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A key challenge in agent‐based mobility simulations is the synthesis of individual agent socioeconomic profiles. Such profiles include locations of agent activities, which dictate the quality of the simulated travel patterns. These locations are typically represented in origin‐destination matrices that are sampled using coarse travel surveys. This is because fine‐grained trip profiles are scarce and fragmented due to privacy and cost reasons. The discrepancy between data and sampling resolutions renders agent traits nonidentifiable due to the combinatorial space of data‐consistent individual attributes. This problem is pertinent to any agent‐based inference setting where the latent state is discrete. Existing approaches have used continuous relaxations of the underlying location assignments and subsequent ad hoc discretisation thereof. We propose a framework to efficiently navigate this space offering improved reconstruction and coverage as well as linear‐time sampling of the ground truth origin‐destination table. This allows us to avoid factorially growing rejection rates and poor summary statistic consistency inherent in discrete choice modelling. We achieve this by introducing joint sampling schemes for the continuous intensity and discrete table of agent trips, as well as Markov bases that can efficiently traverse this combinatorial space subject to summary statistic constraints. Our framework's benefits are demonstrated in multiple controlled experiments and a large‐scale application to agent work trip reconstruction in Cambridge, UK. [ABSTRACT FROM AUTHOR]

To mitigate the current COVID-19 pandemic, policy makers at the Greater London Authority, the regional governance body of London, UK, are reliant upon prompt, accurate and actionable estimations of lockdown and social distancing policy adherence. Transport for London, the local transportation department, reports they implemented over 700 interventions such as greater signage and expansion of pedestrian zoning at the height of the pandemic's first wave with our platform providing key data for those decisions. Large well-defined heterogeneous compositions of pedestrian footfall and physical proximity are difficult to acquire, yet necessary to monitor city-wide activity (busyness) and consequently discern actionable policy decisions. To meet this challenge, we leverage our existing large-scale data processing urban air quality machine learning infrastructure to process over 900 camera feeds in near real-time to generate new estimates of social distancing adherence, group detection and camera stability. In this work, we describe our development and deployment of a computer vision and machine learning pipeline. It provides near immediate sampling and contextualization of activity and physical distancing on the streets of London via live traffic camera feeds. We introduce a platform for inspecting, calibrating and improving upon existing methods, describe the active deployment on real-time feeds and provide analysis over an 18 month period. [ABSTRACT FROM AUTHOR]

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control. We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics. Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models. [ABSTRACT FROM AUTHOR]

Many materials and structures consist of numerous slender struts or fibers. Due to the manufacturing processes of different types of struts and the growth processes of natural fibers, their mechanical response frequently fluctuates from strut to strut, as well as locally within each strut. In associated mechanical models each strut is often represented by a string of beam elements, since the use of conventional three‐dimensional finite elements renders the simulations computationally inefficient. The parameter input fields of each string of beam elements are ideally such that the local fluctuations and fluctuations between individual strings of beam elements are accurately captured. The goal of this study is to capture these fluctuations in several intercorrelated bounded random fields. Two formulations to describe the intercorrelations between each random field, as well as the case without any intercorrelation, are investigated. As only a few sets of input fields are available (due to time constraints of the supposed experimental techniques), the identification of the random fields' parameters involves substantial uncertainties. A probabilistic identification approach based on Bayes' theorem is employed to treat the involved uncertainties. [ABSTRACT FROM AUTHOR]

Conventional damage detection techniques are gradually being replaced by state-of-the-art smart monitoring and decision-making solutions. Near real-time and online damage assessment in structural health monitoring (SHM) systems is a promising transition toward bridging the gaps between the past's applicative inefficiencies and the emerging technologies of the future. In the age of the smart city, Internet of Things (IoT), and big data analytics, the complex nature of data-driven civil infrastructures monitoring frameworks has not been fully matured. Machine learning (ML) algorithms are thus providing the necessary tools to augment the capabilities of SHM systems and provide intelligent solutions for the challenges of the past. This article aims to clarify and review the ML frontiers involved in modern SHM systems. A detailed analysis of the ML pipelines is provided, and the in-demand methods and algorithms are summarized in augmentative tables and figures. Connecting the ubiquitous sensing and big data processing of critical information in infrastructures through the IoT paradigm is the future of SHM systems. In line with these digital advancements, considering the next-generation SHM and ML combinations, recent breakthroughs in (1) mobile device-assisted, (2) unmanned aerial vehicles, (3) virtual/augmented reality, and (4) digital twins are discussed at length. Finally, the current and future challenges and open research issues in SHM-ML conjunction are examined. The roadmap of utilizing emerging technologies within ML-engaged SHM is still in its infancy; thus, the article offers an outlook on the future of monitoring systems in assessing civil infrastructure integrity. [ABSTRACT FROM AUTHOR]

The monitoring of infrastructure assets using sensor networks is becoming increasingly prevalent. A digital twin in the form of a finite element (FE) model, as commonly used in design and construction, can help make sense of the copious amount of collected sensor data. This paper demonstrates the application of the statistical finite element method (statFEM), which provides a principled means of synthesizing data and physics-based models, in developing a digital twin of a self-sensing structure. As a case study, an instrumented steel railway bridge of 27:34m length located along the West Coast Mainline near Staffordshire in the UK is considered. Using strain data captured from fiber Bragg grating sensors at 108 locations along the bridge superstructure, statFEM can predict the "true" system response while taking into account the uncertainties in sensor readings, applied loading, and FE model misspecification errors. Longitudinal strain distributions along the two main I-beams are both measured and modeled during the passage of a passenger train. The statFEM digital twin is able to generate reasonable strain distribution predictions at locations where no measurement data are available, including at several points along the main I-beams and on structural elements on which sensors are not even installed. The implications for long-term structural health monitoring and assessment include optimization of sensor placement and performing more reliable what-if analyses at locations and under loading scenarios for which no measurement data are available. [ABSTRACT FROM AUTHOR]

Aeroengine performance is determined by temperature and pressure profiles along various axial stations within an engine. Given limited sensor measurements, we require a statistically principled approach for inferring these profiles. In this paper we detail a Bayesian methodology for interpolating the spatial temperature or pressure profile at axial stations within an aeroengine. The profile at any given axial station is represented as a spatial Gaussian random field on an annulus, with circumferential variations modelled using a Fourier basis and radial variations modelled with a squared exponential kernel. This Gaussian random field is extended to ingest data from multiple axial measurement planes, with the aim of transferring information across the planes. To facilitate this type of transfer learning, a novel planar covariance kernel is proposed. In the scenario where frequencies comprising the temperature field are unknown, we utilise a sparsity-promoting prior on the frequencies to encourage sparse representations. This easily extends to cases with multiple engine planes whilst accommodating frequency variations between the planes. The main quantity of interest, the spatial area average is readily obtained in closed form. We term this the Bayesian area average and demonstrate how this metric offers far more representative averages than a sector area average--a widely used area averaging approach. Furthermore, the Bayesian area average naturally decomposes the posterior uncertainty into terms characterising insufficient sampling and sensor measurement error respectively. This too provides a significant improvement over prior standard deviation based uncertainty breakdowns. [ABSTRACT FROM AUTHOR]

We suggest a probabilistic approach to study crime data in London and highlight the benefits of defining a statistical joint crime distribution model which provides insights into urban criminal activity. This is achieved by developing a hierarchical mixture model for observations, crime occurrences over a geographical study area, that are grouped according to multiple time stamps and crime categories. The mixture components correspond to spatial crime distributions over the study area and the goal is to infer, based on the observations, how and to what degree the latent distributions are shared across the groups. [ABSTRACT FROM AUTHOR]

In this article, a novel propagative broad learning approach is proposed for nonparametric modeling of the ambient effects on structural health indicators. Structural health indicators interpret the structural health condition of the underlying dynamical system. Long-term structural health monitoring on in-service civil engineering infrastructures has demonstrated that commonly used structural health indicators, such as modal frequencies, depend on the ambient conditions. Therefore, it is crucial to detrend the ambient effects on the structural health indicators for reliable judgment on the variation of structural integrity. However, two major challenging problems are encountered. First, it is not trivial to formulate an appropriate parametric expression for the complicated relationship between the operating conditions and the structural health indicators. Second, since continuous data stream is generated during long-term structural health monitoring, it is required to handle the growing data efficiently. The proposed propagative broad learning provides an effective tool to address these problems. In particular, it is a model-free data-driven machine learning approach for nonparametric modeling of the ambient-influenced structural health indicators. Moreover, the learning network can be updated and reconfigured incrementally to adapt newly available data as well as network architecture modifications. The proposed approach is applied to develop the ambient-influenced structural health indicator model based on the measurements of 3-year full-scale continuous monitoring on a reinforced concrete building. [ABSTRACT FROM AUTHOR]

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin represents the monitored system as accurately as possible. One way this is achieved is by calibration of simulation models, whether data-derived or physics-based, or a combination of both. Traditional manual calibration is not possible in this context; hence, new methods are required for continuous calibration. In this paper, a particle filter methodology for continuous calibration of the physics-based model element of a digital twin is presented and applied to an example of an underground farm. The methodology is applied to a synthetic problem with known calibration parameter values prior to being used in conjunction with monitored data. The proposed methodology is compared against static and sequential Bayesian calibration approaches and compares favourably in terms of determination of the distribution of parameter values and analysis run times, both essential requirements. The methodology is shown to be potentially useful as a means to ensure continuing model fidelity. [ABSTRACT FROM AUTHOR]

Summary: To obtain operational insights regarding the crime of burglary in London, we consider the estimation of the effects of covariates on the intensity of spatial point patterns. Inspired by localized properties of criminal behaviour, we propose a spatial extension to mixtures of generalized linear models from the mixture modelling literature. The Bayesian model proposed is a finite mixture of Poisson generalized linear models such that each location is probabilistically assigned to one of the groups. Each group is characterized by the regression coefficients, which we subsequently use to interpret the localized effects of the covariates. By using a blocks structure of the study region, our approach enables specifying spatial dependence between nearby locations. We estimate the proposed model by using Markov chain Monte Carlo methods and we provide a Python implementation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the Bayesian framework. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well-defined, encompassing both non-linear and non-Gaussian models. For general computation, a numerical approximation scheme is proposed and its asymptotic convergence established. The theoretical development is then extended to pipelines of computation, wherein probabilistic numerical methods are composed to solve more challenging numerical tasks. The contribution highlights an important research frontier at the interface of numerical analysis and uncertainty quantification, with a challenging industrial application presented. [ABSTRACT FROM AUTHOR]

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about, for example, the magnitude of the error. In this paper we propose a novel statistical model for this error, set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging. [ABSTRACT FROM AUTHOR]

The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has a complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank–Nicolson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics and on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. The use of uninformative priors on sensor noise enables optimal weighting among multiple sensors even if noise levels are uncertain. [ABSTRACT FROM AUTHOR]

The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multimodal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty, using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank-Nicholson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics or on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. Use of uninformative priors on sensor noise can improve inversion results by enabling optimal weighting among multiple sensors even if noise levels are uncertain. Efficiency could be further increased by using posterior gradient information within proposals, which Obsidian does not currently support, but which could be emulated using posterior surrogates. [ABSTRACT FROM AUTHOR]

Passive acoustic sensing has emerged as a powerful tool for quantifying anthropogenic impacts on biodiversity, especially for echolocating bat species. To better assess bat population trends there is a critical need for accurate, reliable, and open source tools that allow the detection and classification of bat calls in large collections of audio recordings. The majority of existing tools are commercial or have focused on the species classification task, neglecting the important problem of first localizing echolocation calls in audio which is particularly problematic in noisy recordings. We developed a convolutional neural network based open-source pipeline for detecting ultrasonic, full-spectrum, search-phase calls produced by echolocating bats. Our deep learning algorithms were trained on full-spectrum ultrasonic audio collected along road-transects across Europe and labelled by citizen scientists from . When compared to other existing algorithms and commercial systems, we show significantly higher detection performance of search-phase echolocation calls with our test sets. As an example application, we ran our detection pipeline on bat monitoring data collected over five years from Jersey (UK), and compared results to a widely-used commercial system. Our detection pipeline can be used for the automatic detection and monitoring of bat populations, and further facilitates their use as indicator species on a large scale. Our proposed pipeline makes only a small number of bat specific design decisions, and with appropriate training data it could be applied to detecting other species in audio. A crucial novelty of our work is showing that with careful, non-trivial, design and implementation considerations, state-of-the-art deep learning methods can be used for accurate and efficient monitoring in audio. [ABSTRACT FROM AUTHOR]

Bat echolocation call identification methods are important in developing efficient cost-effective methods for large-scale bioacoustic surveys for global biodiversity monitoring and conservation planning. Such methods need to provide interpretable probabilistic predictions of species since they will be applied across many different taxa in a diverse set of applications and environments. We develop such a method using a multinomial probit likelihood with independent Gaussian process priors and study its feasibility on a data set from an on-going study of 21 species, five families and 1800 bat echolocation calls collected from Mexico, a hotspot of bat biodiversity. We propose an efficient approximate inference scheme based on the expectation propagation algorithm and observe that the overall methodology significantly improves on currently adopted approaches to bat call classification by providing an approach which can be easily generalized across different species and call types and is fully probabilistic. Implementation of this method has the potential to provide robust species identification tools for biodiversity acoustic bat monitoring programmes across a range of taxa and spatial scales. [ABSTRACT FROM AUTHOR]

In this paper, we present a formal quantification of uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due to the finite-dimensional approximation of an unknown and implicitly defined function. When statistically analysing models based on differential equations describing physical, or other naturally occurring, phenomena, it can be important to explicitly account for the uncertainty introduced by the numerical method. Doing so enables objective determination of this source of uncertainty, relative to other uncertainties, such as those caused by data contaminated with noise or model error induced by missing physical or inadequate descriptors. As ever larger scale mathematical models are being used in the sciences, often sacrificing complete resolution of the differential equation on the grids used, formally accounting for the uncertainty in the numerical method is becoming increasingly more important. This paper provides the formal means to incorporate this uncertainty in a statistical model and its subsequent analysis. We show that a wide variety of existing solvers can be randomised, inducing a probability measure over the solutions of such differential equations. These measures exhibit contraction to a Dirac measure around the true unknown solution, where the rates of convergence are consistent with the underlying deterministic numerical method. Furthermore, we employ the method of modified equations to demonstrate enhanced rates of convergence to stochastic perturbations of the original deterministic problem. Ordinary differential equations and elliptic partial differential equations are used to illustrate the approach to quantify uncertainty in both the statistical analysis of the forward and inverse problems. [ABSTRACT FROM AUTHOR]

A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalized. The novel contribution of this work is based on two important insights: a trade-off between random sampling and deterministic approximation and a new gradient-based function space derived from Stein's identity. Unlike classical control variates, our estimators improve rates of convergence, often requiring orders of magnitude fewer simulations to achieve a fixed level of precision. Theoretical and empirical results are presented, the latter focusing on integration problems arising in hierarchical models and models based on non-linear ordinary differential equations. [ABSTRACT FROM AUTHOR]

We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the auxiliary model can be computed without evaluating determinants, which are often hard to compute in high dimensions. We develop a Markov chain Monte Carlo sampling scheme for the auxiliary model that requires no more than the application of inverse-matrix-square-roots and the solution of linear systems. These operations can be performed at large scales with rational approximations. We provide an empirical study on both synthetic and real-world data for sparse Gaussian processes and for large-scale Gaussian Markov random fields. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Approximation of the model evidence is well known to be challenging. One promising approach is based on thermodynamic integration, but a key concern is that the thermodynamic integral can suffer from high variability in many applications. This article considers the reduction of variance that can be achieved by exploiting control variates in this setting. Our methodology applies whenever the gradient of both the log-likelihood and the log-prior with respect to the parameters can be efficiently evaluated. Results obtained on regression models and popular benchmark datasets demonstrate a significant and sometimes dramatic reduction in estimator variance and provide insight into the wider applicability of control variates to evidence estimation. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

We present a novel class of mixed membership models for combining information from multiple data sources inferring inter-view and intra-view statistical associations. An important contemporary application of this work is the meaningful synthesis of data sources corresponding to smartphone application usage, app developers' descriptions and customer feedback. We demonstrate the ability of the model to infer meaningful, interpretable and informative app usage patterns based on the app usage data augmented with rich text data describing the apps. We provide quantitative model evaluations showing the model provides significantly better predictive ability than comparative related existing methods. © 2016 The Authors. Stat Published by John Wiley & Sons Ltd [ABSTRACT FROM AUTHOR]

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations. [ABSTRACT FROM AUTHOR]

Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis–Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC’s benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggest that our method improves RHMC’s overall computational efficiency in the cases considered. All computer programs and datasets are available online (http://www.ics.uci.edu/babaks/Site/Codes.html) to allow replication of the results reported in this article. [ABSTRACT FROM PUBLISHER]

Analysis of trace logging data collections of interactions of a heterogenous and diverse population of consumers of digital software with mobile devices provides unprecedented possibilities for understanding how software is actually used and for finding recurring patterns of software usage over the population that are exhibited to a greater or lesser degree in each individual software user. In this work, we consider an elementary mobile game played by a population of mobile gamers and collect pieces of game sessions over an extended period, resulting in a collection of users' trace logs for multiple sessions. We develop a simple, yet flexible, non-parametric Bayes approach to infer playing strategies adopted in the population from the logged traces of game interactions. We demonstrate that our approach finds interpretable strategies and provides good predictive performance compared with alternative modelling assumptions using a non-parametric Bayes framework. [ABSTRACT FROM AUTHOR]

The main challenges that arise when adopting Gaussian process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior. This is particularly important as it offers a powerful tool to carry out full Bayesian inference of Gaussian Process based hierarchic statistical models in general. The results also demonstrate that Monte Carlo based integration of all model parameters is actually feasible in this class of models providing a superior quantification of uncertainty in predictions. Extensive comparisons with respect to state-of-the-art probabilistic classifiers confirm this assertion. [ABSTRACT FROM AUTHOR]