A Bayesian approach to wavelet-based modelling of discontinuous functions applied to inverse problems

Inverse problems are examples of regression with more unknowns than the amount of information in the data and hence constraints are imposed through prior information. The proposed method defines the underlying function as a wavelet approximation which is related to the data through a convolution. The wavelets provide a sparse and multi-resolution solution which can capture local behaviour in an adaptive way. Varied prior models are considered along with level-specific prior parameter estimation. Archaeological stratigraphy data are considered where vertical earth cores are analysed producing clear piecewise constant function estimates

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python

Clinically Unapparent Infantile Thiamin Deficiency in Vientiane, Laos

Infantile beriberi, or clinical thiamin (vitamin B1) deficiency in infants, is a forgotten disease in Asia, where 100 years ago it was a major public health problem. Infants with this deficiency, commonly aged ∼ 2–3 months, present in cardiac failure but usually rapidly improve if given thiamin injections. It remains relatively common in Vientiane, Lao PDR (Laos), probably because of prolonged intra- and post-partum food avoidance behaviours. Clinical disease may be the tip of an iceberg with subclinical thiamin deficiency contributing to sickness in infants without overt clinical beriberi. We therefore recruited 778 sick infants admitted during one year at Mahosot Hospital, Vientiane, without clinical evidence of beriberi, and performed erythrocyte transketolase (ETK) assays. 13.4 % of infants had basal ETK<0.59 micromoles/min/gHb suggesting biochemical thiamin deficiency. Mortality was 5.5% but, among infants ≥2 months old, mortality was higher in those with basal ETK<0.59 micromoles/min/gHb (3/47, 6.4%) than in those with basal ETK≥0.59 micromoles/min/gHb (1/146, 0.7%) (P = 0.045, relative risk = 9.32 (95%CI 0.99 to 87.5)). We conclude that clinically unapparent thiamin deficiency is common among sick infants (≥2 months old) admitted to hospital in Vientiane. This may contribute to mortality and a low clinical threshold for providing thiamin to sick infants may be needed

Recent developments of control charts and identification of big data sources and future trends of current research

Control charts are one of the principal tools to monitor dynamic processes with the aim of rapid identification of changes in the behaviour of these processes. Such changes are usually associated with a move from an in-control condition to an out-of-control condition. The paper briefly reviews the historical origins and includes examples of recent developments, focussing on their use in fields different from the industrial applications in which they were initially derived and often employed. It also focusses on cases which depart from the commonly used Gaussian assumption and then considers potential effects of the big data revolution on future uses. A bibliometric analysis is also presented to identify distinct groups of research themes, including emerging and underdeveloped areas, which are hence potential topics for future research

Iterative reconstruction incorporating background correction improves quantification of [18F]-NaF PET/CT images of patients with abdominal aortic aneurysm

Background A confounding issue in [18F]-NaF PET/CT imaging of abdominal aortic aneurysms (AAA) is the spill in contamination from the bone into the aneurysm. This study investigates and corrects for this spill in contamination using the background correction (BC) technique without the need to manually exclude the part of the AAA region close to the bone. Methods Seventy-two (72) datasets of patients with AAA were reconstructed with the standard ordered subset expectation maximization (OSEM) algorithm incorporating point spread function (PSF) modelling. The spill in effect in the aneurysm was investigated using two target regions of interest (ROIs): one covering the entire aneurysm (AAA), and the other covering the aneurysm but excluding the part close to the bone (AAAexc). ROI analysis was performed by comparing the maximum SUV in the target ROI (SUVmax(T)), the corrected cSUVmax (SUVmax(T) − SUVmean(B)) and the target-to-blood ratio (TBR = SUVmax(T)/SUVmean(B)) with respect to the mean SUV in the right atrium region. Results There is a statistically significant higher [18F]-NaF uptake in the aneurysm than normal aorta and this is not correlated with the aneurysm size. There is also a significant difference in aneurysm uptake for OSEM and OSEM + PSF (but not OSEM + PSF + BC) when quantifying with AAA and AAAexc due to the spill in from the bone. This spill in effect depends on proximity of the aneurysms to the bone as close aneurysms suffer more from spill in than farther ones. Conclusion The background correction (OSEM + PSF + BC) technique provided more robust AAA quantitative assessments regardless of the AAA ROI delineation method, and thus it can be considered as an effective spill in correction method for [18F]-NaF AAA studies

A História da Alimentação: balizas historiográficas

Os M. pretenderam traçar um quadro da História da Alimentação, não como um novo ramo epistemológico da disciplina, mas como um campo em desenvolvimento de práticas e atividades especializadas, incluindo pesquisa, formação, publicações, associações, encontros acadêmicos, etc. Um breve relato das condições em que tal campo se assentou faz-se preceder de um panorama dos estudos de alimentação e temas correia tos, em geral, segundo cinco abardagens Ia biológica, a econômica, a social, a cultural e a filosófica!, assim como da identificação das contribuições mais relevantes da Antropologia, Arqueologia, Sociologia e Geografia. A fim de comentar a multiforme e volumosa bibliografia histórica, foi ela organizada segundo critérios morfológicos. A seguir, alguns tópicos importantes mereceram tratamento à parte: a fome, o alimento e o domínio religioso, as descobertas européias e a difusão mundial de alimentos, gosto e gastronomia. O artigo se encerra com um rápido balanço crítico da historiografia brasileira sobre o tema

Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields

This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of inhomogeneous model is proposed. This inhomogeneous model uses a Markov random field to describe spatial variation of the smoothing parameter in a second random field which describes the spatial variation in the observed intensity image. The coupled Markov random fields will be used as prior distributions, and combined with Gaussian noise models to produce posterior distributions on which estimation will be based. All model parameters are estimated, in a fully Bayesian setting, using the Metropolis-Hastings algorithm. The models and algorithms will be illustrated using various artificial examples. The full posterior estimation procedures using homogeneous and inhomogeneous models will be compared. For the examples considered the fully Bayesian estimation for inhomogeneous models performs very favourably when compared to methods using homogeneous models, allowing differential smo..

Automatic Reconstruction with Inhomogeneous Models

We present a complete approach for simultaneous and automatic parameter estimation and image reconstruction which allows variable amounts of spatial smoothing. Procedures based on a Bayesian approach have been proposed, and successfully incorporate prior knowledge to produce much improved reconstructions. These procedures, however, usually assume that any prior parameters are known. In practice this is not the case and suitable values are often determined by &quot;trial and error&quot;. We describe a Metropolis/EM reconstruction procedure having first derived a calibration curve for prior parameter estimation. We present an inhomogeneous Markov random field model which allows spatially varying degrees of smoothing in the reconstructions and propose a re-parameterisation which implicitly introduces a local correlation structure in the smoothing parameters, and use a re-scaled version of the homogeneous model calibration curve for parameter estimation. We present an analysis of SPECT data of the b..

A wavelet approach to shape analysis for spinal curves

We present a new method to describe shape change and shape differences in curves, by constructing a deformation function in terms of a wavelet decomposition. Wavelets form an orthonormal basis which allows representations at multiple resolutions. The deformation function is estimated, in a fully Bayesian framework, using a Markov chain Monte Carlo algorithm. This Bayesian formulation incorporates prior information about the wavelets and the deformation function. The flexibility of the MCMC approach allows estimation of complex but clinically important summary statistics, such as curvature in our case, as well as estimates of deformation functions with variance estimates, and allows thorough investigation of the posterior distribution. This work is motivated by multi-disciplinary research involving a large-scale longitudinal study of idiopathic scoliosis in UK children. This paper provides novel statistical tools to study this spinal deformity, from which 5% of UK children suffer. Using the data we consider statistical inference for shape differences between normals, scoliotics and developers of scoliosis, in particular for spinal curvature, and look at longitudinal deformations to describe shape changes with time.