## another first

Posted in Statistics with tags , , , , , , , , on July 1, 2022 by xi'an

A question related to the earlier post on the first importance sampling in print, about the fist Markov chain Monte Carlo in print. Again uncovered by Charly, a 1973 Chemical Physics paper by Patey and Valleau, the latter inventing umbrella sampling with Torrie at about the same time. (In a 1972 paper in the same journal with Card, Valleau uses Metropolis Monte Carlo. While Hastings, also at the University of Toronto uses Markov chain sampling.)

## of first importance

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , on June 14, 2022 by xi'an

My PhD student Charly Andral came with the question of the birthdate of importance sampling. I was under the impression that it had been created at the same time as the plain Monte Carlo method, being essentially the same thing since

$\int_{\mathfrak X} h(x)f(x)\,\text dx = \int_{\mathfrak X} h(x)\frac{f(x)}{g(x)}g(x)\,\text dx$

hence due to von Neumann or Ulam, but he could not find a reference earlier than a 1949 proceeding publication by Hermann Kahn in a seminar on scientific computation run by IBM. Despite writing a series of Monte Carlo papers in the late 1940’s and 1950’s, Kahn is not well-known in these circles (although mentioned in Fishman’s book), while being popular to some extent for his theorisation of nuclear war escalation and deterence. (I wonder if the concept is developed in some of his earlier 1948 papers. In a 1951 paper with Goertzel, a footnote signals than the approach was called quota sampling in their earlier papers. Charly has actually traced the earliest proposal as being Kahn’s, in a 14 June 1949 RAND preprint, beating Goertzel’s Oak Ridge National Laboratory preprint on quota sampling and importance functions by five days.)

(As a further marginalia, Kahn wrote with T.E. Harris an earlier preprint on Monte Carlo methods in April 1949, the same Harris as in Harris recurrence.)

## Berni Alder obituary in Nature [and the Metropolis algorithm]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , on December 4, 2020 by xi'an

When reading through the 15 October issue of Nature, I came across an obituary by David Ceperley for Berni Alder (1925-2020). With Thomas Wainwright, Alder invented the technique of molecular dynamics, “silencing criticism that the results were the product of inaccurate computer arithmetic.”

“Berni Alder pioneered computer simulation, in particular of the dynamics of atoms and molecules in condensed matter. To answer fundamental questions, he encouraged the view that computer simulation was a new way of doing science, one that could connect theory with experiment. Alder’s vision transformed the field of statistical mechanics and many other areas of applied science.”

As I was completely unaware of Alder’s contributions to the field, I was most surprised to read the following

“During his PhD, he and the computer scientist Stan Frankel developed an early Monte Carlo algorithm — one in which the spheres are given random displacements — to calculate the properties of the hard-sphere fluid. The advance was scooped by Nicholas Metropolis and his group at the Los Alamos National Laboratory in New Mexico.”

that would imply missing credit is due!, but I could only find the following information on Stan Frankel’s Wikipedia page: Frankel “worked with PhD candidate Berni Alder in 1949–1950 to develop what is now known as Monte Carlo analysis. They used techniques that Enrico Fermi had pioneered in the 1930s. Due to a lack of local computing resources, Frankel travelled to England in 1950 to run Alder’s project on the Manchester Mark 1 computer. Unfortunately, Alder’s thesis advisor [John Kirkwood] was unimpressed, so Alder and Frankel delayed publication of their results until 1955, in the Journal of Chemical Physics. This left the major credit for the technique to a parallel project by a team including Teller and Metropolis who published similar work in the same journal in 1953.” The (short) paper by Alder, Frankel and Lewinson is however totally silent on a potential precursor to the Metropolis et al. algorithm (included in its references)… It also contains a proposal for a completely uniform filling of a box by particles, provided they do not overlap, but the authors had to stop at 98 particles due to its inefficiency.