Responsible Release of AI-Generated Mathematics September 29, 2026 Back to main page Download PDF At present, some frontier AI labs are testing advanced mathematical problems on proprietary models …

In our field of applied mathematics, the long, human process of trial and error — not just the solutions themselves — is often what has led to progress.

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Andrew Gelman, Aki Vehtari, and Richard McElreath discuss their new book on Bayesian workflow, reverse Bayes and hierarchical pooling.

Publish your Python applications, R applications, and documents from GitHub to Posit Connect Cloud

The London School of Hygiene & Tropical Medicine (LSHTM) is one of the world’s leading public health universities. Our mission is to improve health and health equity in the UK and worldwide; working i...

I recently learned that Springer Nature is about to make the reference journal Statistics and Computing, where I published close to twenty papers over the years, fully “open access”, wh…

In survival studies, treatments can benefit patients through different mechanisms: a treatment may increase the probability of being cured or delay failure among patients who are not cured. Quantifyin...

These functions have been deprecated in favor of pak, as that is what we now recommend for package installation. There are a few functions which have no pak equivalent, where you can instead call the ...

The Fields medallist discusses how ever-evolving technology is transforming mathematicians’ work.

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Explore UCL Statistics research studentships: funding, opportunities, and support for PhD students to advance statistical science through innovative research and collaboration.

The great debate: is delivering innovation compatible with sustainable and equitable cancer care?The current state of cancer care in England is a regular news feature, whether its long waiting

Statistics on relative deprivation in small areas in England. Further details are provided at the bottom of this page and in the FAQ document.

High-dimensional model selection with the modelSelection R package

Sample selection bias arises when missingness in the outcome of interest correlates with the outcome itself, leading to non-randomly selected samples. A common approach to correct bias from sample selection is to use sample selection models that jointly model the selection mechanism and the outcome of interest. Formulating these models typically rely on exclusion restrictions (variables that are predictors of selection but not appearing in the outcome equation) to ensure identifiability of the parameters. However, the choice of exclusion restrictions often depends on heuristics or expert judgment, potentially leading to the inclusion of irrelevant variables or the omission of important ones. Additionally, distributional misspecification and omitted variable bias are frequent challenges in this framework. To formally address these issues, we propose a Bayesian variable selection (BVS) methodology that incorporates both local priors (LPs) and non-local priors (NLPs), enabling the identification of variables with predictive power for the outcome and selection processes. We develop computational tools to conduct BVS in sample selection models based on a Laplace approximation of the marginal likelihood, and characterize the resulting Bayes factor rates under model misspecification. We establish model selection consistency for both classes of priors, showing that the proposed methodology correctly identifies active variables for both the selection process and outcome process asymptotically. The priors are calibrated to account for the possibility of distributional misspecification and omitted variable bias. We present a simulation study and real-data applications to explore the finite-sample effects of model misspecification on BVS. We compare the performance of the proposed methodology against BVS based on spike-and-slab (SS) priors and the Adaptive LASSO (ALASSO), an adaptive weighting of the least absolute shrinkage and selection operator (LASSO).

Promotion Time Cure Models with a General Hazard structure - FJRubio67/PTCMGH

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This thoroughly revised and expanded second edition of the Handbook of Markov Chain Monte Carlo reflects the dramatic evolution of MCMC methods since the publication of the first edition. With the add...

The interplay between missing data and model uncertainty—two classic statistical problems—leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the probabilistic justification of Rubin’s rules applied to the usual components of Bayesian variable selection, arguing that prior predictive marginals should be central to the pursued methodology. In the regression settings, we explore the conditions of prior distributions that make the missing data mechanism ignorable, provided that it is missing at random or completely at random. Moreover, when comparing multiple linear models, we provide a complete methodology for dealing with special cases, such as variable selection or uncertainty regarding model errors. In numerous simulation experiments, we demonstrate that our method outperforms or equals others, in consistently producing results close to those obtained using the full dataset. In general, the difference increases with the percentage of missing data and the correlation between the variables used for imputation. Finally, we summarize possible directions for future research.