An Introduction To Uncertainty: Probability, Statistics, and Modeling of All Kinds

This is a teaser, the first part of a 3,200-word narrative outline for the book that I’ve started to shop around. The current title is in the headline. Regular readers know it has undergone many changes, thus it is rational to conclude it might change again.

Why is this rotten thing taking so long? It took me forever to realize what I could leave out—which is a lot. I wanted to introduce to people not used to it to Aristotelian epistemology, and what this fine and true subject meant for the practical understanding and communication of uncertainty. But there’s no way to be complete about this without going on and on, at book length, by which time the reader, anxious to get to the “good stuff”, will have been put to sleep.

So out goes everything except the bare necessities. Besides, if readers are into that sort of thing, there’s plenty of other books to read. What’s left is an explanation of what probability is, what it means to “do” modeling, how to communicate results properly, and how to purge the magical thinking from our midsts.

I sent the outline to one well known publisher, who that very same day wrote back and called my bluff. The editor labeled the proposal “intriguing” and said that it “raises a lot of important points” but then asked me to immediately ship off two chapters. Sure. As if these were ready, and that, even if they were, I could pick the right two.

Finishing these chapters so that they are at least not embarrassing is what I’ll be doing for the next week.

Incidentally, the “Why?” which follows, suitably fleshed out, will become either the Preface or Chapter 1.

Why?

Fellow users of probability, statistics, and computer “learning” algorithms; physics and social science modelers; big data handlers; spreadsheet mavens; other respected citizens. We’re doing it wrong.

Not completely wrong: not everywhere: not all the time: but far more pervasively, far more often, and in far more places than you’d imagine.

What are we doing wrong? Probability, induction, statistics, the nature of causality, modeling, communicating results, expressing uncertainty. In short: everything.

Your natural reaction will be (this is a prediction based on observation and induction), “Harumph.” I can’t and shouldn’t put a probability measure to this guess, though. That would lead to over-certainty, which I will prove to you is already at pandemic levels.

You may well say “Harumph”, but consider: there are people who think statistical models are causal, that no probability can known with certainty until at the close of the universe, that probabilities can be read from mood rings, that induction is a “problem”, that randomness is a magical cause, that parameters exist, that computers learn, that models are realer than observations, that model fit is more important than model performance.

And that is only a sampling of the oddities which beset our field. How did we get this way? Best answer is that it is well known that the human race is insane.

More practically, our training lacks a proper foundation, a philosophical grounding. Introductory books plunge the student into data and never look back. The philosophical concepts which are necessarily present aren’t discussed well or openly. This is rectified once, and if, the student progresses to the highest levels, but by that time his interest has been turned either to mathematics or to solving specific problems. And when the student finally and inevitably weighs in on, say, “What models really are”, he lacks depth. Points are missed. Falsity is embraced.

So here is a philosophical introduction to uncertainty and the practice of probability, statistics, and modeling of all kinds. The approach is Aristotelian, even Thomistic. Truth exists, we can know it, and we can sometimes but not always measure its uncertainty, and there are good and bad ways of doing it.

This isn’t a recipe book. Except for simple (but common: regression, “binomial”) examples, this book does not contain lists of algorithms. Rather, this is a guide on how to create such recipes and lists. It is thus ideal for students and researchers looking for problems upon which to work. The mathematical requirements are modest: this is not a math book.

Do I have everything right? Well, I’m as certain I do as you were that you had everything right before you read this introduction. One thing which is certain is that we’re not done.