6 research outputs found
Bayesian design for calibration of physical models
No full textWe often want to learn about physical processes that are described by complex nonlinear mathematical models implemented as computer simulators. To use a simulator to make predictions about the real physical process, it is necessary to first perform calibration; that is, to use data obtained from a physical experiment to make inference about unknown parameters whilst acknowledging discrepancies between the simulator and reality. The computational expense of many simulators makes calibration challenging. Thus, usually in calibration, we use a computationally cheaper approximation to the simulator, often referred to as an emulator, constructed by fitting a statistical model to the results of a relatively small computer experiment. Although there is a substantial literature on the choice of the design of the computer experiment, the problem of designing the physical experiment in calibration is much less well-studied. This thesis is concerned with methodology for Bayesian optimal designs for the physical experiment when the aim is estimation of the unknown parameters in the simulator.Optimal Bayesian design for most realistic statistical models, including those incorporating expensive computer simulators, is complicated by the need to numerically approximate an analytically intractable expected utility; for example, the expected gain in Shannon information from the prior to posterior distribution. The standard approximation method is "double-loop" Monte Carlo integration using nested sampling from the prior distribution. Although this method is easy to implement, it produces biased approximations and is computationally expensive. For the Shannon information gain utility, we propose new approximation methods which combine features of importance sampling and Laplace approximations.These approximations are then used within an optimisation algorithm to find optimal designs for three problems: (i) estimation of the parameters in a nonlinear regression model; (ii) parameter estimation for a misspecified regression model subject to discrepancy; and (iii) estimation of the calibration parameters for a computational expensive simulator. Through examples, we demonstrate the advantages of this combination of methodology over existing methods.<br/
Approximate Laplace importance sampling for the estimation of expected Shannon information gain in high-dimensional Bayesian design for nonlinear models
No full textOne of the major challenges in Bayesian optimal design is to approximate the expected utility function in an accurate and computationally efficient manner. We focus on Shannon information gain, one of the most widely used utilities when the experimental goal is parameter inference. We compare the performance of various methods for approximating expected Shannon information gain in common nonlinear models from the statistics literature, with a particular emphasis on Laplace importance sampling (LIS) and approximate Laplace importance sampling (ALIS), a new method that aims to reduce the computational cost of LIS. Specifically, in order to centre the importance distributions LIS requires computation of the posterior mode for each of a large number of simulated possibilities for the response vector. ALIS substantially reduces the amount of numerical optimization that is required, in some cases eliminating all optimization, by centering the importance distributions on the data-generating parameter values wherever possible. Both methods are thoroughly compared with existing approximations including Double Loop Monte Carlo, nested importance sampling, and Laplace approximation. It is found that LIS and ALIS both give an efficient trade-off between mean squared error and computational cost for utility estimation, and ALIS can be up to 70% cheaper than LIS. Usually ALIS gives an approximation that is cheaper but less accurate than LIS, while still being efficient, giving a useful addition to the suite of efficient methods. However, we observed one case where ALIS is both cheaper and more accurate. In addition, for the first time we show that LIS and ALIS yield superior designs to existing methods in problems with large numbers of model parameters when combined with the approximate co-ordinate exchange algorithm for design optimization
Simultaneous identification of sensor faults and origin-destination matrix estimation
No full textEfficient estimation of the origin-destination (OD) matrix is a crucial requirement for traffic monitoring and control. The OD matrix estimation problem has received significant attention over the past decades and various approaches using traffic counts from fixed location sensors have been developed and tested. A significant challenge when using information obtained from traffic sensors, is that such sensors are subject to considerable disruptions due to system errors, that affect the quality and reliability of the information provided. This paper presents a novel approach for OD matrix estimation in the presence of faulty sensors. For the purposes of this work we assume that the network under study operates under free-flow conditions and utilise a variation of the cell transmission model to capture the traffic flow dynamics in a pre-specified time window. The problem is formulated in an optimisation framework and solved by taking into account the presence of faulty measurements. We test and validate the proposed methodology on a sample network and investigate the advantage of OD matrix estimation in the presence of faulty measurements compared to OD matrix estimation when faulty sensors are not considered.This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101003435.
2022 IFAC. Personal use of this material is permitted. Permission from IFAC must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Y. Englezou, S. Timotheou and C. G. Panayiotou, "Simultaneous identification of sensor faults and origin-destination matrix estimation," IFAC-PapersOnLine, 2022, pp. 151-156, doi: 10.1016/j.ifacol.2022.07.121
Probabilistic traffic density estimation using measurements from Unmanned Aerial Vehicles
No full textTraffic state estimation (TSE) is an important task for traffic management, however it can be challenging due to the sparse deployment of traffic sensors in the network. The advancement of new technologies, such as the Unmanned Aerial Vehicles (UAVs), provide new capabilities for traffic state estimation using measurements at irregular time-points from all links of a given network under study. This work proposes a probabilistic traffic density estimation method utilising measurements collected from a swarm of UAVs deployed over the network under study and no traffic models or historical data are required. We propose the use of the Gaussian process model to interpolate measurements obtained from a swarm of UAVs and derive fine-grained traffic density estimations of distinct road segments in an offline Bayesian framework both under free-flow and congested conditions. The proposed approach is validated using a macroscopic simulation scenario of a part of the M25 highway stretch in London, England. Preliminary results show the effectiveness of UAVs in traffic density estimation and the efficiency of the proposed probabilistic method.This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101003435.
2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Y. Englezou, S. Timotheou and C. G. Panayiotou, "Probabilistic traffic density estimation using measurements from Unmanned Aerial Vehicles," 2022 International Conference on Unmanned Aircraft Systems (ICUAS), 2022, pp. 1381-1388, doi: 10.1109/ICUAS54217.2022.9836098
Approximate Laplace importance sampling for the estimation of expected Shannon information gain in high-dimensional Bayesian design for nonlinear models
No full textOne of the major challenges in Bayesian optimal design is to approximate the expected utility function in an accurate and computationally efficient manner. We focus on Shannon information gain, one of the most widely used utilities when the experimental goal is parameter inference. We compare the performance of various methods for approximating expected Shannon information gain in common nonlinear models from the statistics literature, with a particular emphasis on Laplace Importance Sampling (LIS) and approximate Laplace Importance Sampling (ALIS), a new method that aims to reduce the computational cost of LIS. Specifically, in order to centre the importance distributions LIS requires computation of the posterior mode for each of a large number of simulated possibilities for the response vector. ALIS substantially reduces the amount of numerical optimization that is required, in some cases eliminating all optimization, by centering the importance distributions on the data-generating parameter values wherever possible. Both methods are thoroughly compared with existing approximations including Double Loop Monte Carlo, nested importance sampling, and Laplace approximation. It is found that LIS and ALIS both give an efficient trade-off between mean squared error and computational cost for utility estimation, and ALIS can be up to 70% cheaper than LIS. Usually ALIS gives an approximation that is cheaper but less accurate than LIS, while still being efficient, giving a useful addition to the suite of efficient methods. However, we observed one case where ALIS is both cheaper and more accurate. In addition, for the first time we show that LIS and ALIS yield superior designs to existing methods in problems with large numbers of model parameters when combined with the approximate co-ordinate exchange algorithm for design optimization
Neural correlates of pain acceptance and the role of the cerebellum: Functional connectivity and anatomical differences in individuals with headaches versus matched controls
No full textBackground: Despite functional connectivity network dysfunction among individuals with headaches, no studies have examined functional connectivity neural correlates and anatomical differences in coping with headaches. Methods: This study investigated inter-individual variability in whole-brain functional connectivity and anatomical differences among 37 individuals with primary headaches and 24 age- and gender-matched controls, and neural correlates of psychological flexibility (PF) that was previously found to contribute to headache adjustment. Participants (84% women; M headache severity = 4/10; M age = 43 years) underwent functional magnetic resonance imaging scans and completed questionnaires to examine global and subnetwork brain areas, and their relations with PF components, controlling for age, gender, education, and head-motion. Results: Seed and voxel-based contrast analyses between groups showed atypical functional connectivity of regions involved in pain matrix and core resting-state networks. Pain acceptance was the sole PF component that correlated with the cerebellum (x, y, z: 28, −72, −34, p-false discovery rate <0.001), where individuals with headaches showed higher grey matter density compared to controls. Conclusions: The cerebellum, recently implicated in modulating emotional and cognitive processes, was indicated to process information resembling what individuals do when practicing pain acceptance. Our findings establish for the first time this connection of the cerebellum and its role in pain acceptance. We propose that pain acceptance might be a behavioural biomarker target that could modulate problematic headache perceptions and brain networks abnormalities. Significance: This study highlights the potential use of emerging behavioural biomarkers in headache management, such as pain acceptance, and their role in modifying the headache experience. Notably, grey matter reorganization in the cerebellum and other known brain pain networks, could indicate brain networks that can be modified from targeted behavioural interventions to help decode the nociplastic mechanisms that predominates in headaches. © 2024 The Author(s). European Journal of Pain published by John Wiley & Sons Ltd on behalf of European Pain Federation - EFIC ®
