Uncertainty quantification of coal seam gas production prediction using Polynomial Chaos

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability distributions of the uncertain input variables (parameters); this allows for both uncertainty quantification and global sensitivity analysis. In this paper we apply these techniques to a commercial solver for the estimation of peak gas rate and cumulative gas extraction from a coal seam gas well. The polynomial expansion is shown to honour the underlying geophysics with low error when compared to a much more complex and computationally slower commercial solver. We make use of advanced numerical integration techniques to achieve this accuracy using relatively small amounts of training data

The Fisher Geometry and Geodesics of the Multivariate Normals, without Differential Geometry

Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical distance, and paths of shorter distance improve sampling techniques that leverage a sequence of distributions in their operation. Unfortunately, even for a distribution as generally tractable as the multivariate normal distribution, this information geometry proves unwieldy enough that closed-form solutions for shortest-distance paths or their lengths remain unavailable outside of limited special cases. In this review we present for general statisticians the most practical aspects of the Fisher geometry for this fundamental distribution family. Rather than a differential geometric treatment, we use an intuitive understanding of the covariance-induced curvature of this manifold to unify the special cases with known closed-form solution and review approximate solutions for the general case. We also use the multivariate normal information geometry to better understand the paths or distances commonly used in statistics (annealing, Wasserstein). Given the unavailability of a general solution, we also discuss the methods used for numerically obtaining geodesics in the space of multivariate normals, identifying remaining challenges and suggesting methodological improvements.Comment: 22 pages, 8 figures, further figures and algorithms in supplemen

Inference of ventricular activation properties from non-invasive electrocardiography

The realisation of precision cardiology requires novel techniques for the non-invasive characterisation of individual patients' cardiac function to inform therapeutic and diagnostic decision-making. The electrocardiogram (ECG) is the most widely used clinical tool for cardiac diagnosis. Its interpretation is, however, confounded by functional and anatomical variability in heart and torso. In this study, we develop new computational techniques to estimate key ventricular activation properties for individual subjects by exploiting the synergy between non-invasive electrocardiography and image-based torso-biventricular modelling and simulation. More precisely, we present an efficient sequential Monte Carlo approximate Bayesian computation-based inference method, integrated with Eikonal simulations and torso-biventricular models constructed based on clinical cardiac magnetic resonance (CMR) imaging. The method also includes a novel strategy to treat combined continuous (conduction speeds) and discrete (earliest activation sites) parameter spaces, and an efficient dynamic time warping-based ECG comparison algorithm. We demonstrate results from our inference method on a cohort of twenty virtual subjects with cardiac volumes ranging from 74 cm3 to 171 cm3 and considering low versus high resolution for the endocardial discretisation (which determines possible locations of the earliest activation sites). Results show that our method can successfully infer the ventricular activation properties from non-invasive data, with higher accuracy for earliest activation sites, endocardial speed, and sheet (transmural) speed in sinus rhythm, rather than the fibre or sheet-normal speeds.Comment: Submitted to Medical Image Analysi

Bioenergetic model sensitivity to diet diversity across space, time and ontogeny

Consumption is the primary trophic interaction in ecosystems and its accurate estimation is required for reliable ecosystem modeling. When estimating consumption, species' diets are commonly assumed to be the average of those that occur among habitats, seasons, and life stages which introduces uncertainty and error into consumption rate estimates. We present a case study of a teleost (Yellowfin Bream Acanthopagrus australis) that quantifies the potential error in consumption (in mass) and growth rate estimates when using diet data from different regions and times and ignoring ontogenetic variability. Ontogenetic diet trends were examined through gut content analysis (n = 1,130 fish) and incorporated into a bioenergetic model (the "primary " model) that included diet variability (n = 144 prey sources) and ontogenetic changes in metabolism (1-7 year) to estimate lifetime consumption. We quantified error by building nine model scenarios that each incorporated different spatiotemporal diet data of four published studies. The model scenarios produced individual lifetime consumption estimates that were between 25% lower and 15% higher than the primary model (maximum difference was 53%, range 11.7-17.8 kg). When consumption (in mass) was held constant, differences in diet quality among models caused a several-fold range in growth rate (0.04-1.07 g day(-1)). Our findings showcase the large uncertainty in consumption rate estimates due to diet diversity, and illustrate that caution is required when considering bioenergetic results among locations, times, and ontogeny

Analysis of sloppiness in model simulations: unveiling parameter uncertainty when mathematical models are fitted to data

This work introduces a Bayesian approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This novel approach identifies stiff parameter combinations that strongly affect the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily from the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of our technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting

Contrasting Sorption Behaviours Affecting Groundwater Arsenic Concentration in Kandal Province, Cambodia

Natural arsenic (As) contamination of groundwater which provides drinking water and/or irrigation supplies remains a major public health issue, particularly in South and Southeast Asia. A number of studies have evaluated various aspects of the biogeochemical controls on As mobilization in aquifers typical to this region, however many are predicated on the assumption that key biogeochemical processes may be deduced by sampled water chemistry. The validity of this assumption has not been clearly established even though the role of sorption/desorption of As and other heavy metals onto Fe/Mn (hydr)oxides is an important control in As mobilization. Here, selective chemical extractions of sand-rich and clay-rich sediments from an As-affected aquifer in Kandal Province, Cambodia, were undertaken to explore the potential role of partial re-equilibrium through sorption/desorption reactions of As and related solutes (Fe, Mn and P) between groundwater and the associated solid aquifer matrix. In general, groundwater As is strongly affected by both pH and Eh throughout the study area. However, contrasting sorption behaviour is observed in two distinct sand-dominated (T-Sand) and clay dominated (T-Clay) transects, and plausibly attributed to differing dominant lithologies, biogeochemical and/or hydrogeological conditions. Sorption/desorption processes appear to be re-setting groundwater As concentrations in both transects, but to varying extents and in different ways. In T-Sand, which is typically highly reducing, correlations suggest that dissolved As may be sequestered by sorption/re-adsorption to Fe-bearing mineral phases and/or sedimentary organic matter; in T-Clay Eh is a major control on As mobilization although binding/occlusion of Fe-bearing minerals to sedimentary organic matter may also occur. Multiple linear regression analysis was conducted with groups categorised by transect and by Eh, and the output correlations support the contrasting sorption behaviours encountered in this study area. Irrespective of transect, however, the key biogeochemical processes which initially control As mobilization in such aquifers, may be “masked” by the re-setting of As concentrations through in-aquifer sorption/desorption processes

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention