Page 14 ... Optimality of scalar field Conjugate. Priors for Exp. Fam. 4. The discovery of Antidata and virtual data. 5. Optimality of Priors with tails following.
I have a brain I obs. x I want to understand x I need to predict future x’
How?
dataTheory no inmaculate obs. no theoretical vacuum no fact w/o. fiction no data w/o. theory.
Why ?
is a logical proposition in a domain of discourse
data must have meaning by
meaning
I mean
Theory
Theory
= explanation = compressing code = Probability distribution
obs.
hidden
The
tatistical Manifold
data manifold
finite measures
Sufficient map
Canonical Example:
Example: Car insurance.
Any!!
iid
Wrong!
Wrong!
Ignorance = Independence & Uniformity
spread
concentrate
What’s New? 1. Objective proc. for transforming prior info into prior distributions. 2. A new understanding of Data, Prior, and Likelihood. 3. Optimality of scalar field Conjugate Priors for Exp. Fam. 4. The discovery of Antidata and virtual data. 5. Optimality of Priors with tails following power laws. 6. Evaporation of the Bayesian/Freq. divide. 7. A dent at the Mind/Body problem. 8. A justification of Perelman’s Action. (That proved Thurston’s Geometrization Conjecture.) 9. A Geometric Theory of Ignorance. 10.The solution to a 260 year old problem: Objective Quantification of Ignorance in Statistical Inference.
Max (Ignorance) s.t. Whatever is known
(I forgot to mention that Bayes Theorem follows from this as a special case and in 2 very different ways!)
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