This is only a sketch of what’s to come. In essence, today we begin the Class anew. Everything is about to get much harder, or much easier, depending on your viewpoint. If you like math, easier. But with that comes the ubiquitous Deadly Sin of Reification, in which you love your model more than life. I will warn you when the time is right, and you will say “I will not sin.” But oh, yes. You will.
Video
Links: YouTube * Twitter – X * Rumble * Bitchute * Class Page * Jaynes Book * Uncertainty
HOMEWORK: Given below; see end of lecture.
Lecture
Any time you reason, or try to reason, from some accepted or believed or supposed collection of evidence to some proposition, you are modeling. All models fit the schema Pr(Y|e), where Y is what you want to know, simple or complex, and e is the whole list of evidence, perhaps shifting in time, unquantified, or otherwise vague. Math can be brought it, and is helpful. But since most mathematical models are a good deal ad hoc, the Deadly Sin of Reification can strike. Beautiful theory replaces ugly Reality. It happens with distressing frequency.
The video contains a lot more information.
This is an excerpt from Chapter 8 of Uncertainty.
“But what a weak barrier is truth when it stands in the way of an hypothesis.”—Mary Wollstonecraft Shelley.
A model is an argument. Models are collections of various premises which we assign to an observable proposition (or just “observable”) [in Science]. That is, modelling reverses the probability equation: the proposition of interest or conclusion, i.e. the observable Y, is specified first after which premises X thought probative of the observable are sought or discovered. The ultimate goal is to discover just those premises X which cause or which determine Y. Absent these—and there may be many causes of Y—it is hoped to find X which give Y probabilities close to 0 or 1, given X in its various states.
Not all probability models apply to observable Y. But an implicit premise to all observables is that Y is contingent. Given just that premise, (as we have seen) the probability of Y is the unit interval sans endpoints [i.e. the 0 and 1; absolute certainty is out]. Models which supply X which sharpen this probability are of potential interest. The more the probabilities are sharpened the more interesting the model. Interestingness and usefulness are not identical. A model’s usefulness is described by what decisions are made with it, and how costly and how rewarding those decisions are. When calculations of usefulness are possible, which is rare for “public models” (such as those which appear in academic journals) except by gross approximation, usefulness is reckoned by a proper score. The usefulness of models are easily compared by scores; when one model has a better score than another, the superior model is said to have skill with respect to the lesser (conditional on the score type). Only proper scores should be used.
A probability model is the same as a causal or deterministic model except that the propositions of interest Y are not all certainly true or false given the collection of premises X. Our old friend, given X = “This is a two-sided object which when flipped must show one of H or T” the proposition Y = “An H shows” is neither true nor false, but in-between. There needn’t be a real object which conforms to these premises, although many can. Do not forget the empirical bias in discussions of probability. To implement this “coin” model in real life, simply find any two-sided or two-state object which conforms to the premises or something like them. This becomes a model. Whether this model is useful for this object is a different question.
Probability models can and do have causative elements. But these are generally found in very large, integrated physical models, such as weather and climate models, engineering models which investigate air or water flow over vessels, and that sort of thing. These are models which might even be fully causal or deterministic in the sense given last chapter, but which are treated as probabilistic in practice. Tacit premises are added to the predictions from these models which adds uncertainty so that falsification is avoided.
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