Sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution

Understanding how virus strains offer protection against closely related emerging strains is vital for creating effective vaccines. For many viruses, including Foot-and-Mouth Disease Virus (FMDV) and the Influenza virus where multiple serotypes often co-circulate, in vitro testing of large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Vaccines will offer cross-protection against closely related strains, but not against those that are antigenically distinct. To be able to predict cross-protection we must understand the antigenic variability within a virus serotype, distinct lineages of a virus, and identify the antigenic residues and evolutionary changes that cause the variability. In this thesis we present a family of sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution (SABRE), as well as an extended version of the method, the extended SABRE (eSABRE) method, which better takes into account the data collection process. The SABRE methods are a family of sparse Bayesian hierarchical models that use spike and slab priors to identify sites in the viral protein which are important for the neutralisation of the virus. In this thesis we demonstrate how the SABRE methods can be used to identify antigenic residues within different serotypes and show how the SABRE method outperforms established methods, mixed-effects models based on forward variable selection or l1 regularisation, on both synthetic and viral datasets. In addition we also test a number of different versions of the SABRE method, compare conjugate and semi-conjugate prior specifications and an alternative to the spike and slab prior; the binary mask model. We also propose novel proposal mechanisms for the Markov chain Monte Carlo (MCMC) simulations, which improve mixing and convergence over that of the established component-wise Gibbs sampler. The SABRE method is then applied to datasets from FMDV and the Influenza virus in order to identify a number of known antigenic residue and to provide hypotheses of other potentially antigenic residues. We also demonstrate how the SABRE methods can be used to create accurate predictions of the important evolutionary changes of the FMDV serotypes. In this thesis we provide an extended version of the SABRE method, the eSABRE method, based on a latent variable model. The eSABRE method takes further into account the structure of the datasets for FMDV and the Influenza virus through the latent variable model and gives an improvement in the modelling of the error. We show how the eSABRE method outperforms the SABRE methods in simulation studies and propose a new information criterion for selecting the random effects factors that should be included in the eSABRE method; block integrated Widely Applicable Information Criterion (biWAIC). We demonstrate how biWAIC performs equally to two other methods for selecting the random effects factors and combine it with the eSABRE method to apply it to two large Influenza datasets. Inference in these large datasets is computationally infeasible with the SABRE methods, but as a result of the improved structure of the likelihood, we are able to show how the eSABRE method offers a computational improvement, leading it to be used on these datasets. The results of the eSABRE method show that we can use the method in a fully automatic manner to identify a large number of antigenic residues on a variety of the antigenic sites of two Influenza serotypes, as well as making predictions of a number of nearby sites that may also be antigenic and are worthy of further experiment investigation.

Essays on the term structure of interest rates

This PhD thesis contains three main chapters on macro finance, with a focus on the term structure of interest rates and the applications of state-of-the-art Bayesian econometrics. Except for Chapter 1 and Chapter 5, which set out the general introduction and conclusion, each of the chapters can be considered as a standalone piece of work. In Chapter 2, we model and predict the term structure of US interest rates in a data rich environment. We allow the model dimension and parameters to change over time, accounting for model uncertainty and sudden structural changes. The proposed timevarying parameter Nelson-Siegel Dynamic Model Averaging (DMA) predicts yields better than standard benchmarks. DMA performs better since it incorporates more macro-finance information during recessions. The proposed method allows us to estimate plausible realtime term premia, whose countercyclicality weakened during the financial crisis. Chapter 3 investigates global term structure dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. More than half of the variation in the bond yields of seven advanced economies is due to global co-movement. Our results suggest that global inflation is the most important factor among global macro fundamentals. Non-fundamental factors are essential in driving global co-movements, and are closely related to sentiment and economic uncertainty. Lastly, we analyze asymmetric spillovers in global bond markets connected to diverging monetary policies. Chapter 4 proposes a no-arbitrage framework of term structure modeling with learning and model uncertainty. The representative agent considers parameter instability, as well as the uncertainty in learning speed and model restrictions. The empirical evidence shows that apart from observational variance, parameter instability is the dominant source of predictive variance when compared with uncertainty in learning speed or model restrictions. When accounting for ambiguity aversion, the out-of-sample predictability of excess returns implied by the learning model can be translated into significant and consistent economic gains over the Expectations Hypothesis benchmark.

Essays on the term structure of interest rates

This PhD thesis contains three main chapters on macro finance, with a focus on the term structure of interest rates and the applications of state-of-the-art Bayesian econometrics. Except for Chapter 1 and Chapter 5, which set out the general introduction and conclusion, each of the chapters can be considered as a standalone piece of work. In Chapter 2, we model and predict the term structure of US interest rates in a data rich environment. We allow the model dimension and parameters to change over time, accounting for model uncertainty and sudden structural changes. The proposed time-varying parameter Nelson-Siegel Dynamic Model Averaging (DMA) predicts yields better than standard benchmarks. DMA performs better since it incorporates more macro-finance information during recessions. The proposed method allows us to estimate plausible real-time term premia, whose countercyclicality weakened during the financial crisis. Chapter 3 investigates global term structure dynamics using a Bayesian hierarchical factor model augmented with macroeconomic fundamentals. More than half of the variation in the bond yields of seven advanced economies is due to global co-movement. Our results suggest that global inflation is the most important factor among global macro fundamentals. Non-fundamental factors are essential in driving global co-movements, and are closely related to sentiment and economic uncertainty. Lastly, we analyze asymmetric spillovers in global bond markets connected to diverging monetary policies. Chapter 4 proposes a no-arbitrage framework of term structure modeling with learning and model uncertainty. The representative agent considers parameter instability, as well as the uncertainty in learning speed and model restrictions. The empirical evidence shows that apart from observational variance, parameter instability is the dominant source of predictive variance when compared with uncertainty in learning speed or model restrictions. When accounting for ambiguity aversion, the out-of-sample predictability of excess returns implied by the learning model can be translated into significant and consistent economic gains over the Expectations Hypothesis benchmark.