I have just heard that Charles Stein, Professor at Stanford University, passed away last night. Although the sentence is definitely over-used, I truly feel this is the departure of a giant of mathematical statistics. He has been deeply influential on the fields of probability and statistics, primarily in decision theory and approximation techniques. On the first field, he led to considerable changes in the perception of optimality by exhibiting the Stein phenomenon, where the aggregation of several admissible estimators of unrelated quantities may (and will) become inadmissible for the joint estimation of those quantities! Although the result can be explained by mathematical and statistical reasoning, it was still dubbed a paradox due to its counter-intuitive nature. More foundationally, it led to expose the ill-posed nature of frequentist optimality criteria and certainly contributed to the Bayesian renewal of the 1980’s, before the MCMC revolution. (It definitely contributed to my own move, as I started working on the Stein phenomenon during my thesis, before realising the fundamentally Bayesian nature of the domination results.)
“…the Bayesian point of view is often accompanied by an insistence that people ought to agree to a certain doctrine even without really knowing what this doctrine is.” (Statistical Science, 1986)
The second major contribution of Charles Stein was the introduction of a new technique for normal approximation that is now called the Stein method. It relies on a differential operator and produces estimates of approximation error in Central Limit theorems, even in dependent settings. While I am much less familiar with this aspect of Charles Stein’s work, I believe the impact it has had on the field is much more profound and durable than the Stein effect in Normal mean estimation.
(During the Vietnam War, he was quite active in the anti-war movement and the above picture from 2003 shows that his opinions had not shifted over time!)
