Monday, August 30, 2010

How can we define "Useful", when it comes to our models of reality?

Wikimedia Commons: "N-Gauge Cassiopeia E26 & EF81 from Kato"
A comment to "Useful models, model checking, and external validation: a mini-discussion" by Andrew Gelman - Statistical Modeling, Causal Inference, and Social Science

Gelman wrote (with Cosma Shalizi) a very fine philosophical justification for real-world, effective Bayesian techniques, which differs greatly from the usual philosophy associated with Bayesians.

Gelman, Shalizi: Philosophy and the practice of Bayesian statistics in the social sciences

My own recurring criticism of Gelman is of using Bayesian/statistical models to the exclusion of others.  I am more comfortable with the idea of models of different type in competition.
The multiple models you then have will now compete in different uses - based on predictive power, accuracy, ability to calculate meaningful error ranges, cost of collecting data, cost of computation, cost of comparison, ability to predict outcomes from interventions, cost of understanding, etc.

quoting Gelman:
"We always talk about a model being "useful" but the concept is hard to quantify."
My comment:
Simply build a model of costs and gains and methods of comparison between models!  If a model is good enough for your work, a model must be good enough as a working definition of "useful"!

Sometimes the best answer to "Why" is "Just because".  Sometimes the best mechanism for rating different models is another model.  The Skeptics will always howl, so you simply have to demonstrate that their own behavior is consistent with putting undue confidence in their own model, whether a conscious model or unconscious.  (And, it must simply terminate with a model, because of the limits of the tools available to the human brain.  Only a model, probably over-simplified, can be manipulated with the agility needed to predict future outcomes of the universe from actions considered now, in real-time.)

Just keep asking the Skeptic "Why" with regards to their own personal actions, and when they hit the "Just because" point, they probably have described a model of utility, assumed true without proof, as an answer to "Why" in the previous step.

If the Skeptic refuses ultimate responsibility over their personal actions, and tries to plead pure capriciousness or mystery, then their model is simply statistical, based on stimulus and internal states (like stress) that can be approximately discovered with objective external measures (like galvanic skin response).  Of course, it is easier to plead pure capriciousness or mystery than demonstrate it - if their behavior is well predicted by a deterministic model suggested by another, the Skeptic is shut up.  Most times the reason for behaviors is gross and banal, no matter how elevated the sophistry of the Skeptic.
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