Oct 17

3:30 pm

## Log-concave Density Estimation with Applications

### Richard Samworth

Seminar

University of Cambridge - Statistical Laboratory

The set of log-concave densities on $mathbb{R}^d$ forms a very attractive infinite-dimensional class. It is large enough to include many standard parametric families and yet it retains many of the desirable properties of Gaussian densities, e.g. closure under marginalisation, conditioning and convolution operations. Importantly, the class is also small enough to allow fully automatic estimation procedures, e.g. using maximum likelihood, where more traditional nonparametric methods would require troublesome choices of smoothing parameters. I will begin by describing the log-concave density estimation problem, including recent theoretical results. I will also show how related ideas of log-concave projections are relevant for other inferential problems including regression, testing and Independent Component Analysis.

Bio: I obtained my PhD in Statistics from the University of Cambridge in 2004. Following a research fellowship at St John's College, Cambridge, I was appointed to a lectureship in Statistics at the Statistical Laboratory in Cambridge in 2005. I was promoted to a readership in 2010 and to a full professorship from October 2013. I remain a fellow of St John's College, and currently hold an EPSRC Early Career Fellowship (worth GBP 1.2M) for five years from December 2012. My main research interests are in nonparametric and high-dimensional statistics. Particular topics include shape-constrained density and other nonparametric function estimation problems, nonparametric classification, clustering and regression, Independent Component Analysis, the bootstrap and high-dimensional variable selection problems. I was awarded the Royal Statistical Society Research prize (2008), a Leverhulme Research Fellowship (2011) and the Royal Statistical Society Guy Medal in Bronze (2012). I currently serve as an Associate Editor for the Annals of Statistics, the Journal of the Royal Statistical Society Series B, Biometrika and Statistica Sinica.