Necessary/recommended level of theory for developing statistical intuition

[R_cubed]

@ChristopherTong

I am not aware of an empirical failure of the option-implied probability method.

In the literature, the implied probability density is known as the “risk neutral density”. Changes in information on actual probabilities or changes in risk preference can affect the output of the model.

There has been much written about the limitations of textbook decision theory in the economics and operations research literature. Textbook decision theory assumes probability estimates are independent of utility. I alluded to it in this post:

Who should define reasonable priors and how?

I pulled off Savage’s Foundations of Statistics from my shelf. I can’t find a direct quote, but both the chapter on elicitation of personal probabilities and personal utilities involved gambling games, so distinguishing one from another is a challenge. He mentions in passing (p. 95): Blockquote It seems mystical to talk about moral worth [ie. utility] apart from probability… A direct reference to the problem of separating personal probabilities from utilities can be found in: Joseph B. K…

I speculate that changes in risk preference (ie. utility) are related to those factors K^2 call “evolutionary” and are hard to put into words. Regardless, IJ Good would consider changes in utility as information.

Being derived entirely from logical considerations, theoretical and empirical option pricing models are a beautiful achievement of the De Finetti - Savage - Radical Subjective Bayesian school of thought (which is closely related to the Cox-Jaynes Maximum Entropy perspective). They deserve greater attention if we wish to place applied stats in an information theoretic perspective.

The true value of implied probabilities is to get an individual to think: “What do I know that has not been factored into the price?” I’ve found the device of betting games and their valuation extremely useful in detecting when the data analysis practices in entire fields of inquiry are so bad as to be called “pathological.”

Preprint: Analysis of Likert Type Data Using Metric Methods

Dennis Boos and Judy Chen (2022). Analysis of Likert-Type Data Using Metric Methods. I edited this to bring the main points earlier, and the decision theoretic justification later in the post. Introduction The authors defend the common practice of using parametric models on ordinal data on the basis of pragmatics (ie.“easier” to for researchers understand), and perceived robustness in that parametric methods on empirical or simulated data sets are not sufficiently inaccurate that skepti…

The End of the "Syndrome" in Critical Care

I have been periodically discussing the state of RCT in critical care. While there have been but few on-line comments, I have been encouraged by the off-line comments and approvals of that which I am trying to teach here. This work comes from 40 years in the ICU watching the evolution of the science and I speak primarily to the young who may still be developing an overarching cognitive construct of critical care science. This is the evolution I observed over 40yrs: The emergence of “thresh…

For Further Study
Harry Crane on Fundamental Principle of Probability

Harry Crane - Fundamental Principle of Probability

Glenn Shafer on Testing by Betting as a method of Scientific Communication. This was presented a few years before his more formal paper in the Royal Statistical Society.

Glenn Shafer The Language of Betting as a Strategy for Communicating Statistical Results