Hierarchical Emulation: a method for modeling and comparing nested simulators

Computer simulators often contain options to include extensions, leading to different versions of a particular simulator with slightly different input spaces. We develop hierarchical emulation, a method for emulating such simulators and for learning about the differences between versions of a simulator. In an example using data from an ocean carbon cycle model, hierarchical emulators outperformed standard emulators both in their predictive accuracy and their coherence with the emulation model. The hierarchical emulator performed particularly well when a comparatively small amount of training data came from the extended simulator. This benefit of hierarchical emulation is advantageous when the extended simulator is costly to run compared to the simpler version

A Bayesian shifting method for uncertainty in the open-hole gamma-ray log around casing points

The wireline gamma-ray log is sensitive to open-hole conditions and, in particular, the diameter. This means that the log can jump at casing points. Although environmental corrections exist, they can fail at these points. We present a Bayesian method for deriving a new quantity – the shifted gamma–ray index – that takes these shifts into account by fitting a piecewise linear function to open-hole data in a depth window around the casing point. Because it is Bayesian, the method enables us to assess our uncertainty about its performance. This method requires very little knowledge of the borehole or drilling conditions but relies on the assumption that the lithology is consistent. Investigating the other wireline logs enables us to assess whether this assumption is valid. We demonstrate our method using well data from offshore mid-Norway

A sequential dynamic Bayesian network for pore pressure estimation with uncertainty quantification

Pore-pressure estimation is an important part of oil-well drilling, since drilling into unexpected highly pressured fluids can be costly and dangerous. However, standard estimation methods rarely account for the many sources of uncertainty, or for the multivariate nature of the system. We propose the pore pressure sequential dynamic Bayesian network (PP SDBN) as an appropriate solution to both these issues. The PP SDBN models the relationships between quantities in the pore pressure system, such as pressures, porosity, lithology and wireline log data, using conditional probability distributions based on geophysical relationships to capture our uncertainty about these variables and the relationships between them. When wireline log data is given to the PP SDBN, the probability distributions are updated, providing an estimate of pore pressure along with a probabilistic measure of uncertainty that reflects the data acquired and our understanding of the system. This is the advantage of a Bayesian approach. Our model provides a coherent statistical framework for modelling the pore pressure system. The specific geophysical relationships used can be changed to better suit a particular setting, or reflect geoscientists’ knowledge. We demonstrate the PP SDBN on an offshore well from West Africa. We also perform a sensitivity analysis, demonstrating how this can be used to better understand the working of the model and which parameters are the most influential. The dynamic nature of the model makes it suitable for real time estimation during logging while drilling. The PP SDBN models shale pore pressure in shale rich formations with mechanical compaction as the overriding source of overpressure. The PP SDBN improves on existing methods since it produces a probabilistic estimate that reflects the many sources of uncertainty present

Identification of genetic variants associated with Huntington's disease progression: a genome-wide association study

Background Huntington's disease is caused by a CAG repeat expansion in the huntingtin gene, HTT. Age at onset has been used as a quantitative phenotype in genetic analysis looking for Huntington's disease modifiers, but is hard to define and not always available. Therefore, we aimed to generate a novel measure of disease progression and to identify genetic markers associated with this progression measure. Methods We generated a progression score on the basis of principal component analysis of prospectively acquired longitudinal changes in motor, cognitive, and imaging measures in the 218 indivduals in the TRACK-HD cohort of Huntington's disease gene mutation carriers (data collected 2008–11). We generated a parallel progression score using data from 1773 previously genotyped participants from the European Huntington's Disease Network REGISTRY study of Huntington's disease mutation carriers (data collected 2003–13). We did a genome-wide association analyses in terms of progression for 216 TRACK-HD participants and 1773 REGISTRY participants, then a meta-analysis of these results was undertaken. Findings Longitudinal motor, cognitive, and imaging scores were correlated with each other in TRACK-HD participants, justifying use of a single, cross-domain measure of disease progression in both studies. The TRACK-HD and REGISTRY progression measures were correlated with each other (r=0·674), and with age at onset (TRACK-HD, r=0·315; REGISTRY, r=0·234). The meta-analysis of progression in TRACK-HD and REGISTRY gave a genome-wide significant signal (p=1·12 × 10−10) on chromosome 5 spanning three genes: MSH3, DHFR, and MTRNR2L2. The genes in this locus were associated with progression in TRACK-HD (MSH3 p=2·94 × 10−8 DHFR p=8·37 × 10−7 MTRNR2L2 p=2·15 × 10−9) and to a lesser extent in REGISTRY (MSH3 p=9·36 × 10−4 DHFR p=8·45 × 10−4 MTRNR2L2 p=1·20 × 10−3). The lead single nucleotide polymorphism (SNP) in TRACK-HD (rs557874766) was genome-wide significant in the meta-analysis (p=1·58 × 10−8), and encodes an aminoacid change (Pro67Ala) in MSH3. In TRACK-HD, each copy of the minor allele at this SNP was associated with a 0·4 units per year (95% CI 0·16–0·66) reduction in the rate of change of the Unified Huntington's Disease Rating Scale (UHDRS) Total Motor Score, and a reduction of 0·12 units per year (95% CI 0·06–0·18) in the rate of change of UHDRS Total Functional Capacity score. These associations remained significant after adjusting for age of onset. Interpretation The multidomain progression measure in TRACK-HD was associated with a functional variant that was genome-wide significant in our meta-analysis. The association in only 216 participants implies that the progression measure is a sensitive reflection of disease burden, that the effect size at this locus is large, or both. Knockout of Msh3 reduces somatic expansion in Huntington's disease mouse models, suggesting this mechanism as an area for future therapeutic investigation

Going round in circles: Geometry in the early years

The research described here came from a collaboration between university-based mathematicians and early years (EY) educators. The project emerged naturally, driven by the felt need of the EY educators to develop a broader understanding and appreciation of mathematics so that they were able to expose the children to new, challenging and exciting ideas, and to engage with their mathematical curiosities. Every few weeks, the group of three EY educators and five academic mathematicians met over Zoom. Discussions in the meetings were wide-ranging, encompassing particular mathematical ideas or theorems, and more general concepts such as ‘When are two things the same?’ or ‘What is a theorem?’. The EY educators would give updates about any mathematical ideas or activities in nursery, or themes the children were exploring. The goal of the academics was to explore and extend the mathematical thinking the children were already doing, rather than to follow a particular schedule, or to teach the EY educators maths teaching methods or activities. The mathematicians were led by the EY staff, as they in turn were led by the children in their setting. The expertise of the EY educators is crucial, as they determine how best to use the content of the meetings with their particular children in their day-today work

Reduced Cancer Incidence in Huntington's Disease: Analysis in the Registry Study

Background: People with Huntington's disease (HD) have been observed to have lower rates of cancers. Objective: To investigate the relationship between age of onset of HD, CAG repeat length, and cancer diagnosis. Methods: Data were obtained from the European Huntington's disease network REGISTRY study for 6540 subjects. Population cancer incidence was ascertained from the GLOBOCAN database to obtain standardised incidence ratios of cancers in the REGISTRY subjects. Results: 173/6528 HD REGISTRY subjects had had a cancer diagnosis. The age-standardised incidence rate of all cancers in the REGISTRY HD population was 0.26 (CI 0.22-0.30). Individual cancers showed a lower age-standardised incidence rate compared with the control population with prostate and colorectal cancers showing the lowest rates. There was no effect of CAG length on the likelihood of cancer, but a cancer diagnosis within the last year was associated with a greatly increased rate of HD onset (Hazard Ratio 18.94, p < 0.001). Conclusions: Cancer is less common than expected in the HD population, confirming previous reports. However, this does not appear to be related to CAG length in HTT. A recent diagnosis of cancer increases the risk of HD onset at any age, likely due to increased investigation following a cancer diagnosis