Bayesian vs frequentist statistics – how to decide?

Which predicts better, Bayesian or frequentist statistics? This is an empirical question. To find out, should we compare their predictions to the data using Bayesian or frequentist statistics? What if Bayesian statistics says frequentist is better and frequentist says Bayesian is better (Liar’s paradox)? To find the best method for measuring the quality of the predictions, should we use Bayesianism or frequentism? And to find the best method to find the best method for comparing predictions to data? How to decide how to decide how to decide, as in Lipman (1991)?

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