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Publications (2017) by Andrew Zammit Mangion

Environmental Informatics uses a panoply of tools from the Statistics, Mathematics, Computing, an... more Environmental Informatics uses a panoply of tools from the Statistics, Mathematics, Computing, and Visualisation disciplines. It uses these tools to reveal, quantify, and validate scienti fic hypotheses in the
environmental sciences, with the quanti fication of uncertainty central to its approach. There is now a strong recognition that scienti fic models need to incorporate stochastic components throughout: While it has always been recognised that data have a component of measurement error, attention is now being given to the quantifi cation of model error, and it is becoming accepted by environmental scientists that probability models for the latter allows for a coherent way to make scienti fic inference. In Environmental Informatics, uncertainty may be assigned
not only to datasets of measurements, but also to computer-generated climate-model output. Methodological advances, in the form of hierarchical statistical models and the accompanying computational developments, have expanded the scope of statistical analyses into very large spatial domains. This has led to studies of the dynamical evolution of entire spatial fields of geophysical variables, where results are given in
terms of predictive distributions. Environmental Informatics is not only involved in characterising the environment, it can also be used to make decisions about mitigation and adaptation strategies. The steps taken by environmental scientists, from data to information, from information to knowledge, and from knowledge to decisions, are all taken in the presence of uncertainty. Environmental Informatics encompasses all these aspects.

A Common Task Framework (CTF) for Objective Comparison of Spatial Prediction Methodologies, 2017

We investigate the mass balance of East Antarctica for the period 2003–2013 using a Bayesian stat... more We investigate the mass balance of East Antarctica for the period 2003–2013 using a Bayesian statistical framework. We combine satellite altimetry, gravimetry, and GPS with prior assumptions characterizing the underlying geophysical processes. We run three experiments based on two different assumptions to study possible solutions to the mass balance. We solve for trends in surface mass balance, ice dynamics, and glacial isostatic adjustment. The first assumption assigns low probability to ice dynamic mass loss in regions of slow flow, giving a mean dynamic trend of 17 ± 10 Gt yr −1 and a total mass imbalance of 57 ± 20 Gt yr −1. The second assumption considers a long-term dynamic thickening hypothesis and an a priori solution for surface mass balance from a regional climate model. The latter results in estimates 3 to 5 times larger for the ice dynamic trends but similar total mass imbalance. In both cases, gains in East Antarctica are smaller than losses in West Antarctica.

Maximum likelihood (ML) estimation with spatial econometric models is a long-standing problem tha... more Maximum likelihood (ML) estimation with spatial econometric models is a long-standing problem that finds application in several areas of economic importance. The problem is particularly challenging in the presence of missing data, since there is an implied dependence between all units, irrespective of whether they are observed or not. Out of the several approaches adopted for ML estimation in this context, that of LeSage and Pace [Models for spatially dependent missing data. J Real Estate Financ Econ. 2004;29(2):233¿254] stands out as one of the most commonly used with spatial econometric models due to its ability to scale with the number of units. Here, we review their algorithm, and consider several similar alternatives that are also suitable for large datasets. We compare the methods through an extensive empirical study and conclude that, while the approximate approaches are suitable for large sampling ratios, for small sampling ratios the only reliable algorithms are those that yield exact ML or restricted ML estimates.

Publications (2016) by Andrew Zammit Mangion

Atmospheric trace-gas inversion is the procedure by which the sources and sinks of a trace gas ar... more Atmospheric trace-gas inversion is the procedure by which the sources and sinks of a trace gas are identified from observations of its mole fraction at isolated locations in space and time. This is inherently a spatio-temporal bivariate inversion problem, since the mole-fraction field evolves in space and time and the flux is also spatio-temporally distributed. Further, the bivariate model is likely to be non-Gaussian since the flux field is rarely Gaussian. Here, we use conditioning to construct a non-Gaussian bivariate model, and we describe some of its properties through auto- and cross-cumulant functions. A bivariate non-Gaussian, specifically trans-Gaussian, model is then achieved through the use of Box–Cox transformations, and we facilitate Bayesian inference by approximating the likelihood in a hierarchical framework. Trace-gas inversion, especially at high spatial resolution, is frequently highly sensitive to prior specification. Therefore, unlike conventional approaches, we assimilate trace-gas inventory information with the observational data at the parameter layer, thus shifting prior sensitivity from the inventory itself to its spatial characteristics (e.g., its spatial length scale). We demonstrate the approach in controlled-experiment studies of methane inversion, using fluxes extracted from inventories of the UK and Ireland and of Northern Australia.

In this work we assess the most recent estimates of glacio isostatic adjustment (GIA) for Antarct... more In this work we assess the most recent estimates of glacio isostatic adjustment (GIA) for Antarctica, including those from both forward and inverse methods. The assessment is based on a comparison of the estimated uplift rates with a set of elastic-corrected GPS vertical velocities. These have been observed from an extensive GPS network and computed using data over the period 2009–2014. We find systematic underestimations of the observed uplift rates in both inverse and forward methods over specific regions of Antarctica characterized by low mantle viscosities and thin lithosphere, such as the northern Antarctic Peninsula and the Amundsen Sea Embayment, where its recent ice discharge history is likely to be playing a role in current GIA. Uplift estimates for regions where many GIA models have traditionally placed their uplift maxima, such as the margins of Filchner-Ronne and Ross ice shelves are found to be overestimated. GIA estimates show large variability over the interior of East Antarctica which results in increased uncertainties on the ice-sheet mass balance derived from gravimetry methods.

Multivariate geostatistics is based on modelling all covariances between all possible combination... more Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built with care, since any covariance matrix that is derived from such a model must be nonnegative-definite. In this article, we develop a conditional approach for spatial model construction whose validity conditions are easy to check. We start with bivariate spatial covariance models and go on to demonstrate the approach’s connection to multivariate models defined by networks of spatial variables. In some circumstances, such as modelling respiratory illness conditional on air pollution, the direction of conditional dependence is clear. When it is not, the two directional models can be compared. More generally, the graph structure of the network reduces the number of possible models to compare. Model selection then amounts to finding possible causative links in the network. We demonstrate our conditional approach on surface temperature and pressure data, where the role of the two variables is seen to be asymmetric.

In geostatistics (and also in other applications in science and engineering) we are now performin... more In geostatistics (and also in other applications in science and engineering) we are now performing updates on Gaussian process models with thousands of components. These large-scale inferences involve computational challenges, because the updating equations cannot be solved as written, owing to the size and cost of the matrix operations. They also involve representational challenges, to account for judgements of heterogeneity concerning the underlying fields, and diverse sources of observations. Diagnostics are particularly valuable in this situation. We present a diagnostic and visualisation tool for large-scale Gaussian updates, the `medal plot'. This shows the initial and updated uncertainty for each observation, and also summarises the sharing of information across observations, as a proxy for the sharing of information across the state vector. It allows us to `sanity-check' the code implementing the update, but it can also reveal unexpected features in our modelling. We discuss computational issues for large-scale updates, and we illustrate with an application to assess mass trends in the West Antarctic Ice Sheet.

We present spatiotemporal mass balance trends for the Antarctic Ice Sheet from a statistical inve... more We present spatiotemporal mass balance trends for the Antarctic Ice Sheet from a statistical inversion of satellite altimetry, gravimetry, and elastic-corrected GPS data for the period 2003–2013. Our method simultaneously determines annual trends in ice dynamics, surface mass balance anomalies, and a time-invariant solution for glacio-isostatic adjustment while remaining largely independent of forward models. We establish that over the period 2003–2013, Antarctica has been losing mass at a rate of −84 ± 22 Gt yr −1 , with a sustained negative mean trend of dynamic imbalance of −111 ± 13 Gt yr −1. West Antarctica is the largest contributor with −112 ± 10 Gt yr −1 , mainly triggered by high thinning rates of glaciers draining into the Amundsen Sea Embayment. The Antarctic Peninsula has experienced a dramatic increase in mass loss in the last decade, with a mean rate of −28 ± 7 Gt yr −1 and significantly higher values for the most recent years following the destabilization of the Southern Antarctic Peninsula around 2010. The total mass loss is partly compensated by a significant mass gain of 56 ± 18 Gt yr −1 in East Antarctica due to a positive trend of surface mass balance anomalies.

Analysis of spatio-temporal point patterns plays an important role in several disciplines, yet in... more Analysis of spatio-temporal point patterns plays an important role in several disciplines, yet inference in these systems remains computationally challenging due to the high resolution modelling generally required by large data sets and the analytically intractable likelihood function. Here, we exploit the sparsity structure of a fully-discretised log-Gaussian Cox process model by using expectation constrained approximate inference. The resulting family of expectation propagation algorithms scale well with the state dimension and the length of the temporal horizon with moderate loss in distributional accuracy. They hence provide a flexible and faster alternative to both the filtering-smoothing type algorithms and the approaches which implement the Laplace method or expectation propagation on (block) sparse latent Gaussian models. We demonstrate the use of the proposed method in the reconstruction of conflict intensity levels in Afghanistan from a WikiLeaks data set.

Publications (2015) by Andrew Zammit Mangion

Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal flux... more Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a data-assimilation flavour, which implicitly consider univariate statistical models with the flux as the variate of interest. This univariate approach typically assumes that the flux field is either a spatially correlated Gaussian process or a spatially
uncorrelated non-Gaussian process with prior expectation fixed using flux inventories (e.g., NAEI or EDGAR in Europe). Here, we extend this approach in three ways. First, we develop a bivariate model for the mole-fraction field and the flux field. The bivariate approach allows optimal prediction of both the flux field and the mole-fraction field, and it leads to significant
computational savings over the univariate approach. Second, we employ a lognormal spatial process for the flux field that captures both the lognormal characteristics of the flux field (when appropriate) and its spatial dependence. Third, we propose a new, geostatistical approach to incorporate the flux inventories in our updates, such that the posterior spatial distribution of the flux field is predominantly data-driven. The approach is illustrated on a case study of methane (CH4) emissions in the United Kingdom and Ireland.

Antarctica is the world’s largest fresh-water reservoir, with the potential to raise sea levels b... more Antarctica is the world’s largest fresh-water reservoir, with the potential to raise sea levels by about 60 m. An ice sheet
contributes to sea-level rise (SLR) when its rate of ice discharge and/or surface melting exceeds accumulation through
snowfall. Constraining the contribution of the ice sheets to present-day SLR is vital both for coastal development and
planning, and climate projections. Information on various ice sheet processes is available from several remote sensing data
sets, as well as in situ data such as global positioning system data. These data have differing coverage, spatial support,
temporal sampling and sensing characteristics, and thus, it is advantageous to combine them all in a single framework for
estimation of the SLR contribution and the assessment of processes controlling mass exchange with the ocean.
In this paper, we predict the rate of height change due to salient geophysical processes in Antarctica and use these to
provide estimates of SLR contribution with associated uncertainties. We employ a multivariate spatio-temporal model,
approximated as a Gaussian Markov random field, to take advantage of differing spatio-temporal properties of the processes
to separate the causes of the observed change. The process parameters are estimated from geophysical models,
while the remaining parameters are estimated using a Markov chain Monte Carlo scheme, designed to operate in a high performance computing environment across multiple nodes. We validate our methods against a separate data set and
compare the results to those from studies that invariably employ numerical model outputs directly. We conclude that it is
possible, and insightful, to assess Antarctica’s contribution without explicit use of numerical models. Further, the results
obtained here can be used to test the geophysical numerical models for which in situ data are hard to obtain.

Combinations of various numerical models and data sets with diverse observation characteristics h... more Combinations of various numerical models and data sets with diverse observation characteristics have been used to assess an ice sheet's mass evolution. As a consequence, a wide range of estimates have been produced using markedly different methodologies, data, approximation methods and model assumptions. Current attempts to reconcile these estimates using simple combination methods are unsatisfactory as common sources of errors across different methodologies may not be accurately quantified, such as systematic biases in models. Here we provide a general approach which deals with this issue by considering all data sources simultaneously, and, crucially, by reducing the dependence on numerical models. The methodology is based on exploiting the different space-time characteristics of the relevant ice-sheet processes, and using statistical smoothing methods to establish the causes of the observed change. In omitting direct dependence on numerical models, the methodology provides a novel means for assessing glacio-isostatic adjustment and climate models alike using remote-sensing data sets. This is particularly advantageous in Antarctica where in-situ measurements are difficult to obtain. We illustrate the methodology by using it to infer Antarctica's mass trend between 2003--2009 and produce surface mass balance anomaly estimates to validate the regional climate model RACMO2.1.

The Antarctic Ice Sheet is the largest potential source of future sea-level rise. Mass loss has b... more The Antarctic Ice Sheet is the largest potential source of future sea-level rise. Mass loss has been increasing over the last two decades in the West Antarctic Ice Sheet (WAIS), but with significant discrepancies between estimates, especially for the Antarctic Peninsula. Most of these estimates utilise geophysical models to explicitly correct the observations for (unobserved) processes. Systematic errors in these models introduce biases in the results which are difficult to quantify. In this study, we provide a statistically rigorous, error-bounded trend estimate of ice mass loss over the WAIS from 2003–2009 which is almost entirely data-driven. Using altimetry, gravimetry, and GPS data in a hierarchical Bayesian framework, we derive spatial fields for ice mass change, surface mass balance, and glacial isostatic adjustment (GIA) without relying explicitly on forward models. The approach we use separates mass and height change contributions from different processes, reproducing spatial features found in, for example, regional climate and GIA forward models, and provides an independent estimate, which can be used to validate and test the models. In addition, full spatial error estimates are derived for each field. The mass loss estimates we obtain are smaller than some recent results, with a time-averaged mean rate of −76 ± 15 GT yr−1 for the WAIS and Antarctic Peninsula (AP), including the major Antarctic Islands. The GIA estimate compares very well with results obtained from recent forward models (IJ05-R2) and inversion methods (AGE-1). Due to its computational efficiency, the method is sufficiently scalable to include the whole of Antarctica, can be adapted for other ice sheets and can easily be adapted to assimilate data from other sources such as ice cores, accumulation radar data and other measurements that contain information about any of the processes that are solved for.

Publications (2014) by Andrew Zammit Mangion

Environmetrics, Dec 2013

Determining the Antarctic contribution to sea-level rise from observational data is a complex pro... more Determining the Antarctic contribution to sea-level rise from observational data is a complex problem. The number of physical processes involved (such as ice dynamics and surface climate) exceeds the number of observables, some of which have very poor spatial definition. This has led, in general, to solutions that utilise strong prior assumptions or physically-based deterministic models to simplify the problem. Here, we present a new approach for estimating the Antarctic contribution which only incorporates descriptive aspects of the physically-based models in the analysis and in a statistical manner. By combining physical insights with modern spatial statistical modelling techniques, we are able to provide probability distributions on all processes deemed to play a role in both the observed data and the contribution to sea-level rise. Specifically, we use stochastic partial differential equations and their relation to geo-statistical fields to capture our physical understanding and employ a Gaussian Markov random field approach for efficient computation. The method, an instantiation of Bayesian hierarchical modelling, naturally incorporates uncertainty in order to reveal credible intervals on all estimated quantities. The estimated sea-level rise contribution using this approach corroborates those found using a statistically independent method.

We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is us... more We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDF) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgement. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties, than traditional methods.

Publications (2013) by Andrew Zammit Mangion

Accepted for publication in the American Journal of Physiology: Renal Physiology (2013)

Publications (2012) by Andrew Zammit Mangion

Spatiotemporal models are ubiquitous in science and engineering, yet estimation in these models f... more Spatiotemporal models are ubiquitous in science and engineering, yet estimation in these models from discrete observations remains computationally challenging. We propose a practical novel approach to inference in spatiotemporal processes, both from continuous and from discrete (point-process) observations. The method is based on a finite-dimensional reduction of the spatiotemporal model, followed by a mean field variational approximate inference approach. To cater for the point-process case, a variational-Laplace approach is proposed which yields tractable computations of approximate variational posteriors. Results show that variational Bayes is a viable and practical alternative to statistical methods such as expectation maximization or Markov chain Monte Carlo.

Modern conflicts are characterized by an ever increasing use of information and sensing technolog... more Modern conflicts are characterized by an ever increasing use of information and sensing technology, resulting in vast amounts of high resolution data. Modelling and prediction of conflict, however, remain challenging tasks due to the heterogeneous and dynamic nature of the data typically available. Here we propose the use of dynamic spatiotemporal modelling tools for the identification of complex underlying processes in conflict, such as diffusion, relocation, heterogeneous escalation, and volatility. Using ideas from statistics, signal processing, and ecology, we provide a predictive framework able to assimilate data and give confidence estimates on the predictions. We demonstrate our methods on the WikiLeaks Afghan War Diary. Our results show that the approach allows deeper insights into conflict dynamics and allows a strikingly statistically accurate forward prediction of armed opposition group activity in 2010, based solely on data from previous years.

Publications (2011) by Andrew Zammit Mangion

We present a variational Bayesian (VB) approach for the state and parameter inference of a state-... more We present a variational Bayesian (VB) approach for the state and parameter inference of a state-space model with point-process observations, a physiologically plausible model for signal processing of spike data. We also give the derivation of a variational smoother, as well as an efficient online filtering algorithm, which can also be used to track changes in physiological parameters. The methods are assessed on simulated data, and results are compared to expectation-maximization, as well as Monte Carlo estimation techniques, in order to evaluate the accuracy of the proposed approach. The VB filter is further assessed on a data set of taste-response neural cells, showing that the proposed approach can effectively capture dynamical changes in neural responses in real time.

A Common Task Framework (CTF) for Objective Comparison of Spatial Prediction Methodologies, 2017

Environmetrics, Dec 2013

Abstract: Haptics refers to a widespread area of research that focuses on the interaction between... more Abstract: Haptics refers to a widespread area of research that focuses on the interaction between humans and machine interfaces as applied to the sense of touch. A haptic interface is designed to increase the realism of tactile and kinesthetic sensations in applications such as virtual ...

This paper investigates the use of novel hardware and techniques to increase the speed of simulat... more This paper investigates the use of novel hardware and techniques to increase the speed of simulation for large gas turbine engine models. In particular, the work shows the results of attempting to accelerate an engine system model using multiple processor cores and a FPGA co-processor. Strengths and weaknesses of the technologies are illustrated and an account of the lessons learnt for distributing models over disparate technologies is provided.

Haptics refers to a widespread area of research that focuses on the interaction between humans an... more Haptics refers to a widespread area of research that focuses on the interaction between humans and machine interfaces as applied to the sense of touch. A haptic interface is designed to increase the realism of tactile and kinesthetic sensations in applications such as virtual reality, teleoperation, and other scenarios where situational awareness is considered important, if not vital. This paper investigates the use of electric actuators and non-linear algorithms to provide force feedback to an input command device for providing haptics to the human operator. In particular, this work involves the study and implementation of a special case of feedback linearization known as inverse dynamics control and several outer loop impedance control topologies. It also investigates the issues concerned with force sensing and the application of model based controller functions in order to vary the desired inertia and the desired mass matrix. Results of the controllers’ abilities to display any desired impedance and provide the required kinesthetic constraint of virtual environments are shown on two experimental test rigs
designed for this purpose.

A dual variational Bayes filter for states and parameter estimation in IDE based spatiotemporal d... more A dual variational Bayes filter for states and parameter estimation in IDE based spatiotemporal dynamic systems is developed. Recursive updates are obtained from a restricted variational Bayesian perspective, using a dual filtering formulation where parameters are allowed to evolve in time. The added benefit over conventional point estimate filters is that parameter distributions are readily available for one to take advantage of in the design of complex experiments or in adaptive control scenarios. The dual filter is evaluated in a simulation study and seen to perform favorably when compared to a standard SMC approach.

Control of a spatiotemporal field with mobile agents has received considerable recent interest. A... more Control of a spatiotemporal field with mobile agents has received considerable recent interest. A key problem in this area is the tendency of agents to become static once a local control objective is met. To overcome this issue, we propose a novel approach inspired by classic control theory, cautious control, that augments the control cost with field uncertainty. This provokes the agents into exploring the field by being attracted to regions of high uncertainty, in addition to satisfying the control objective. A top-down approach is employed to reduce the potentially complex, abstract problem into an N-step ahead decision making problem, which is easy to implement and shown to give improved results when compared to both static agents and agents which do not take into account field uncertainty. The ensuing intuitive conclusion is that, when faced with the problem of spatiotemporal control with mobile agents, it is largely advantageous to include field uncertainty in the trajectory planning control objective.

In this work we assess the most recent estimates of glacial isostatic adjustment (GIA) for Antarc... more In this work we assess the most recent estimates of glacial isostatic adjustment (GIA) for Antarctica, including those from both forward and inverse methods. The assessment is based on a comparison of the estimated uplift rates with a set of elastic-corrected GPS vertical velocities. These have been observed from an extensive GPS network and computed using data over the period 2009–2014. We find systematic underestimations of the observed uplift rates in both inverse and forward methods over specific regions of Antarctica characterized by low mantle viscosities and thin lithosphere, such as the northern Antarctic Peninsula and the Amundsen Sea Embayment, where its recent ice discharge history is likely to be playing a role in current GIA. Uplift estimates for regions where many GIA models have traditionally placed their uplift maxima, such as the margins of Filchner-Ronne and Ross ice shelves, are found to be overestimated. GIA estimates show large variability over the interior of East Antarctica which results in increased uncertainties on the ice-sheet mass balance derived from gravimetry methods.

Journal of Geophysical Research: Earth Surface, 2015