There is another way of thinking about the Oliver problem, which I find more intuitive: The odds that Oliver spilled blood is “odds”=”prior odds” * “bayes factor”. Now, the bayes factor is all about blood types and not about prior evidence. Thus, it is the same as if there were no prior evidence. In that case, the prior odds for Oliver would be 2:N, i.e. 2 persons spilled blood out of a population of N people. Now, after the blood evidence the odds would have changed to 1:(0.6N) since Oliver is one of 0.6N people with blood type O. Thus, in this uninformative case, the Bayes factor would be (1:0.6N)/(2:N)=0.83 Since the Bayes factor is not about the prior evidence, this is the same Bayes factor as with prior evidence. Thus, the probability that Oliver spilled the blood decreased by a factor 0.83 due to the blood type evidence.

## One thought on “Oliver’s blood”

There is another way of thinking about the Oliver problem, which I find more intuitive: The odds that Oliver spilled blood is “odds”=”prior odds” * “bayes factor”. Now, the bayes factor is all about blood types and not about prior evidence. Thus, it is the same as if there were no prior evidence. In that case, the prior odds for Oliver would be 2:N, i.e. 2 persons spilled blood out of a population of N people. Now, after the blood evidence the odds would have changed to 1:(0.6N) since Oliver is one of 0.6N people with blood type O. Thus, in this uninformative case, the Bayes factor would be (1:0.6N)/(2:N)=0.83 Since the Bayes factor is not about the prior evidence, this is the same Bayes factor as with prior evidence. Thus, the probability that Oliver spilled the blood decreased by a factor 0.83 due to the blood type evidence.

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