The fundamental insight of bayesian reasoning is that prior probabilities can matter a lot in some situations, even when the evidence seems fairly strong. Look

The fundamental insight of bayesian reasoning is that prior probabilities can matter a lot in some situations, even when the evidence seems fairly strong. Look at scientific papers. Usually there is something called a p-value attached to it, which is usually around 0.05. This means there is only a 5% chance that the same result could have been produced by random chance. How strong is that evidence, really? What if you started with a prior probability of 1 in 1,000 that it's actually true. That is, before you saw the paper, you would estimate there's only a 0.001% chance it's true. Out of 1,000 similar studies, 49 will be false and yet return a <0.05 p value. Only 1 will publish actually true results.