I think it's easier to explain this in terms of likelihood theory. Likelihood is the probability of observed data GIVEN A SPECIFIC MODEL. This is NOT to be conf

I think it's easier to explain this in terms of likelihood theory. Likelihood is the probability of observed data GIVEN A SPECIFIC MODEL. This is NOT to be confused with the probability of a specific model being correct GIVEN THE OBSERVED DATA. It is the later probability that people want to really know, but confusing it with the former probability can have catastrophic consequences in fields like medicine, engineering, jurisprudence, finance and insurance. The problem is related to the Prosecutor's Fallacy (https://en.wikipedia.org/wiki/Prosecutor%27s_fallacy https://en.wikipedia.org/wiki/Prosecutor%27s_fallacy): "Consider this case: a lottery winner is accused of cheating, based on the improbability of winning. At the trial, the prosecutor calculates the (very small) probability of winning the lottery without cheating and argues that this is the chance of innocence. The logical flaw is that the prosecutor has failed to account for the large number of people who play the lottery." There is a mathematical statistics professor at the University of Toronto named D.A.S. Fraser (http://www.utstat.utoronto.ca/dfraser/ http://www.utstat.utoronto.ca/dfraser/) who is an expert in likelihood theory and has commented on this issue: "...statistics does have the answer! The answer is contained in the p-value function from likelihood theory: p(delta) Here delta is the relevant parameter with delta_0 as the null value and delta_1 as the alternative needing detection. Then p(delta_0) is the observed p-value, p(delta_1) is the detection probability, and the rest is judgement: the route to the Higgs boson."