Further Reflections on Simplicity: Mechanisms

To continue with some philosophical reflections on the papers from the “Ockham’s razor” conference, let me respond to something in Shalizi’s recent comments (http://cscs.umich.edu/~crshalizi/weblog/). His emphasis on the interest in understanding processes and mechanisms, as opposed to mere prediction, seems exactly right. But he raises a question that seems to me simply answered (on grounds of evidence):  If “a model didn’t seem to need” a mechanism, it is left out, why?

“It’s this, the leave-out-processes-you-don’t-need, which seems to me the core of the Razor for scientific model-building. This is definitely not the same as parameter-counting, and I think it’s also different from capacity control and even from description-length-measuring (cf.), though I am open to Peter persuading me otherwise. I am not, however, altogether sure how to formalize it, or what would justify it, beyond an aesthetic preference for tidy models. (And who died and left the tidy-minded in charge?) The best hope for such justification, I think, is something like Kevin’s idea that the Razor helps us get to the truth faster, or at least with fewer needless detours. Positing processes and mechanisms which aren’t strictly called for to account for the phenomena is asking for trouble needlessly.”

But it is easy to see that if a model M is adequate for data x regarding an aspect of a phenomenon (i.e., M had passed reasonably severe tests with x) , then a model M’ that added an “unnecessary” mechanism would have passed with very low severity, or, if one prefers, M’ would be very poorly corroborated.  To justify “leaving-out-processes-you-don’t-need” then, the appeal is not to aesthetics or heuristics but to the severity or well-testedness of M and M’.

Granted, “There is also the very subtle issue of what phenomena need to be accounted for.”  If a new question is raised, of course, taking us to what I might dub a different “level” of inquiry, then the original model M could not be said to have passed a good, or indeed, any kind of test with the given data. But then M would not be adequate.

“Positing processes and mechanisms which aren’t strictly called for to account for the phenomena is asking for trouble needlessly — unless those posits happen to be right. “

They might be needless to account for one aspect, but not for understanding others; but even if the posits happen to be right, the existing data had not probed them, at least if M was adequate. The data may be remodeled to ask a different question, (in which case M is no longer adequate for the new data y).  Raising new questions, “getting into trouble” is what science is all about. Raising questions, of course, is distinct from having any evidence for their answers.


I began this blog when I was first writing about prion theory and protein folding mechanisms (How Experiment Gets a Life (of its own)).  Here’s a snippet (from a working draft) that bears on the question of probing mechanisms.

10.2 The Only Correct Interpretation of the Data: It Is in the Folding

An important mode of learning from error is to consider why certain experiments are incapable of telling experimenters what they want to know; and this case offers several illustrations. By mixing synthetic versions of the two proteins together in a test tube, they were able to convert common prions (PrP-C) into scrapie prions (PrP-Sc) (in vitro), but they did not understand what was actually causing the switch. Moreover, they knew they did not, and they knew something about why. The infectious form has the same amino acid sequence as the normal type: studying the amino acid sequence is unable to reveal what made the difference.  If exceptions to the “central dogma” were precluded, and it is assumed that only nucleic acid directs replication of pathogens, there was no other place to look. But what if transmission by pathogenic proteins occurs in a different way?

Maybe the difference is in the way the protein is folded. Researchers hypothesized that the scrapie protein propagates itself by getting normal prions to flip from their usual shape to a scrapie shape.  This would explain “transmission” without nucleic acid, and sure enough they were able to replicate such flipping in vitro. But understanding the mechanism of pathological folding required knowing something about the structures of common as opposed to scrapie prions. A big experimental obstacle was not being able to discern the prion’s 3-D structure at the atomic level.  Exploiting the obstacle provided the key.

10.3 Magic Angle Spinning: Exploiting an Obstacle

The central difference between normal and pathogenic prions permits the normal but not the abnormal prion to have its structure discerned by known techniques, e.g., nuclear magnetic resonance (NMR) for solutions: The normal form, PrP-c, is soluble; PrP-Sc is not.

NMR spectroscopy provides an image of molecular structure: Put a material inside a very high magnetic field, hit it with targeted radio waves, and its particles react to reveal their structure.  But it will not work for clumpy scrapie prions, PrP-Sc.  Maybe solid-state NMR could detect them?

Even so, they would need trillions of molecules to get a signal—amplification—but this would also amplify the interference of neighboring molecules in the non-soluble PrP-Sc.They want to find out what it would be like if they were able to make it soluble, even though they cannot literally do so. They need to amplify to get a signal, but also somehow subtract the interference of neighboring molecules.  Here is where “magic angle spinning” enters.

The Magic is to erase the influence of these neighboring molecules.

Categories: philosophy of science, Statistics | Tags: , , , , | 4 Comments

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4 thoughts on “Further Reflections on Simplicity: Mechanisms

  1. Eileen

    Except if the new model M’ adds something irrelevant, it might be just as severely tested as M.

    • Eileen: Sorry to have missed this. If M’ adds something irrelevant, it will be less severely tested by the data regarded as having well-tested M, at least as I am understanding your point about irrelevance. There are different cases that would need to be delineated. In some cases of irrelevance (e.g., M and M’ do not even share data models), M’ can be horribly tested. Consider,
      Data x indicate M storms caused power outages.
      Data x do not indicate M’: storms caused power outages and “God particle” is discovered.

  2. Aris Spanos

    Let me add my two cents on the main argument made above by Mayo. Focusing exclusively on the statistical model level, simplicity has a very limited role to play. As I argue in my 2007 paper, a statistical model should be as elaborate as necessary to account for the statistical information in the data, but no more elaborate. On one hand, any elaborations on a statistically adequate model will result in overparameterization and thus ruin the adequacy. On the other hand, any attempt to make a statistically adequate model simpler will also ruin the adequacy. A statistically inadequate model will provide a very poor basis for inference because the assumed (nominal) error probabilities are likely to be very different from the actual ones.

    • Aris: Thanks! I linked to your 2007 paper in my post today. Of course, I see the argument as holding generally, not only for formal statistical contexts. I stated the position simply in my post, but it actually requires a complex, piece-meal effort to show how it holds generally.

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