| Alright lets do some calculations. Feel free to dissect the assumptions. K event = Kim says Material L is RTSC D event = DFT says L is RTSC S event = L is actually RTSC we have assumed P(S/K) and P(S/D) are each 0.1, though we could have chosen other numbers for them as well. We want to estimate P = P(S/(K and D)) P = P((K and D)/S)P(S)/P(K and D) Assuming Kim and DFT are in the business of making positive predictions, they always get it right when L is actually RTSC. so P(K/S),P(D/S) and P((K and D)/S) are all taken as 1 hence P = P(S)/P(K and D) = P(S)/(P(K)P(D/K))
= P(S/K)/P(D/K) = 0.1/P(D/K) (similarly, P = P(S/D)/P(K/D) = 0.1/P(K/D)) But ofcourse we dont know P(D/K) or P(K/D). We could check historical data on how often D aligns with K, a messy exercise at best. Say they dont perfectly align, then the conditionals are less than 1,and P>0.1. Even intuitively when K (or D) gets additional support in the form of D (or K), your P should increase, not decrease. If we assume D and K align on average, then P(D/K) or P(K/D) is 0.5, and we get P = 0.2. You may estimate everything above differently, thus getting a different P. You can also come up with your own way of modelling this. I came up with my particular estimate to understand how frequently should i follow the news, and care about the whole thing. You should model it according to your usecase. |
Furthermore, you can’t just say “I understand things semantically different than everyone else talking about probabilities so when I say the probability of two events happening is 20% I actually mean something completely different and my math works this way I invented to describe why my messy naive intuitions about probability don’t match the reality of how probability works”.