Many varieties of cross validation would be statistically appealing for the estimation of smoothing and other penalized regression hyperparameters, were it not for the high cost of evaluating such criteria. Here it is shown how to efficiently and accurately compute and optimize a broad variety of cross validation criteria for a wide range of models estimated by minimizing a quadratically penalized loss. The leading order computational cost of hyperparameter estimation is made comparable to the cost of a single model fit given hyperparameters. In many cases this represents an $O(n)$ computational saving when modelling $n$ data. This development makes if feasible, for the first time, to use leave-out-neighbourhood cross validation to deal with the wide spread problem of un-modelled short range autocorrelation which otherwise leads to underestimation of smoothing parameters. It is also shown how to accurately quantifying uncertainty in this case, despite the un-modelled autocorrelation. Practical examples are provided including smooth quantile regression, generalized additive models for location scale and shape, and focussing particularly on dealing with un-modelled autocorrelation.

Simon N. Wood

This paper discusses some statistical aspects of the U.K. Covid-19 pandemic response, focussing particularly on cases where we believe that a statistically questionable approach or presentation has had a substantial impact on public perception, or government policy, or both. We discuss the presentation of statistics relating to Covid risk, and the risk of the response measures, arguing that biases tended to operate in opposite directions, overplaying Covid risk and underplaying the response risks. We also discuss some issues around presentation of life loss data, excess deaths and the use of case data. The consequences of neglect of most individual variability from epidemic models, alongside the consequences of some other statistically important omissions are also covered. Finally the evidence for full stay at home lockdowns having been necessary to reverse waves of infection is examined, with new analyses provided for a number of European countries.

Simon N. Wood Ernst C. Wit Paul M. McKeigue Danshu Hu Beth Flood Lauren Corcoran Thea Abou Jawad

Some time ago, the standard geometric framework of Einstein gravity was extended by gauging the Maxwell algebra as well as the so called AdS-Maxwell algebra. In this letter it is shown that the actions for these four-dimensional extended Einstein gravities can be obtained from the five-dimensional Chern-Simons gravities actions by using the Randall-Sundrum compactification procedure. It is found that the In\"on\"u-Wigner contraction procedure, in the Weimar-Woods sense, can be used both to obtain the Maxwell-Chern-Simons action from the AdS-Maxwell-Chern-Simons action and to obtain the Maxwell extension of Einstein gravity in 4D from the four-dimensional extended AdS-Maxwell-Einstein-Hilbert action. It is also shown that the extended four-dimensional gravities belongs to the Horndeski family of scalar-tensor theories.

L. Avilés J. Diaz D. M. Penafiel V. C. Orozco P. Salgado

Generalized additive models (GAMs, Hastie & Tibshirani, 1990; Wood, 2017) are an extension of the generalized linear model that allows the effects of covariates to be modelled as smooth functions. GAMs are increasingly used in many areas of science (e.g. Pedersen, Miller, Simpson, & Ross, 2019; Simpson, 2018) because the smooth functions allow nonlinear relationships between covariates and the response to be learned from the data through the use of penalized splines. Within the R (R Core Team, 2024) ecosystem, Simon Wood's mgcv package (Wood, 2017) is widely used to fit GAMs and is a Recommended package that ships with R as part of the default install. A growing number of other R packages build upon mgcv, for example as an engine to fit specialised models not handled by mgcv itself (e.g. GJMR, Marra & Radice, 2023), or to make use of the wide range of splines available in mgcv (e.g. brms, B\"urkner, 2017). The gratia package builds upon mgcv by providing functions that make working with GAMs easier. gratia takes a tidy approach (Wickham, 2014) providing ggplot2 (Wickham, 2016) replacements for mgcv's base graphics-based plots, functions for model diagnostics and exploration of fitted models, and a family of functions for drawing samples from the posterior distribution of a fitted GAM. Additional functionality is provided to facilitate the teaching and understanding of GAMs.

Gavin L. Simpson

A PROP is a symmetric monoidal category whose objects are the nonnegative integers and whose tensor product on objects is addition. A morphism from $m$ to $n$ in a PROP can be visualized as a string diagram with $m$ input wires and $n$ output wires. For a field $k$, the PROP $\mathrm{FinVect}_k$ where morphisms are $k$-linear maps is used by Baez and Erbele to study signal-flow diagrams. We aim to generalize their result characterizing this PROP in terms of generators and relations by looking at the PROP $\mathrm{Mat}(R)$ of matrices of values in $R$, where $R$ is a commutative rig (that is, a generalization of a ring where the condition that each element has an additive inverse is relaxed). To this end, we show that the category of symmetric monoidal functors out of $\mathrm{Mat}(R)$ is equivalent to the category of bicommutative bimonoids equipped with a certain map of rigs; such functors are called algebras. By choosing $R$ correctly, we will see that the algebras of the PROP $\mathrm{FinSpan}$ of finite sets and spans between them are bicommutative bimonoids, while the algebras of the PROP $\mathrm{FinRel}$ of finite sets and relations between them are special bicommuative bimonoids and the algebras of $\mathrm{Mat}(\mathbb Z)$ are bicommutative Hopf monoids.

Simon Wadsley Nick Woods

A problem that tends to be ignored in the statistical analysis of experimental data in the language sciences is that responses often constitute time series, which raises the problem of autocorrelated errors. If the errors indeed show autocorrelational structure, evaluation of the significance of predictors in the model becomes problematic due to potential anti-conservatism of p-values. This paper illustrates two tools offered by Generalized Additive Mixed Models (GAMMs) (Lin and Zhang, 1999; Wood, 2006, 2011, 2013) for dealing with autocorrelated errors, as implemented in the current version of the fourth author's mgcv package (1.8.9): the possibility to specify an ar(1) error model for Gaussian models, and the possibility of using factor smooths for random-effect factors such as subject and item. These factor smooths are set up to have the same smoothing parameters, and are penalized to yield the non-linear equivalent of random intercepts and random slopes in the classical linear framework. Three case studies illustrate these issues.

R. Harald Baayen Jacolien van Rij Cecile de Cat Simon N. Wood

Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the assumption that the response distribution is modelled parametrically, here we discuss more flexible methods that do not entail any parametric assumption. In particular, this article introduces the qgam package, which is an extension of mgcv providing fast calibrated Bayesian methods for fitting quantile GAMs (QGAMs) in R. QGAMs are based on a smooth version of the pinball loss of Koenker (2005), rather than on a likelihood function, hence jointly achieving satisfactory accuracy of the quantile point estimates and coverage of the corresponding credible intervals requires adopting the specialized Bayesian fitting framework of Fasiolo, Wood, Zaffran, Nedellec, and Goude (2020b). Here we detail how this framework is implemented in qgam and we provide examples illustrating how the package should be used in practice.

Matteo Fasiolo Simon N. Wood Margaux Zaffran Raphaël Nedellec Yannig Goude

We report the discovery of a new M9.0 dwarf at only 8.2 pc, which we identified in our search for nearby ultracool dwarf (I-J >= 3.0, later than M8.0) in the DENIS database. We measure a very high proper motion of 2.5 arc-sec/yr. The PC3 index measured from its low-resolution spectrum gives a spectrophotometric distance of 8.2 pc. This makes it the third closest M9.0 dwarf.

N. Phan-Bao M. S. Bessell E. L. Martin G. Simon J. Guibert T. Forveille X. Delfosse F. Crifo N. Epchtein P. Wood F. Tajahmady

In this letter we examine a model recently proposed to produce phase synchronization [K. Wood et al, Phys. Rev. Lett. 96, 145701 (2006)] and we show that the onset to synchronization corresponds to the emergence of an intermittent process that is non-Poisson and renewal at the same time. We argue that this makes the model appropriate for the physics of blinking quantum dots, and the dynamics of human brain as well.

Simone Bianco Elvis Geneston Paolo Grigolini Massimiliano Ignaccolo

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.

Marco Baumgartl Simon Wood