March 1, 2021

statistics

When we talk about a “possible variation”, “distribution”, “random drift”, this should tip us off to the usefulness of statsitical models in describing biological population. The mathematics we can use here are extremely useful, amazingly so in many cases. But we need to take caution against treating the model as if it were reality. Many of us are tempted to seek completeness in mathematical modeling, either through formal precision or computational power.

Some even are tempted towards denialism in modeling efforts – as if lack of completeness means total infeasibility. Mathematical models are tools, not reality, we tell ourselves, but these temptations remain.

How to confront them? The proper response is to use models not as descriptions of reality, but as hypotheses. Hence, we need to design experiments to falsify models in light of real-world evidence. The key here is in falsification. Like a roadmap, a model may be useful enough in many cases, but imperfect as a picture of reality. We can easily discard models when we need higher precision – eg. we say the usefulness at a given level of detail is falsified. The principle progress in science is in designing experiments that allow us to tell useful models from useless ones.

Another problem, however, does pop up if our efforts lead us to generate a very large number of useful models of very specific applicability. To use the map metaphor again, we my find a London subway map and a Tokyo subway map very useful in guiding our way through either cty; be we wouldn’t try exchanging one map for the other.

This is why Platt (1964) 🔗 emphasizes generalizable models as the principle drivers of scientific progress. He call this strong inference. A well-designed experiment entertains a collection of hypotheses that my each be falsified, one-by-one. Once there’s a clean result, the experiment is repeated with a collection of sub-hypotheses from those original hypotheses that remain.

A biologist will recognize the effet of a selection procedure (distinct, of course, from natural selection). A chemist may recognize the practice of purifying a solution.

Content by © Jared Davis 2019-2020

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