Bayesian Methods for Inferring Gene Regulatory Networks

Thesis (Ph.D.)--University of Washington, 2016-08

'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126,

Leveraging Multiple Features for Image Retrieval and Matching

The goal of image retrieval and matching is to find and locate object instances in images from a large-scale image database. While visual features are abundant, how to combine them to improve performance by individual features remains a challenging task. In this work, we focus on leveraging multiple features for accurate and efficient image retrieval and matching. We first propose two graph-based approaches to rerank initially retrieved images for generic image retrieval. In the graph, vertices are images while edges are similarities between image pairs. Our first approach employs a mixture Markov model based on a random walk model on multiple graphs to fuse graphs. We introduce a probabilistic model to compute the importance of each feature for graph fusion under a naive Bayesian formulation, which requires statistics of similarities from a manually labeled dataset containing irrelevant images. To reduce human labeling, we further propose a fully unsupervised reranking algorithm based on a submodular objective function that can be efficiently optimized by greedy algorithm. By maximizing an information gain term over the graph, our submodular function favors a subset of database images that are similar to query images and resemble each other. The function also exploits the rank relationships of images from multiple ranked lists obtained by different features. We then study a more well-defined application, person re-identification, where the database contains labeled images of human bodies captured by multiple cameras. Re-identifications from multiple cameras are regarded as related tasks to exploit shared information. We apply a novel multi-task learning algorithm using both low level features and attributes. A low rank attribute embedding is joint learned within the multi-task learning formulation to embed original binary attributes to a continuous attribute space, where incorrect and incomplete attributes are rectified and recovered. To locate objects in images, we design an object detector based on object proposals and deep convolutional neural networks (CNN) in view of the emergence of deep networks. We improve a Fast RCNN framework and investigate two new strategies to detect objects accurately and efficiently: scale-dependent pooling (SDP) and cascaded rejection classifiers (CRC). The SDP improves detection accuracy by exploiting appropriate convolutional features depending on the scale of input object proposals. The CRC effectively utilizes convolutional features and greatly eliminates negative proposals in a cascaded manner, while maintaining a high recall for true objects. The two strategies together improve the detection accuracy and reduce the computational cost.

Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization–maximization (MM) algorithm with a Nelder–Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

A flexible bio-inspired hierarchical model for analyzing musical timbre

A flexible and multipurpose bio-inspired hierarchical model for analyzing musical timbre is presented in this paper. Inspired by findings in the fields of neuroscience, computational neuroscience, and psychoacoustics, not only does the model extract spectral and temporal characteristics of a signal, but it also analyzes amplitude modulations on different timescales. It uses a cochlear filter bank to resolve the spectral components of a sound, lateral inhibition to enhance spectral resolution, and a modulation filter bank to extract the global temporal envelope and roughness of the sound from amplitude modulations. The model was evaluated in three applications. First, it was used to simulate subjective data from two roughness experiments. Second, it was used for musical instrument classification using the k-NN algorithm and a Bayesian network. Third, it was applied to find the features that characterize sounds whose timbres were labeled in an audiovisual experiment. The successful application of the proposed model in these diverse tasks revealed its potential in capturing timbral information.

A numerical model for prediction of oil, trajectory due to extraction activity in the north coasts of the Persian Gulf

This thesis considers a three- dimensional numerical model based on 3-D Navier— Stokes and continuity equations involving various wind speeds (North west), water surface levels, horizontal shier stresses, eddy viscosity, densities of oil and gas condensate- water mixture flows. The model is used to simulate the prediction of the surface movement of oil and gas condensate slicks from spill accident in the north coasts of Persian Gulf.

'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126,

Quantification of air quality in space and time and its effects on health

The long-term adverse effects on health associated with air pollution exposure can be estimated using either cohort or spatio-temporal ecological designs. In a cohort study, the health status of a cohort of people are assessed periodically over a number of years, and then related to estimated ambient pollution concentrations in the cities in which they live. However, such cohort studies are expensive and time consuming to implement, due to the long-term follow up required for the cohort. Therefore, spatio-temporal ecological studies are also being used to estimate the long-term health effects of air pollution as they are easy to implement due to the routine availability of the required data. Spatio-temporal ecological studies estimate the health impact of air pollution by utilising geographical and temporal contrasts in air pollution and disease risk across $n$ contiguous small-areas, such as census tracts or electoral wards, for multiple time periods. The disease data are counts of the numbers of disease cases occurring in each areal unit and time period, and thus Poisson log-linear models are typically used for the analysis. The linear predictor includes pollutant concentrations and known confounders such as socio-economic deprivation. However, as the disease data typically contain residual spatial or spatio-temporal autocorrelation after the covariate effects have been accounted for, these known covariates are augmented by a set of random effects. One key problem in these studies is estimating spatially representative pollution concentrations in each areal which are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over modelled concentrations (grid level) from an atmospheric dispersion model. The aim of this thesis is to investigate the health effects of long-term exposure to Nitrogen Dioxide (NO2) and Particular matter (PM10) in mainland Scotland, UK. In order to have an initial impression about the air pollution health effects in mainland Scotland, chapter 3 presents a standard epidemiological study using a benchmark method. The remaining main chapters (4, 5, 6) cover the main methodological focus in this thesis which has been threefold: (i) how to better estimate pollution by developing a multivariate spatio-temporal fusion model that relates monitored and modelled pollution data over space, time and pollutant; (ii) how to simultaneously estimate the joint effects of multiple pollutants; and (iii) how to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. Specifically, chapters 4 and 5 are developed to achieve (i), while chapter 6 focuses on (ii) and (iii). In chapter 4, I propose an integrated model for estimating the long-term health effects of NO2, that fuses modelled and measured pollution data to provide improved predictions of areal level pollution concentrations and hence health effects. The air pollution fusion model proposed is a Bayesian space-time linear regression model for relating the measured concentrations to the modelled concentrations for a single pollutant, whilst allowing for additional covariate information such as site type (e.g. roadside, rural, etc) and temperature. However, it is known that some pollutants might be correlated because they may be generated by common processes or be driven by similar factors such as meteorology. The correlation between pollutants can help to predict one pollutant by borrowing strength from the others. Therefore, in chapter 5, I propose a multi-pollutant model which is a multivariate spatio-temporal fusion model that extends the single pollutant model in chapter 4, which relates monitored and modelled pollution data over space, time and pollutant to predict pollution across mainland Scotland. Considering that we are exposed to multiple pollutants simultaneously because the air we breathe contains a complex mixture of particle and gas phase pollutants, the health effects of exposure to multiple pollutants have been investigated in chapter 6. Therefore, this is a natural extension to the single pollutant health effects in chapter 4. Given NO2 and PM10 are highly correlated (multicollinearity issue) in my data, I first propose a temporally-varying linear model to regress one pollutant (e.g. NO2) against another (e.g. PM10) and then use the residuals in the disease model as well as PM10, thus investigating the health effects of exposure to both pollutants simultaneously. Another issue considered in chapter 6 is to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. There are in total four approaches being developed to adjust the exposure uncertainty. Finally, chapter 7 summarises the work contained within this thesis and discusses the implications for future research.

SOVLENT REACTIVITY AND INTERFACE EVOLUTION AT MODEL ELECTRODES FOR ENERGY APPLICATIONS

The Li-ion rechargeable battery (LIB) is widely used as an energy storage device, but has significant limitations in battery cycle life and safety. During initial charging, decomposition of the ethylene carbonate (EC)-based electrolytes of the LIB leads to the formation of a passivating layer on the anode known as the solid electrolyte interphase (SEI). The formation of an SEI has great impact on the cycle life and safety of LIB, yet mechanistic aspects of SEI formation are not fully understood. In this dissertation, two surface science model systems have been created under ultra-high vacuum (UHV) to probe the very initial stage of SEI formation at the model carbon anode surfaces of LIB. The first model system, Model System I, is an lithium-carbonate electrolyte/graphite C(0001) system. I have developed a temperature programmed desorption/temperature programmed reaction spectroscopy (TPD/TPRS) instrument as part of my dissertation to study Model System I in quantitative detail. The binding strengths and film growth mechanisms of key electrolyte molecules on model carbon anode surfaces with varying extents of lithiation were measured by TPD. TPRS was further used to track the gases evolved from different reduction products in the early-stage SEI formation. The branching ratio of multiple reaction pathways was quantified for the first time and determined to be 70.% organolithium products vs. 30% inorganic lithium product. The obtained branching ratio provides important information on the distribution of lithium salts that form at the very onset of SEI formation. One of the key reduction products formed from EC in early-stage SEI formation is lithium ethylene dicarbonate (LEDC). Despite intensive studies, the LEDC structure in either the bulk or thin-film (SEI) form is unknown. To enable structural study, pure LEDC was synthesized and subject to synchrotron X-ray diffraction measurements (bulk material) and STM measurements (deposited films). To enable studies of LEDC thin films, Model System II, a lithium ethylene dicarbonate (LEDC)-dimethylformamide (DMF)/Ag(111) system was created by a solution microaerosol deposition technique. Produced films were then imaged by ultra-high vacuum scanning tunneling microscopy (UHV-STM). As a control, the dimethylformamide (DMF)-Ag(111) system was first prepared and its complex 2D phase behavior was mapped out as a function of coverage. The evolution of three distinct monolayer phases of DMF was observed with increasing surface pressure — a 2D gas phase, an ordered DMF phase, and an ordered Ag(DMF)2 complex phase. The addition of LEDC to this mixture, seeded the nucleation of the ordered DMF islands at lower surface pressures (DMF coverages), and was interpreted through nucleation theory. A structural model of the nucleation seed was proposed, and the implication of ionic SEI products, such as LEDC, in early-stage SEI formation was discussed.

A Bayesian network dealing with measurements and residuals for system monitoring

International audience

What to do when K-means clustering fails:a simple yet principled alternative algorithm

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

A Bayesian approach to study the risk variables for tuberculosis occurrence in domestic and wild ungulates in South Central Spain

BACKGROUND Bovine tuberculosis (bTB) is a chronic infectious disease mainly caused by Mycobacterium bovis. Although eradication is a priority for the European authorities, bTB remains active or even increasing in many countries, causing significant economic losses. The integral consideration of epidemiological factors is crucial to more cost-effectively allocate control measures. The aim of this study was to identify the nature and extent of the association between TB distribution and a list of potential risk factors regarding cattle, wild ungulates and environmental aspects in Ciudad Real, a Spanish province with one of the highest TB herd prevalences. RESULTS We used a Bayesian mixed effects multivariable logistic regression model to predict TB occurrence in either domestic or wild mammals per municipality in 2007 by using information from the previous year. The municipal TB distribution and endemicity was clustered in the western part of the region and clearly overlapped with the explanatory variables identified in the final model: (1) incident cattle farms, (2) number of years of veterinary inspection of big game hunting events, (3) prevalence in wild boar, (4) number of sampled cattle, (5) persistent bTB-infected cattle farms, (6) prevalence in red deer, (7) proportion of beef farms, and (8) farms devoted to bullfighting cattle. CONCLUSIONS The combination of these eight variables in the final model highlights the importance of the persistence of the infection in the hosts, surveillance efforts and some cattle management choices in the circulation of M. bovis in the region. The spatial distribution of these variables, together with particular Mediterranean features that favour the wildlife-livestock interface may explain the M. bovis persistence in this region. Sanitary authorities should allocate efforts towards specific areas and epidemiological situations where the wildlife-livestock interface seems to critically hamper the definitive bTB eradication success.

Assessment of the sensitivity and specificity of serological (IFAT) and molecular (direct PCR) techniques for diagnosis of leishmaniasis in lagomorphs using a Bayesian approach

Leishmaniasis, caused by Leishmania infantum, is a vector-borne zoonotic disease that is endemic to the Mediterranean basin. The potential of rabbits and hares to serve as competent reservoirs for the disease has recently been demonstrated, although assessment of the importance of their role on disease dynamics is hampered by the absence of quantitative knowledge on the accuracy of diagnostic techniques in these species. A Bayesian latent-class model was used here to estimate the sensitivity and specificity of the Immuno-fluorescence antibody test (IFAT) in serum and a Leishmania-nested PCR (Ln-PCR) in skin for samples collected from 217 rabbits and 70 hares from two different populations in the region of Madrid, Spain. A two-population model, assuming conditional independence between test results and incorporating prior information on the performance of the tests in other animal species obtained from the literature, was used. Two alternative cut-off values were assumed for the interpretation of the IFAT results: 1/50 for conservative and 1/25 for sensitive interpretation. Results suggest that sensitivity and specificity of the IFAT were around 70–80%, whereas the Ln-PCR was highly specific (96%) but had a limited sensitivity (28.9% applying the conservative interpretation and 21.3% with the sensitive one). Prevalence was higher in the rabbit population (50.5% and 72.6%, for the conservative and sensitive interpretation, respectively) than in hares (6.7% and 13.2%). Our results demonstrate that the IFAT may be a useful screening tool for diagnosis of leishmaniasis in rabbits and hares. These results will help to design and implement surveillance programmes in wild species, with the ultimate objective of early detecting and preventing incursions of the disease into domestic and human populations.

Breaking the curve with candels: a Bayesian approach to reveal the non-universality of the dust-attenuation law at high redshift

Dust attenuation affects nearly all observational aspects of galaxy evolution, yet very little is known about the form of the dust-attenuation law in the distant universe. Here, we model the spectral energy distributions of galaxies at z ~ 1.5–3 from CANDELS with rest-frame UV to near-IR imaging under different assumptions about the dust law, and compare the amount of inferred attenuated light with the observed infrared (IR) luminosities. Some individual galaxies show strong Bayesian evidence in preference of one dust law over another, and this preference agrees with their observed location on the plane of infrared excess (IRX, L_TIR/L_UV) and UV slope (β). We generalize the shape of the dust law with an empirical model, A_ λ,σ =E(B-V)k_ λ (λ / λ v)^ σ where k_λ is the dust law of Calzetti et al., and show that there exists a correlation between the color excess E(B-V) and tilt δ with δ =(0.62±0.05)log(E(B-V))+(0.26±0.02). Galaxies with high color excess have a shallower, starburst-like law, and those with low color excess have a steeper, SMC-like law. Surprisingly, the galaxies in our sample show no correlation between the shape of the dust law and stellar mass, star formation rate, or β. The change in the dust law with color excess is consistent with a model where attenuation is caused by scattering, a mixed star–dust geometry, and/or trends with stellar population age, metallicity, and dust grain size. This rest-frame UV-to-near-IR method shows potential to constrain the dust law at even higher redshifts (z>3).

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.