Multiple imputation for continuous variables using a Bayesian principal component analysis

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the PCA model. Using a simulation study and real data sets, the method is compared to two classical approaches: multiple imputation based on joint modelling and on fully conditional modelling. Contrary to the others, the proposed method can be easily used on data sets where the number of individuals is less than the number of variables and when the variables are highly correlated. In addition, it provides unbiased point estimates of quantities of interest, such as an expectation, a regression coefficient or a correlation coefficient, with a smaller mean squared error. Furthermore, the widths of the confidence intervals built for the quantities of interest are often smaller whilst ensuring a valid coverage.Comment: 16 page

Adaptive Higher-order Spectral Estimators

Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has approximately low rank. In this article, we generalize this approach to the estimation of a tensor of parameters from noisy tensor data. We develop new classes of estimators that shrink or threshold the mode-specific singular values from the higher-order singular value decomposition. These classes of estimators are indexed by tuning parameters, which we adaptively choose from the data by minimizing Stein's unbiased risk estimate. In particular, this procedure provides a way to estimate the multilinear rank of the underlying signal tensor. Using simulation studies under a variety of conditions, we show that our estimators perform well when the mean tensor has approximately low multilinear rank, and perform competitively when the signal tensor does not have approximately low multilinear rank. We illustrate the use of these methods in an application to multivariate relational data.Comment: 29 pages, 3 figure

R-miss-tastic: a unified platform for missing values methods and workflows

Missing values are unavoidable when working with data. Their occurrence is exacerbated as more data from different sources become available. However, most statistical models and visualization methods require complete data, and improper handling of missing data results in information loss, or biased analyses. Since the seminal work of Rubin (1976), there has been a burgeoning literature on missing values with heterogeneous aims and motivations. This has resulted in the development of various methods, formalizations, and tools (including a large number of R packages and Python modules). However, for practitioners, it remains challenging to decide which method is most suited for their problem, partially because handling missing data is still not a topic systematically covered in statistics or data science curricula. To help address this challenge, we have launched a unified platform: "R-miss-tastic", which aims to provide an overview of standard missing values problems, methods, how to handle them in analyses, and relevant implementations of methodologies. In the same perspective, we have also developed several pipelines in R and Python to allow for a hands-on illustration of how to handle missing values in various statistical tasks such as estimation and prediction, while ensuring reproducibility of the analyses. This will hopefully also provide some guidance on deciding which method to choose for a specific problem and data. The objective of this work is not only to comprehensively organize materials, but also to create standardized analysis workflows, and to provide a common ground for discussions among the community. This platform is thus suited for beginners, students, more advanced analysts and researchers.Comment: 38 pages, 9 figure

Statistical Modelling of Craniofacial Shape

With prior knowledge and experience, people can easily observe rich shape and texture variation for a certain type of objects, such as human faces, cats or chairs, in both 2D and 3D images. This ability helps us recognise the same person, distinguish different kinds of creatures and sketch unseen samples of the same object class. The process of capturing this prior knowledge is mathematically interpreted as statistical modelling. The outcome is a morphable model, a vector space representation of objects, that captures the variation of shape and texture. This thesis presents research aimed at constructing 3DMMs of craniofacial shape and texture using new algorithms and processing pipelines to offer enhanced modelling abilities over existing techniques. In particular, we present several fully automatic modelling approaches and apply them to a large dataset of 3D images of the human head, the Headspace dataset, thus generating the first public shape-and- texture 3D Morphable Model (3DMM) of the full human head. We call this the Liverpool-York Head Model, reflecting the data collection and statistical modelling respectively. We also explore the craniofacial symmetry and asymmetry in template morphing and statistical modelling. We propose a Symmetry-aware Coherent Point Drift (SA-CPD) algorithm, which mitigates the tangential sliding problem seen in competing morphing algorithms. Based on the symmetry-constrained correspondence output of SA-CPD, we present a symmetry-factored statistical modelling method for craniofacial shape. Also, we propose an iterative process of refinement for a 3DMM of the human ear that employs data augmentation. Then we merge the proposed 3DMMs of the ear with the full head model. As craniofacial clinicians like to look at head profiles, we propose a new pipeline to build a 2D morphable model of the craniofacial sagittal profile and augment it with profile models from frontal and top-down views. Our models and data are made publicly available online for research purposes

Gaussian Based Visualization of Gaussian and Non-Gaussian Based Clustering

International audienceA generic method is introduced to visualize in a "Gaussian-like way", and onto R 2 , results of Gaussian or non-Gaussian based clustering. The key point is to explicitly force a visualization based on a spherical Gaussian mixture to inherit from the within cluster overlap that is present in the initial clustering mixture. The result is a particularly user-friendly drawing of the clusters, providing any practitioner with an overview of the potentially complex clustering result. An entropic measure provides information about the quality of the drawn overlap compared to the true one in the initial space. The proposed method is illustrated on four real data sets of different types (categorical, mixed, functional and network) and is implemented on the R package ClusVis

Quantitative electron microscopy for microstructural characterisation

Development of materials for high-performance applications requires accurate and useful analysis tools. In parallel with advances in electron microscopy hardware, we require analysis approaches to better understand microstructural behaviour. Such improvements in characterisation capability permit informed alloy design. New approaches to the characterisation of metallic materials are presented, primarily using signals collected from electron microscopy experiments. Electron backscatter diffraction is regularly used to investigate crystallography in the scanning electron microscope, and combined with energy-dispersive X-ray spectroscopy to simultaneusly investigate chemistry. New algorithms and analysis pipelines are developed to permit accurate and routine microstructural evaluation, leveraging a variety of machine learning approaches. This thesis investigates the structure and behaviour of Co/Ni-base superalloys, derived from V208C. Use of the presently developed techniques permits informed development of a new generation of advanced gas turbine engine materials.Open Acces