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 long-term 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 quasi-stationary 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. “Regeneration-enriched 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 first-jump locations.
Heritability estimation: Inspired by questions raised by Kumar et al. about the validity of the popular random-effects ML method of estimating narrow-sense heritability, I wrote with Ken Wachter and Andy Dahl the paper Statistical properties of simple random-effects models for genetic heritability, analysing the behaviour of this model both in the well-specified case, and under various forms of misspecification. We applied random-matrix theory to describe, in particular, how the method would function in the simple case of completely random genotype data.
Bayesian meta-analysis: Graeme T. Spence, David Steinsaltz, and Thomas R. Fanshawe. "A Bayesian approach to sequential meta‐analysis." Statistics in medicine 35.29 (2016): 5356-5375. (preprint version)