Welsh’s work addresses a particularly wide variety of problems. In a parametric setting, his research on distance sampling and related topics is especially important. His work on semiparametric inference includes his remarkable contributions to robust inference in linear regression, using order statistics. Here he has provided an ingenious solution to a problem that has baffled experienced workers in the field. In the setting of nonparametric inference, his research on applications of smoothing methods to clustered data has produced many surprises, including his demonstration that remarkable improvements in performance can be achieved by taking proper and careful account of the dependence structure when constructing a smoother. All this work, and much more besides, has the unusual but, for Welsh, almost universal characteristic of theoretical depth combined with substantial practical relevance.