This particular statistical perspective formalizes statistical information (chance regularity patterns) in terms of probability theory, e.g. probabilistic assumptions pertaining to the process underlying data Z₀, and the substantive information (meaning of Z₀) is irrelevant to the purely statistical problem of validating the statistical premises. Here, there is a loose analogy with Shannon’s (1948) information theory, which is based on formalizing the informational content of a message by separating ‘regularity patterns’ in strings of ‘bits’ from any substantive ‘meaning’: “Frequently the messages have meaning … These semantic aspects of communication are irrelevant to the engineering problem.”

Returning to your question, this purely probabilistic construal of statistical models renders the traditional distinctions between cross-section, time series and panel data models irrelevant; these different forms of data can all be viewed as realizations of stochastic processes with different index sets N denoting the relevant ordering(s) of interest, that being time, space, gender, etc.

The substantive information, plays a crucial role in evaluating the adequacy of the substantive model vis-a-vis the phenomenon of interest, once the statistical adequacy is secured. The latter is needed to ensure the statistical reliability of the inference procedures used to answer substantive questions of interest. ]]>

http://errorstatistics.com/2013/04/14/does-statistics-have-an-ontology-does-it-need-one-draft-1/

Not that we precisely addressed your question. Neyman seems to me to be an arch instrumentalist when it comes to using statistics and statistical modeling. Of course one knows what one is talking about. One might speak of actual data and modelled data, but events are different. Perhaps Aris will add to this.

]]>You seem to be overlooking the idea that we can ask for more than one “minimal” property. (The word “desideratum” does have a plural form!) Given two consistent estimators, one of which dominates the other with respect to “wrongly” defined MSE, are you *really* going to assert that there’s no reason to prefer the dominant one?

]]>Also, since the notion of admissibility only explicitly references the risk function, i.e., a sample-space expectation, you might want to make it clear why Bayesians would care about it. It’s far from obvious that the risk-Pareto-optimal set of estimators is risk-equivalent to the set of (generalized) Bayes estimators.

]]>Fact remains, for any *particular* model under consideration, you can identify the typical set and then see if the data lie within it.

]]>Thanks for the Mook link. On a quick read (I will read it more carefully later), I can entirely agree that “artificial” experiments can enable the most probative and severe tests. But, Mook emphasizes the hypothetical deductive method (which we may assume would be of the statistical and not purely deductive variety). This requires the very entailments that are questionable in these studies. I have written quite a lot about experimental testing (links to which can be found on this blog), and have argued (in sync with Mook I think) as to why “generalizability”, external validity and the like may miss the point of severe testing, which typically requires honing in on, amplifying, isolating, and even creating effects that would not occur in any natural setting. If our theory T would predict a result or effect with which these experiments conflict, then the argument to the flaw in T holds—as Mook remarks. What is missing from the experiments I criticize is the link that’s needed for testing—the very point that Mook is making. If you can explain where the good test is, then I have no criticism. I don’t even think this counts as a good test of the original positive results, and that’s one of my main points.

Granted, “miles and miles” doesn’t, by itself, describe my criticism (think of severe tests of the Higgs boson in a particle accelerator, or even randomized clinical trials). I’m not in the least saying social science, or even psychology, never attains probative tests. Experimental economics, from what I can tell, often does. Anyway, my main point concerned the nature of the self-scrutiny that would be required here, and also why I think philosophers should criticize the methodology behind experiments on which they might seek to test philosophical theory.

]]>I think you should read Mook’s classic paper:

http://www.uoguelph.ca/~psystats/readings_3380/mook%20article.pdf

Yes, it does appear that it is becoming possible to get replication efforts published. I take this as a good sign because a lot of this work has been occurring, just never making it into publication. We have had many instances of our own in which we tried to replicate an effect so that we could extend the paradigm to investigate related questions, but got stuck never able to get the original result. I think it is a good trend that such attempts can become more widely known so that we can improve understanding of the conditions necessary to obtain the effects.

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