Abstract/Summary

The first part of my research concentrates on Sequential Monte Carlo (SMC) methods for phylogenetics. The aim of the research was to deliver methods that can be used in the inference of the spread of diseases, leveraging a widely used software platform, and enable researchers to easily access, validate and compare. We show the results obtained from developing and integrating an adaptive SMC algorithm in Bayesian Evolutionary Analysis by Sampling Trees version 2 (commonly known as BEAST2), a well-established software platform among researchers. Our adaptive SMC algorithm embedded in BEAST2 has comparable performances to the native Markov Chain Monte Carlo (MCMC) method, in terms of accuracy and efficiency. Our work can be seen as a first step, and future tuning is expected. It is foreseen that an integration of the adaptive SMC package into BEAST2 will be done by the owners of the platform, allowing researchers to use SMC instead of MCMC, following testing and tuning by the platforms developers. The focus of the second part is Active Subspaces (AS). With AS we try to identify a smaller subspace informed by the data and to concentrate the algorithmic effort on this more informative part, primarily to address the curse of dimensionality affecting many Monte Carlo (MC) methods. Existing AS algorithms were mostly biased and targeting distributions only close by some measure to the posterior, leaving users to do substantial post-validation. We built on the foundations of an existing pseudo-marginal-based Active Subspace algorithm and developed non-biased AS algorithms that in stationarity target the correct posterior, using the structure provided by AS within a Gibbs-style MCMC, and within Particle Marginal Metropolis Hastings (PMMH), Metropolis within Particle Gibbs (MwPG), SMC-squared (SMC2 ). We have run experiments that show in specific settings to outperform existing methods and provide explanations on the optimal running conditions for each algorithm. Our work sheds light on the practical applications of Active Subspaces, expanding the range of AS methods available to researchers and providing clearer guidance on which approaches are most effective in specific scenarios.