I'm interested in computational methods for Bayesian inference problems. My research is focused on developing novel bounds for the finite sample error of sequential Monte Carlo samplers (SMC). The endgame is to compare these results to similar quantitative bounds for Markov chain Monte Carlo (MCMC) and parallel tempering. In particular, I demonstrate that SMC requires less computation than MCMC in certain problems. I also show that SMC has similar properties to parallel tempering and is suitable for difficult multi-modal problems. My methods can be easily applied to adaptive sequential Monte Carlo methods, which have good empirical results but are difficult to analyse theoretically.