Probably what could be difficult to understand by non professional statisticians is that the probability of theta1=0 (ie condition for the reduced model) vanishes to zero under the larger model (continuous theta1) embedding the reduced one.

One reason also why some people might believe in Templeton’s incoherence arguments that larger models are necessarily “better” lies in the fact that the maximum value of the (classical) likelihood cannot decrease from a reduced to more complete models when they are nested.

This and the confusion between standard Bayes and ABC also reminds me a sentence by Bradley Efron I guess : “Applying Bayesian statistics does not make you a Bayesian” indicating that there is a big gap between using numerical techniques and understanding their foundations.

In addition, the domain of applications tackled by Templeton in his PNAS article ie origin of man is not at all neutral both scientifically and philosophically speaking and this might be an other reason for making this field especially sensitive to disputes on competing theories. I am not sure that a tough debate around the relevance of Bayesian statistics would have taken place from a paper on the origins of cows.

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