Abstract
On November 25, 2021, Brian Douglas Marx died in his home in Baton Rouge, Louisiana. He had been diagnosed with multiple brain tumors a few months earlier. Statistical Modelling published his obituary in Volume 22 (
Brian’s illness and death came as shock to everyone in the statistical community where he has made various important contributions. He was editor of this journal since its start in 2000 until 2021 and has significantly contributed to its success. Brian also was a strong force for the International Workshop on Statistical Modelling. He attended his first workshop 1989 in Trento and he did not miss a single one since then. We all remember his boyish enthusiasm at the meetings. In 1998, Brian organized the first Workshop outside Europe, in New Orleans.
It was in Trento, where Brian and Paul first met. That was the start of an intense cooperation over more than thirty years, developing and extending P-splines. Brian became Paul’s best friend. We wrote papers, presented at conferences and organized courses. The crown on our work is the book on P-splines that came out in 2021.
Thomas and Brian first met when Brian was a visiting professor in Munich in 2000 and taught a course on generalized regression that Thomas attended as a student. Later, they met at various Statistical Modelling Workshops and (together with Ludwig Fahrmeir and Stefan Lang) they co- authored a book on “Regression - Models, Methods and Applications”.
As a tribute to Brian, the editors of the Statistical Modelling journal together with Paul and Thomas developed the idea to fill a special (double) issue with contributions by his friends on the subject that was close to his heart, P-splines. For this special issue, we approached various potential authors and all their reactions were very positive. We asked authors to not only present their technical material, but also, if they had known Brian personally, to share some of their memories of him. In the following, we summarize the contributions in this double issue devoted to the memory of Brian.
Four papers deal with principal questions of statistical modelling with P-Splines:
Lambert and Gressani study the selection of the penalty parameter in P-Spline and propose asymmetry corrections to the Laplace approximations in Bayesian P-splines models, Hernandez et al. consider derivative curve estimation in longitudinal studies using P-splines where the inclusion of individual-specific curves poses additional challenges concerning effi cient computation as well as penalty construction, Mayr et al. apply a functional gradient descent algorithm with penalized least squares baselearners built from P-Splines to achieve variable selection and model choice with the goal to distinguishing linear from nonlinear effects, and Currie proposes a black box approach to fitting smooth models of mortality with P-Splines.
The paper by Iain Currie deserves special mention. Iain had agreed to contribute, but then he became quite ill. Paul visited him in February 2022. He had lost much of his energy, but his mind was still sharp as ever. He was not sure that the subject he had planned would be interesting enough, but he showed a draft to Paul, who convinced him of its value. At the end of March, Iain sent us a manuscript. The subject of his email was “A last hurrah!”. Iain died on May 25.
Two papers consider bivariate extensions of P-Splines based on tensor products or more gener ally bivariate smoothing:
Boer develops tensor product P-splines using a sparse mixed model formulation and Fahrmeir et al. study bivariate smoothing for spatial data comparing bivariate tensor product P-splines with a neighborhood-based approach relying on either a ridge-type penalty for smoothing or a lasso-type penalty for spatial clustering.
The final four papers investigate distributional forms of regression modelling based on P-Splines:
Eletti et al. utilize monotonic P-splines to model survival functions in a multi-state model based on a general framework for penalized additive models, Stasinopoulos et al. consider P-splines as smoothers in generalized additive models for location, scale and shape (GAMLSS) and the special case of zero-adjusted distributions, Razen et al. study distributional regression modelling beyond the mean with quantile regression and GAMLSS as special cases in a multilevel model specification utilizing P-splines as a building block, and Muggeo et al. develop joint models for non-crossing additive quantile regression via constrained B-spline varying coefficients.
We hope this special issue will be well received by the statistical modelling community, not only because of its scientific content, but even more by refreshing our memories of Brian and how he has influenced our lives in so many positive ways.