How did you get into Bayesian regression? It began when I studied decision analysis and Markov processes under the brilliant Professor Ronald Howard at Stanford four decades ago. I was smitten with both, which were intrinsically Bayesian. I wrote my doctoral dissertation under Ron (and others) entitled “Policy Ordering in Semi-Markov Decision Processes,” and I was a card-carrying member of the Bayes club (indeed almost the Bayes cult!) I wasn’t able to garner Bayesian or Markovian research or project opportunities until the mid-1990s, when an old friend and colleague invited me to work on the problem of pavement performance prediction—what makes roads deteriorate, how fast does it occur, and how should you rehabilitate them? What ameliorates degradation? I became obsessed with classical regression on that problem, but alas, the data was stricken with “adverse selection bias.” You had to be Bayesian. You had to combine judgment with data in order to predict what a pavement would do, how long it would last, what might be causing deterioration, and when you would have to fix it. It was a trillion-dollar problem, and I worked with the great Dr. Arnold Zellner at the University of Chicago to learn and apply Bayesian linear regression to the problem. It worked like a champ. I was hooked.
Why do you like Bayesian stats? Bayes is the right way to solve estimation and prediction problems. It allows you to combine judgment (or no judgment if you wish) with data to make valid probability distributions over certain events. That is the fundamental grist of forecasting and decision making. It also precludes “cheating” in your analysis.
What’s one project or moment in your career you’re proud of? My doctoral dissertation, under Drs. Richard Smallwood, Edward Sondik, and Ronald Howard at Stanford. I was able to solve a problem Ronald Howard had struggled with for over a decade, and I got the solution pretty fast. I will be publishing my thesis as a monograph in Markov Decision Processes, which has become an important AI technique.
Where have you actually used Bayesian methods (industries, real-life)? I use it in any context where one might use classical linear regression. I use it to estimate demand functions, to estimate demand for vehicle miles of auto travel, passenger miles of air travel, and pretty much every variable people want to know about that comes with a data set.
What’s your biggest contribution to the field? Writing the definitive book that contains every equation and concept using common notation and logic under a single cover. People can follow it and understand it at the most fundamental level. They can apply and interpret their work at the most fundamental level. And they can compute it accurately at lightning-fast speed and know exactly what they are computing.
Why did you write Bayesian Linear Regression? Because in my judgment the field has not been unified both for the univariate case and certainly for the extension to the multivariate case. I wanted to unify it.
What was the hardest part about writing it? Making sure that every step of every mathematical development was conceptually and algebraically unassailably correct and rigorous.
Who should read your book? Every practitioner of regression or data science should use it as a reference. Linear regression is the simplest case, and it is amenable to immediate implementation and interpretation. You can always generalize to nonlinear methods later, methods that require huge, intensive simulations of complex relationships and don’t offer the insight that simple analytic relationships in the linear case do. The linear case is the interpretive and methodological key to more complex, often more accurate, nonlinear cases.
What’s the biggest mistake people make with Bayesian stats? Assuming that it allows you to input guesswork or inaccurate or even undefinable judgment into your method. Purists argue they don’t like to use judgment, but by making that very statement, they ARE using judgment. Bayes makes clear what is judgment and what is data.
What should people feel or know after reading your book? That they can do a Bayesian or Classical Linear Regression analysis on their laptop in Excel in less than a day and deliver results to stakeholders.
What do you do when you’re not working? Play jazz piano.
What’s something surprising about you? “Surprise” means that there is something that is out on the tail of a probability distribution. People are surprised at my musical abilities.
Who influenced your thinking the most? Ronald A. Howard, Arnold Zellner, Thomas Bayes, Pierre-Simon Laplace, Ludwig von Beethoven, and Wolfgang Mozart.
Are you working on another book or project? Yes, I am working to publish my doctoral thesis as a monograph on Markov processes for AI. I am working to publish my book “Design of a Free Society.” I am working to publish my book on multiregion economic models of energy and other commodities.
What does “success” as an author mean to you? Large circulation with widespread use in teaching upper division or graduate courses. Acknowledged quality coupled with strong objective review and good circulation.
