Some authors, such as Barber in Bayesian Reasoning and Machine Learning and Rasmussen & Williams in Gaussian Processes for Machine Learning, write phrases such as "model of the data" and "modelling the data". Is this a shorthand for "model of the data generating process" and "modelling the data generating process"?

Edit: This question is different from the question Why do we use term “population” instead of “Data-generating process”?, as I'm not really interested in the philosophical issues related to how the data is generated. Therefore its accepted answer doesn't really help me here.

What I want to see clarified is if the phrase "model of the data" really makes sense by itself, or if it is simply an instance of abuse of terminology and should more correctly be written as "model of the system that we measured/observed" instead.

  • $\begingroup$ I think not in general. Take for example your first link saying "The word ‘causal’ is contentious particularly in cases where the model of the data contains no explicit temporal information, so that formally only correlations or dependencies can be inferred." Later it uses a longer form in "We assume however, that we make no detailed model of the data generating mechanism, asking rather generic questions such as whether the results support some basic hypothesis such as whether two classifiers are performing differently." $\endgroup$
    – Henry
    Commented May 14 at 1:00
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    $\begingroup$ You say you're not interested in the philosophical issues, but what we are doing and talking about here is necessarily partly a philosophical question. $\endgroup$
    – Nick Cox
    Commented May 15 at 11:03
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    $\begingroup$ Statistical people like anybody else tend to use expressions they think will be understood by their readership. Do you fit the data to the model or the model to the data? I tend to say the second, but I've seen both. Is the population a set of people (places, things) being sampled or the set of values being sampled? It could be either. If I am looking at people's heights and weights, I don't feel a need to talk about a system behind the data or a data generating process, but there are contexts where that is a good idea. $\endgroup$
    – Nick Cox
    Commented May 15 at 11:24
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    $\begingroup$ I wouldn't say valid or invalid. It's not an expression I much like or recommend. I might have used it informally. I think much depends on whether your data are in time, space, space-time, or something else. But there are always underlying processes, yet analyses differ greatly in how far those processes are from the data being analysed. With people's heights and weights, there is always a context in terms of age, heredity, environment, people's histories of diet and disease, and so forth, but often there are data on much more than say age. Processes are usually inferred, not observed. $\endgroup$
    – Nick Cox
    Commented May 15 at 11:37
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    $\begingroup$ I can't re-open the question unilaterally. At most I could vote to re-open the question, but to be frank I doubt it's worth it. Good if you found my comments helpful. $\endgroup$
    – Nick Cox
    Commented May 15 at 11:44


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