What is a model?

Writing the tutorial, I’ve realized that we have 2 ways of using the word “model” in our materials. This could sow confusion, so would be nice to reconcile these.

Frequentist use

We introduce the term on the frequentist day of the Boot Camp, saying “a model is a simplified representation of something in the real world”. That “something” in our mathematical model is a biological phenomenon or a data-gathering process or a combination of the two.

“Statistical models are stories about how the data came to be.” (Dave Harris), but the story is simplified and thus an approximation – “all models are wrong” (George Box). Perhaps we should also emphasize that all models are subjective, there is no objectively correct model.

Specifically, a model allows us to calculate the probably of observing the data we have, given some values for the parameters, ie, the likelihood.

Bayesian use

In JAGS, the model code includes both the likelihood and the priors. (I suppose that’s the bottom line, trying to use a different definition is not going to work!)

Andy Gelman considers the priors to be part of the model. The story about “how the data came to be” is incomplete without information about the parameters. Richard McElrath also sees the priors are part of the mechanism of the model.

What to do?

The frequentist definition is fine for MLE and AIC, where prior information about parameter values is deliberately ignored. But in general we should follow the JAGS interpretation.

That means going back and editing the earlier pages.

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