Willful Ignorance

This post is to acknowledge the work of Herbert Weisberg in his book Willful Ignorance: The Mismeasure of Uncertainty, published in 2014 by John Wiley & Sons. Anyone relying on statistical methods and results for their work should read at least a few chapters of this book (I suggest started with Chapters 1, 11, and 12 if you realistically won’t read the whole thing — 2, 3, 9, and 10 are next in line!).

I love the term Willful Ignorance in this context. It does an amazing job capturing a fundamental aspect of how we currently tend to do science and support decision making — and we need to be acknowledging it, and then wrestling with it. This is the first book I read on the topic of how we are using statistical inference in science where I felt “Yes! This is what I have been trying to say!” His ideas are eloquently described and he includes an impressive amount of research on the history of probability and statistics — which is crucially tied to issues with how we are using statistical inference today. This post is coming early in my blog because I want to acknowledge Weisberg’s work, ideas, and language, and because I intend to build off some of the ideas and foundations for my own work. You may see quotes from his book show up fairly often to begin with!

So, what does he mean by Willful Ignorance? In order to carry out statistical inference by relying on probability-based models, we must get to the point where we are willing to ignore information (both information we currently have and that we don’t). We must willfully ignore in order to proceed. So, what is the problem with this? Willfully ignoring information can be incredibly useful — just as any model is a (hopefully useful) simplification of reality, so are notions of probability and the application of games-of-chance-like mechanisms to scientific work. The problem lies in a general failure to acknowledge the usually implicit decision to base inferences on probability models. In our scientific culture today, scientists start from the assumption that they will use probability models in their work — as a default — without ever thinking about or justifying the assumptions underlying that decision. It is simply accepted as the way to do science. We “check”, usually inadequately, the more mathematical assumptions associated with particular models (e.g., linear regression), but forget to think about the fundamental assumptions underlying the decision to use probability in the first place. Acknowledging the act of willfully ignoring, no matter how uncomfortable, is a step toward making the choice explicit and forcing us to take responsibility for justification of that choice — through an understanding of its limitations, not only its potential benefits. We are consistently jumping the gun with no warm up — instead, we need to stop, slow down, and contemplate where the starting line really is and if we’re really trained for the race we signed up for.

I will delve deeper in future posts, but end here with a couple of quotes from the Preface and Chapter 1 of Weisberg’s book.

I have proposed that willful ignorance is the central concept that underlies mathematical probability. In a nutshell, the idea is to deal effectively with an uncertain situation, we must filter out, or ignore, much of what we know about it. In short, we must simplify our conceptions by reducing ambiguity. In fact, being able to frame a mathematical probability implies that we have found some way to resolve the ambiguity to our satisfaction. Attempting to resolve ambiguity fruitfully is an essential aspect of scientific research. However, it always comes at a cost: we purchase clarity and precision at the expense of creativity and possibility.

Page xiii Weisberg (2014). Willful Ignorance: The Mismeasure of Uncertainty. John Wiley and Sons, Inc.

Probability by its very nature entails ambiguity and subjectivity. Embedded within every probability statement are unexamined simplifications and assumptions. We can think of probability as a kind of devil’s bargain. We gain practical advantages by accepting its terms but unwittingly cede control over something fundamental. What we obtain is a special kind of knowledge; what we give up is conceptual understanding. In short, by willingly remaining ignorant, in a particular sense, we may acquire a form of useful knowledge. This is the essential paradox of probability.

Page 6 Weisberg (2014). Willful Ignorance: The Mismeasure of Uncertainty. John Wiley and Sons, Inc.