I have decided to let you, dear reader, help me finish my book, which I have tentatively entitled The Philosophy of Probability and Statistics. This is about the seventeenth version of the title, so it might change again.
I’ve been working on this book piecemeal for some time, but not consistently enough (I’ve been spending more time on another one, a more popular version about over-certainty). So I decided to release it as she is, in separated segments. In a sort of fashion. Kinda sorta. More or less.
Today, an outline. Comments more than welcome.
There’s chapters and fragments of chapters and bare notes floating all over my hard drive and on odd pieces of paper. Putting them up will force me to gather them into something resembling coherence.
The writing will be in Latex, in raw code. Maybe I’ll PDF a few, links at bottom of posts. Luckily, PPS is not a math book. Mathematics is useful to probability, and there exists a mathematical subdivision called measure theory which makes great purpose of it, but I am interested in probability as measures of evidence, probability as she is or should be used for real-life matters. In this sense, probability is not mathematics; therefore I don’t need as much of it as is ordinarily used. Meaning reading Latex code won’t be that difficult for the uninitiated.
Incidentally, there is no difference between probability and statistics, except that the latter is a name for data. So I’ll mostly use probability to mean what people usually mean of either subject.
The new category tag PPS has been added to note posts which are part of the book. Click it to see all post (just this so far).
Rough gross mysterious outline:
1. The way it’s done now has lead to an (unnoticed) epidemic of over-certainty. Logic and probability belong to epistemology, which is the study of what we can know. Truth exists, relativism is silly but understandable, skepticism is stupid and not understandable, Gettier problems aren’t. I am not a Bayesian, but I love much of it.
2. Logic, which isn’t formal. Logic is the study of the relations between propositions. Let’s return to syllogistic logic to educate initiates. Symbolic and mathematical logic, fine things, can be saved for adepts. Math and symbolic logic are formal because they constrain the range of propositions. With freedom comes responsibility!
3. Probability, which is logic, it is its natural extension, or rather, its completion. Every results which holds for logic therefore holds for probability; thus probability isn’t formal until its propositions are constrained. Probability is not (of course it is not) relative frequency, a fallacy which mixes up epistemological propositions with ontological ones, and neither is it subjective. Beliefs, decisions, acts are not logic therefore are not probability. Probability is rarely quantifiable.
4. Causality and Induction, which is fine. Logic is the not the proper language of causality, therefore neither is probability. Causality has four dimensions (formal, material, efficient, and final). Logic-probability can measure relations between causal propositions, but again beliefs etc. are not logic. Induction is fine and rational. Induction is rarely quantifiable. Grue is no problem.
5. Observational propositions, which are statistics. An observational proposition is “I saw m people in the drug group out of n become well, and r people out of s in the placebo group become well.” This is statistics as she is normally thought of. Measurements, except in exceptionally rare circumstances, and possibly not even then, are finite and discrete. Again, not all probability is quantifiable.
6. Probability models, most of which aren’t deduced, but some are. Deduced models aren’t models, but optimal and true statements of probability. Deduced probabilities aren’t well known, aren’t well developed, and will save your soul. Non-deduced, i.e. assumed, habitual, or customary, models are killing science softly and slowly and with a smile. And they lead to endless and incorrect debates about truths of models, which we know are false.
7. Over-certainty, which is parameters, p-values, hypothesis tests, estimation, credible and confidence intervals, and premature jumps to infinity. Domine exaudi orationem meam, let the Cult of Parameter end!
8. Predictive statistics, probability leakage. If you’re going to use a non-deduced model, then at least do it so it can be verified, which means use the model in a predictive sense (Bayesians say “predictive posterior distributions”).
9. Models to decisions to verification. Since probabilities aren’t decisions or acts or beliefs to be useful they must be transformed to decisions acts beliefs. Verifying probabilities is not the same as verifying decisions, since by definition probabilities are true statements and therefore not in need of verification. But decisions can be good or bad, as long as you understand what good and bad are.
10. Examples like time series, regression, and so on will be spread throughout. But maybe a special chapter with the regular suspects. There are thousands of procedures and I can’t hope to do more than a handful.
This not a recipe book, but a starting point for somebody to write one. One step at a time!