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The reconstruction of a phase surface from the observed principal values is required for a number of applications, including synthetic aperture radar (SAR) and magnetic resonance imaging (MRI). However, the process of reconstruction, called

The thesis begins with a general introduction to population genetics in chapter 1. I review the fundamental processes of evolution - mutation, recombination, selection, gene flow and genetic drift - and give an overview of Bayesian inference in statistical population genetics. Later, I introduce the studied species, Alpine ibex (Capra ibex ), and its recent history. This history is intimately linked to the structured population in the Swiss Alps that provides the source of genetic data for this thesis. A particular focus is devoted to approximate Bayesian computation (ABC) in chapter 2, a method of inference that has become important over the last 15 years and is convenient for complex problems of inference. In chapter 3, the biological focus is on estimating the distribution of mutation rates across neutral genetic variation (microsatellites), and on inferring the proportion of male ibex that obtain access to matings each breeding season. The latter is an important determinant of genetic drift. Methodologically, I compare different methods for the choice of summary statistics in ABC. One of the approaches proposed by collaborators and me and based on boosting (a technique developed in machine learning) is found to perform best in this case. Applying that method to microsatellite data from Alpine ibex, I estimate the scaled ancestral mutation rate (THETA anc = 4Neu) to about 1:288, and find that most of the variation across loci of the ancestral mutation rate u is between 7.7*10 -4 and 3.5*10 -3. The proportion of males with access to matings per breeding season is estimated to about 21%. Chapter 4 is devoted to the estimation of migration rates between a large number of pairs of populations. Again, I use ABC for inference. Estimating all rates jointly comes with substantial methodological problems. Therefore, I assess if, by dividing the whole problem into smaller ones and assuming that those are approximately independent, more accuracy may be achieved overall. The net accuracy of the second approach increases with the number of migration rates. Applying that approach to microsatellite data from Alpine ibex, and accounting for the possibility that a model without migration could also explain the data, I find no evidence for substantial gene flow via migration, except for one pair of demes in one direction. While chapters 3 and 4 deal with neutral variation, in chapter 5 I investigate if an allele of the Major Histocompatibility Complex (MHC) has been under selection over the last ten generations. Short- and medium-term methods for detecting signals of selection are combined. For the medium-term analysis, I adapt a matrix iteration approach that allows for joint estimation of the initial allele frequency, the dominance coefficient, and the strength of selection. The focal MHC allele is shared with domestic goat, and an interesting side issue is if this reflects an ancestral polymorphism or is due to recent introgression via hybridization. I find most evidence for asymmetric overdominance (selection coefficient s: 0.974; equilibrium frequency: 0.125) or directional selection against the `goat' allele (s: 0.5) with partial recessivity. Both scenarios suggest a disadvantage of the `goat' homozygote, but differ in the relative fitness of the heterozygotes. Overall, two aspects play a dominating role in this thesis: the biological questions and the process of inference. They are linked, yet while the proximate motivation for the biological component is given by a specific system - the structured population of Alpine ibex in the Swiss Alps - the methods used and advanced here are fairly general and may well be applied in different contexts.

Precise measurements of transit lightcurves can be used to constrain the composition and structure of exoplanet atmospheres. Unfortunately, efforts to extract this information are usually hampered by the presence of correlated noise that is degenerate with the astrophysical signal of interest. A major theme of this thesis is the application of robust analysis methods to properly account for such degeneracies. In particular, I advocate the use of Bayesian inference for lightcurve fitting. For this study, the Bayesian framework is exploited by modelling lightcurves as Gaussian processes (GPs), which offer numerous advantages over traditional decorrelation methods. The main advantage is that GPs do not require a functional form to be specified for the poorly understood lightcurve systematics. Instead, the high-level properties of the signal covariance are parameterised, allowing complex correlations to be marginalised over relatively low-dimension parameter spaces. I use GP models to analyse transit and eclipse lightcurves for the hot Jupiters HD189733b, HD209458b, and HAT-P-32b. The work is spread over three separate projects. Firstly, I re-analyse the majority of the transits and eclipses that have been observed using the Spitzer Space Telescope Infrared Array Camera (IRAC) for HD189733b and HD20945b. The GP analyses generally produce uncertainties for inferred planet parameters that are factors of ~1-5 larger than those quoted in the literature. In a number of cases, I obtain results that are fundamentally different to those published previously, with significant implications for the understanding of the atmospheres. Secondly, I report an eclipse observation for HD189733b that was made using the Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) over the 290-570nm wavelength range. Geometric albedos of Ag=0.37⁺¹²<sub style='position: relative; left: -1.3em;'>-13</sub> and Ag=0.37⁺¹³<sub style='position: relative; left: -1.3em;'>-12</sub> are measured in the wavelength ranges 290-450nm and 450-570nm, respectively. This represents the first ever multi-wavelength eclipse measurement made for an exoplanet at visible wavelengths. The nonzero albedo in the 290-450nm wavelength channel provides evidence for scattering in the atmosphere, possibly by haze/clouds or H2 molecules. The relatively low albedo in the 450-570nm wavelength channel is interpreted as being due to absorption by the wings of the Na 589nm doublet. Thirdly, I present two transit observations for HAT-P-32b made using the Nordic Optical Telescope (NOT) Andalucia Faint Object Spectrograph (ALFOSC) in multi-object spectroscopy mode over the 414-702nm wavelength range. A joint GP model is fit to the two white lightcurves produced by integrating the spectra over the full wavelength range. Spectroscopic lightcurves are also generated by binning into 32nm-wide wavelength channels, and preliminary lightcurve analyses are performed. The extracted transmission spectrum shows some evidence for absorption features, but this interpretation is currently very tentative. Further refinements to the data reduction and lightcurve analysis are suggested, which will allow the transmission spectrum to be evaluated more definitively.

Space missions like Kepler have revolutionized asteroseismology, the science that infers the stellar interiors by studying oscillation frequency spectra of pulsating stars. Great advancements have been made in understanding solar-like oscillators. However, this is not the case for variable stars of intermediate masses, such asScutiand Doradus variables. By studying these stars in eclipsing binaries (EBs), model independent funda- mental parameters such as mass and radius can be inferred. On one hand, this synergy constrains the parameter space and facilitates the asteroseismic modeling, and this is shown for the Scuti type pulsating EB KIC 9851944. On the other hand, studies of binary stars must address the complexities such as mass transfer. KIC 8262223 is such an example, which consists of a mass-gaining Scuti primary and a pre-He white dwarf secondary. Some of the eccentric binary systems, the ‘heartbeat’ stars, show tidally excited oscillations. After briefly reviewing the linear theory of tidally forced stellar oscillations, we study the tidal pulsating binary KIC 3230227 and demonstrate that both amplitude and phase can be used to identify the tidally excited pulsation modes. We also discuss the variability of a Slowly Pulsating B-star KOI-81 and a Cataclysmic variable KIC 9406652. In the second part of this dissertation, we apply Bayesian statistics to some problems in binaries and asteroseismology with the help of packages BUGS and JAGS. Special attention is paid to the inverse problems (tomography) encountered in studying the double-line spectroscopic binaries.

Backward erosion piping (BEP) is one of the major causes of seepage failures in levees. Seepage fields dictate the BEP behaviors and are influenced by the heterogeneity of soil properties. To investigate the effects of the heterogeneity on the seepage failures, we develop a numerical algorithm and conduct simulations to study BEP progressions in geologic media with spatially stochastic parameters. Specifically, the void ratio e, the hydraulic conductivity k, and the ratio of the particle contents r of the media are represented as the stochastic variables. They are characterized by means and variances, the spatial correlation structures, and the cross correlation between variables. Results of the simulations reveal that the heterogeneity accelerates the development of preferential flow paths, which profoundly increase the likelihood of seepage failures. To account for unknown heterogeneity, we define the probability of the seepage instability (PI) to evaluate the failure potential of a given site. Using Monte-Carlo simulation (MCS), we demonstrate that the PI value is significantly influenced by the mean and the variance of ln k and its spatial correlation scales. But the other parameters, such as means and variances of e and r, and their cross correlation, have minor impacts. Based on PI analyses, we introduce a risk rating system to classify the field into different regions according to risk levels. This rating system is useful for seepage failures prevention and assists decision making when BEP occurs.

Master of Science / Department of Diagnostic Medicine/Pathobiology / Melinda J. Wilkerson / Tick-borne bacteria, Ehrlichia canis, Anaplasma platys, and Ehrlichia chaffeensis are significant zoonotic pathogens of dogs and humans worldwide. In tropical regions such as Grenada, West Indies, dogs represent a major reservoir for E. canis and A. platys, and they are often co-infected. The purpose of this study was to develop a serologic, multiplex bead-based assay to detect species-specific exposures to E. canis, A. platys, and E. chaffeensis in dogs for purposes of surveillance and public health. Peptides from specific outer membrane proteins of P30 for E. canis, OMP1X of A. platys, and P28-19/P28-14 of E. chaffeensis were coupled to magnetic beads and assays were optimized using the multiplex Luminex xMAP® platform. In experimentally infected dogs, the multiplex assay successfully detected antibodies for E. canis and E. chaffeensis, but not A. platys. In the Grenadian population (n=104), the multiplex assay and the in-house ELISA, the SNAP® 4Dx®, detected A. platys antibodies as well as Ehrlichia spp.. Multiplex assay results were found to have “good” and “very good” agreement with the ELISA and IFA for E. canis antibody-positive dogs (K value of 0.73 and 0.84 respectively), while ELISA and IFA had “very good” agreement with each other (K value of 0.85). A. platys multiplex results had only “poor” agreement with ELISA and IFA (K value of -0.02 and 0.01, respectively), while the ELISA and IFA tests had “moderate” agreement with each other (K value of 0.5). These tests showed the prevalence of exposure to E. canis to be comparable with previous studies (38% in 2014), but a doubling of exposure to A. platys determined by IFA and 4Dx® from 9% in 2006, to 20% in 2014. Bayesian modeling (performed on E. canis data only) suggested conditional independence between the IFA, 4Dx®, and MAG tests using consensus priors calculated from literature, and that the bead-assay had comparable sensitivity and specificity to the IFA and ELISA tests. In conclusion, the multiplex peptide assay performed well in detecting the seropositive status of dogs to E. canis and had good agreement with commercial assays; however, more work needs to be done to assess performance in populations of dogs with exposures to multiple species of Ehrlichia. Further, the reasons for low seroreactivity to A. platys need to be further investigated.

A metanálise tem sido amplamente utilizada em estudos médicos especialmente em revisões sistemáticas de ensaios clínicos aleatorizados. Para modelos de regressão a técnica ainda é muito escassa e limitada. Geralmente trata-se apenas de uma medida baseada nas médias de estimativas pontuais dos diferentes estudos, perdendo-se muita informação dos dados originais. Atualmente torna-se cada vez mais fundamental o uso da metanálise para sumarizar estudos de mesmo objetivo, em razão do avanço da ciência e o desejo de usar o menor número de seres humanos em ensaios clínicos. Utilizando uma medida metanalítica Bayesiana, o objetivo é propor um método genérico e eficiente para realizar metanálise em modelos de regressão. / Meta analysis has been widely used in medical studies especially in systematic reviews of randomized clinical trials. For regression models the technique is still very scarce and limited. Usually it is just a measure based on the average point estimates of dierent studies, losing a lot of information of the original data. Currently it becomes increasingly important to use the meta-analysis to summarize the same objective studies, due to the advancement of science and the desire to use the smallest number of human subjects in clinical trials. Using a meta-analytic Bayesian measure, the objective is to propose a generic and ecient method to perform meta-analysis in regression models.

This thesis presents research focused on developing statistical methods with emphasis on tools that can be used for the analysis of data in neuroimaging studies and cognitive science. The first contribution addresses the problem of determining the location and dynamics of brain activity when electromagnetic signals are collected using magnetoencephalography (MEG) and electroencephalography (EEG). We formulate a new spatiotemporal model that jointly models MEG and EEG data as a function of unobserved neuronal activation. To fit this model we derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The methodology is evaluated through extensive simulation studies and an application examining the visual response to scrambled faces. In the second contribution we develop a Bayesian spatial model for imaging genetics developed for analyses examining the influence of genetics on brain structure as measured by MRI. We extend the recently developed regression model of Greenlaw et al. (\textit{Bioinformatics}, 2017) to accommodate more realistic correlation structures typically seen in structural brain imaging data. We allow for spatial correlation in the imaging phenotypes obtained from neighbouring regions in the same hemisphere of the brain and we also allow for correlation in the same phenotypes obtained from different hemispheres (left/right) of the brain. This correlation structure is incorporated through the use of a bivariate conditional autoregressive spatial model. Both Markov chain Monte Carlo (MCMC) and variational Bayes approaches are developed to approximate the posterior distribution and Bayesian false discovery rate (FDR) procedures are developed to select SNPs using the posterior distribution while accounting for multiplicity. The methodology is evaluated through an analysis of MRI and genetic data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and we show that the new spatial model exhibits improved performance on real data when compared to the non-spatial model of Greenlaw et al. (2017). In the third and final contribution we develop and investigate tools for the analysis of binary data arising from repeated measures designs. We propose a Bayesian approach for the mixed-effects analysis of accuracy studies using mixed binomial regression models and we investigate techniques for model selection. / Graduate

Diffusion tensor imaging (DTI) is a relatively new technology of magnetic resonance imaging, which enables us to observe the insight structure of the human body in vivo and non-invasively. It displays water molecule movement by a 3×3 diffusion tensor at each voxel. Tensor field processing, visualisation and tractography are all based on the diffusion tensors. The accuracy of estimating diffusion tensor is essential in DTI. This research focuses on exploring the potential improvements at the tensor estimation of DTI. We analyse the noise arising in the measurement of diffusion signals. We present robust methods, least median squares (LMS) and least trimmed squares (LTS) regressions, with forward search algorithm that reduce or eliminate outliers to the desired level. An investigation of the criterion to detect outliers is provided in theory and practice. We compare the results with the generalised non-robust models in simulation studies and applicants and also validated various regressions in terms of FA, MD and orientations. We show that the robust methods can handle the data with up to 50% corruption. The robust regressions have better estimations than generalised models in the presence of outliers. We also consider the multiple tensors problems. We review the recent techniques of multiple tensor problems. Then we provide a new model considering neighbours' information, the Bayesian single and double tensor models using neighbouring tensors as priors, which can identify the double tensors effectively. We design a framework to estimate the diffusion tensor field with detecting whether it is a single tensor model or multiple tensor model. An output of this framework is the Bayesian neighbour (BN) algorithm that improves the accuracy at the intersection of multiple fibres. We examine the dependence of the estimators on the FA and MD and angle between two principal diffusion orientations and the goodness of fit. The Bayesian models are applied to the real data with validation. We show that the double tensors model is more accurate on distinct fibre orientations, more anisotropic or similar mean diffusivity tensors. The final contribution of this research is in covariance tensor estimation. We define the median covariance matrix in terms of Euclidean and various non-Euclidean metrics taking its symmetric semi-positive definiteness into account. We compare with estimation methods, Euclidean, power Euclidean, square root Euclidean, log-Euclidean, Riemannian Euclidean and Procrustes median tensors. We provide an analysis of the different metric between different median covariance tensors. We also provide the weighting functions and define the weighted non-Euclidean covariance tensors. We finish with manifold-valued data applications that improve the illustration of DTI images in tensor field processing with defined non-weighted and weighted median tensors. The validation of non-Euclidean methods is studied in the tensor field processing. We show that the root square median estimator is preferable in general, which can effectively exclude outliers and clearly shows the important structures of the brain. The power Euclidean median estimator is recommended when producing FA map.