John H. Wolfe, an IMS Life Member, passed away peacefully on April 26, 2024, in San Diego, California, after a battle with metastatic cancer. He was 90 years of age. He is best known in statistics as the inventor of model-based clustering in the 1960s, a field that has seen major growth since then, displacing older, heuristic clustering methods such as hierarchical clustering.

John Wolfe was born on October 10, 1933, in Buenos Aires, Argentina, to Wesley and Ruth Wolfe. His father was stationed in Argentina on assignment for a rubber company. A determined student from an early age, John knew he wanted to be a scientist when he was five years old. He graduated from Cal Tech in Mathematics in 1955.

He then went to graduate school in Psychology at the University of California, Berkeley. He worked with Robert Tryon, who had written the first book on cluster analysis in 1939. Tryon encouraged Wolfe to develop hierarchical clustering, but Wolfe recounted that he couldn’t see a rationale for it without arbitrary assumptions at several stages. Around 1959, Paul Lazarsfeld visited Berkeley and gave a lecture on his latent class analysis, which fascinated Wolfe, and led him to start thinking about how one could do the same thing for continuous data.

Wolfe’s 1963 MA thesis was a first attempt to do this. He started by defining a “type” as one of the component distributions of a mixture of distributions. Then he said: “The above definition makes it clear that the problem of identifying and describing types is merely an application of the statistical theory of estimation. The population from which a sample of objects is drawn is assumed to have a particular form of distribution (e.g. a mixture of several normal distributions with unknown parameters, such as means and variances for each type and percentage of objects of each type). The task is to devise a procedure for estimating the population parameters.”

This is effectively the model that underlies continuous model-based clustering to this day. However, the estimation method he used was an effort to use Mahalanobis distances, which was not very effective. He acknowledged this, saying that the methods in the thesis were bad. So his Master’s thesis can be viewed as a heroic failure. However, he did say at the end of the thesis that he had developed a much better method called “maximum likelihood analysis of types.” He later said that his professor didn’t believe him, but grudgingly approved the thesis anyway.

After graduating from Berkeley, Wolfe took a job with the US Navy in San Diego, first as a computer programmer and then as an operations research analyst. He continued his research on model-based clustering and in 1965 he published the paper that really did solve the problem (Wolfe, J. H. 1965. A Computer Program for the Maximum-Likelihood Analysis of Types. USNPRA Technical Bulletin 65-15. U.S. Naval Personnel Research Activity, San Diego. 3, 74, 75.)

In this paper, he considered for the first time some issues which have subsequently been the subject of substantial threads of work in the model-based clustering literature. These include initialization, variable selection for clustering, and choice of the number of clusters. He also considered the problem of excessive computer time, and proposed subsampling of the data as a solution, ahead of his time. This paper also included publicly available software for implementing his methods in Fortran, called NORMIX, which was far from standard at the time.

Wolfe worked for 30 years at the U.S. Navy Personnel Research and Development Center in San Diego, with a particular focus later on Computer Adaptive Testing. He continued to analyze and publish results from this time for an additional 8 years as an emeritus researcher. He continued to publish his personal research on psychology and Scientology into his late 80s.

John will be remembered by friends and family for his kindness, tolerance, and personal and professional integrity. He is survived by his life partner of 43 years, Judy Gilson; his brother Wesley Wolfe; and sister Susan Wolfe.

More about John Wolfe’s achievements can be found on the Wikipedia page about him: https://en.wikipedia.org/wiki/John_H._Wolfe. An annotated list of his publications may be found here: https://johnwolfearticles.wordpress.com/13-2/.

Written by Adrian E. Raftery, University of Washington