by Statistical philosophies and idealizations As has been long and widely emphasized in various terms … frequentism and Bayesianism are incomplete both as learning theories and as philosophies of statistics, in the pragmatic sense that each alone are insufficient for all sound applications. Notably, causal justifications are the foundation for classical frequentism, which demands that all model constraints be deduced from real mechanical constraints on the physical data-generating process. Nonetheless, it seems modeling analyses in health, medical, and social sciences rarely have such physical justification … The deficiency of strict coherent (operational subjective) Bayesianism is its assumption that all aspects of this uncertainty have been captured by
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Statistical philosophies and idealizations
As has been long and widely emphasized in various terms … frequentism and Bayesianism are incomplete both as learning theories and as philosophies of statistics, in the pragmatic sense that each alone are insufficient for all sound applications. Notably, causal justifications are the foundation for classical frequentism, which demands that all model constraints be deduced from real mechanical constraints on the physical data-generating process. Nonetheless, it seems modeling analyses in health, medical, and social sciences rarely have such physical justification …
The deficiency of strict coherent (operational subjective) Bayesianism is its assumption that all aspects of this uncertainty have been captured by the prior and likelihood, thus excluding the possibility of model misspecification. DeFinetti himself was aware of this limitation:
“…everything is based on distinctions which are themselves uncertain and vague, and which we conventionally translate into terms of certainty only because of the logical formulation…In the mathematical formulation of any problem it is necessary to base oneself on some appropriate idealizations and simplification. This is, however, a disadvantage; it is a distorting factor which one should always try to keep in check, and to approach circumspectly. It is unfortunate that the reverse often happens. One loses sight of the original nature of the problem, falls in love with the idealization, and then blames reality for not conforming to it.” [DeFinetti 1975, p. 279]
By asking for physically causal justifications of the data distributions employed in statistical analyses (whether those analyses are labeled frequentist or Bayesian), we may minimize the excessive certainty imposed by simply assuming a probability model and proceeding as if that idealization were a known fact.