From 2010 to his retirement in 2017, Professor Silverman was the Chief Scientific Adviser to the Home Office, a post with three aspects: to provide independent scientific advice to the Home Secretary and other Home Office ministers on the whole range of topics relevant to Home Office business; to lead Home Office Science, and to play a part in the interdepartmental network of Chief Scientific Advisers chaired by the Government Chief Scientific Adviser.

His research interests include: Computational statistics, smoothing methods, functional data analysis, wavelets, empirical Bayes, applications in many scientific areas.

His early research was in smoothing methods, density estimation and nonparametric regression as well as in a variety of other areas in theoretical, computational and applied statistics. More recently, he has focused on two main areas. The first is Functional Data Analysis, which encompasses the notion of statistical problems where the data are functions or images rather than the scalars or vectors of conventional statistics. In two books (joint with Jim Ramsay of McGill University) and a number of papers he explored various aspects of this topic, which is not just a collection of problems but is also an overall way of thinking about this area in which we have no more than scratched the surface. The second is the utilisation of possible sparsity in parameter spaces of high dimension. Such parameter spaces occur particularly in wavelet methods in statistics, but the methods developed are of much wider applicability. His work in this area has been mostly in collaboration with Iain Johnstone (Stanford), and includes both theoretical results exploring various aspects of empirical Bayes, and other, approaches to the general adaptivity problem, and also practical work including the development of a software package EbayesThresh in R. My most recent research includes the use of the empirical Bayes approach to problems in graphical statistics; multiresolution analysis of time and space deformations; and applications of statistical approaches in genomics.