Response to the ASA’s Statement on p-Values
It seems clear to me that Popperian falsification is indeed the only way to separate the wheat from the chaff in theoryspace, however, generating theories generally requires inductive reasoning.<p>You observe data, you make an inference that leads to a theory (induction), you then subject that theory to falsificationist testing.<p>&quot;It appears all the swans I&#x27;ve seen are white, therefore I posit all swans are white. Oh, wait, there&#x27;s a black one, nevermind.&quot;<p>On the Bayesian vs Frequentist aspect... Falsification is what you should do to theories, not model parameters. If you have a coin and you&#x27;re trying to figure out the probability of heads P(H), then you have your model of coin-flipping (Bernoulli process) and you&#x27;re trying to estimate the model&#x27;s parameter, so you do statistical inference given some sequence of coin flips.<p>It doesn&#x27;t seem right to apply frequentist null testing because you want to estimate the model parameter, not make some binary decision. What if you had some prior data you want to include? Or you observe new data in the future? This is exactly what Bayesian inference is setup for. And a lot of science is not about falsifying theories in theoryspace but about estimating model parameters in parameter space in the case we all agree on a particular model.<p>Moreover, a big advantage with Bayesian statistics is that it generally requires you to make your model and assumptions explicit, where it&#x27;s much easier to scrutinize the model compared to a frequentist statistical test.