Peter Pogany, Rethinking the World

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.

Statistical RethinkingA Bayesian Coursewith Examplesin R and StanRichard McElreath

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

Andrew Gelman’s

spake

I told them it was the Sabbath day, and desired them to let me rest

stoutest men, and sent them back to hold the English army in play whilst the rest escaped.

“Wait on the Lord, Be of good courage, and he shall strengthen thine Heart, wait I say on the Lord.”

chapter of Deuteronomy

One of the Indians that came from Medfield fight, had brought some plunder, came to me, and asked me, if I would have a Bible, he had got one in his basket. I was glad of it, and asked him, whether he thought the Indians would let me read? He answered, yes. So I took the Bible,

Then they went and showed me where it was, where I saw the ground was newly digged, and there they told me they had buried it.

my sweet babe like a lamb departed this life on Feb. 18, 1675. It being about six years, and five months old.

Then I took oaken leaves

and my child’s being so exceeding sick,

One of the Indians got up upon a horse, and they set me up behind him, with my poor sick babe in my lap.

still the Lord upheld me with His gracious and merciful spirit, and we were both alive to see the light of the next morning.

but God was with me in a wonderful manner, carrying me along, and bearing up my spirit, that it did not quite fail.

One of the Indians carried my poor wounded babe upon a horse

All was gone, my husband gone (at least separated from me, he being in the Bay; and to add to my grief, the Indians told me they would kill him as he came homeward), my children gone, my relations and friends gone, our house and home and all our comforts—within door and without—all was gone (except my life), and I knew not but the next moment that might go too.

one-eyed John, and Marlborough’s Praying Indians

Oh the roaring, and singing and dancing, and yelling of those black creatures in the night, which made the place a lively resemblance of hell.

“What, will you love English men still?”