weakly informative approach to Bayesian analysis

Science is not described by thefalsification standard, as Popper recognized and argued.4 In fact, deductive falsification isimpossible in nearly every scientific context. In this section, I review two reasons for thisimpossibility.(1) Hypotheses are not models. The relations among hypotheses and different kinds ofmodels are complex. Many models correspond to the same hypothesis, and manyhypotheses correspond to a single model. This makes strict falsification impossible.(2) Measurement matters. Even when we think the data falsify a model, another ob-server will debate our methods and measures. They don’t trust the data. Sometimesthey are right.For both of these reasons, deductive falsification never works. The scientific method cannotbe reduced to a statistical procedure, and so our statistical methods should not pretend.

Statisticians, for theirpart, can derive pleasure from scolding scientists, which just makes the psychological battleworse.

So where do priors come from? They are engineering assumptions, chosen to help themachine learn. The flat prior in Figure 2.5 is very common, but it is hardly ever the best prior.You’ll see later in the book that priors that gently nudge the machine usually improve infer-ence. Such priors are sometimes called regularizing or weakly informative priors.They are so useful that non-Bayesian statistical procedures have adopted a mathematicallyequivalent approach, penalized likelihood. These priors are conservative, in that theytend to guard against inferring strong associations between variables.

The other imagines instead that population size fluctuates through time, which can be trueeven when there is no selective difference among alleles.

one assumes the population size andstructure have been constant long enough for the distribution of alleles to reach a steady state