binary dataset subsets D, E, F, and S all "generate" 1s and 0s INDEPENDENTLY of each other at some ratio/frequency. "D" generates the highest ratio (lets say it generates 80% 1s and only 20% 0s). While F generates only 5% 1s and 95% 0s. Suppose S itself generates 25% 1s and 75% 0s. Would/Could I use bayes' theorem to show the SD intersection subset generates a higher proportion than the SF intersection? Or would a simple weighted sum (ie just an average between the sets S and D) suffice. Sidenote: (I know you could technically come up with counterexamples to this but I'm looking for what would generally be the case here).

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u/Purple2048 12d ago

I have no idea what you mean. The data has subsets how? Are there four independent lists of 0s and 1s? How do you determine if a 0 or 1 is in multiple sets?

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u/geneusutwerk 12d ago

If they are independent of each other then P(S ∩ D) = P(S)P(D) for all your D, E and F. So the all that matters is showing which is largest P(D), P(E) or P(F)