Statistics Research:
Quasistationary Monte Carlo: I've been collaborating with Andi Wang, Gareth Roberts, Martin Kolb, and Murray Pollock, on the foundations of Markov Chain Monte Carlo methods that target a distribution as the limit of a killed diffusion process conditioned on longterm survival. The ScaLE (Scalable Langevin Exact) algorithm was introduced by Pollock et al. in 2016. Some contributions that I have been involved in:

Proving convergence, and deriving a rate of convergence, for a general version of ScaLE:
Andi Q. Wang, Martin Kolb, Gareth O. Roberts, and David Steinsaltz. “Theoretical properties of quasistationary Monte Carlo methods”. In: Annals of Applied Probability 29.1 (2019), pp. 434–457. 
Simulating the quasistationary distribution by rebirth at a point selected from the trajectory's past.
Andi Q. Wang, Murray Pollock, Gareth O. Roberts, and David Steinsaltz. “Regenerationenriched Markov processes with application to Monte Carlo”. To appear in Annals of Applied Probability. 2020. 
Simulating the quasi stationary distribution by replacing "killing" by jumps to a point determined by a fixed distribution.
Andi Q. Wang, Gareth O. Roberts, and David Steinsaltz. “An approximation scheme for quasistationary distributions of killed diffusions”. In: Stochastic Processes and Applications 130.5 (May 2020), pp. 3193–3219. 
Andi Q. Wang and David Steinsaltz: A note on the distribution of firstjump locations.
Heritability estimation: Inspired by questions raised by Kumar et al. about the validity of the popular randomeffects ML method of estimating narrowsense heritability, I wrote with Ken Wachter and Andy Dahl the paper Statistical properties of simple randomeffects models for genetic heritability, analysing the behaviour of this model both in the wellspecified case, and under various forms of misspecification. We applied randommatrix theory to describe, in particular, how the method would function in the simple case of completely random genotype data.
Bayesian metaanalysis: Graeme T. Spence, David Steinsaltz, and Thomas R. Fanshawe. "A Bayesian approach to sequential meta‐analysis." Statistics in medicine 35.29 (2016): 53565375. (preprint version)