Projects
Non-Invasive Methods for Detecting Human Physiological and Psychological Conditions
We develop a machine learning model that uses video images of the human face to pick-up signals and analyze these signals to determine physiological conditions. There are a multitude of applications for this research, from non-invasive measurement of clinical data (such temperature, blood pressure) to lie detection that could be used by law enforcement.
Reduced Order Modelling for Friction Stir Welding
Friction stir welding is a new method to fuse metals that are otherwise difficult to join. This project explores reduced order modelling for friction stir welding. The parameterization of the process requires complex computer simulations and human intuition. We propose to simplify the process by developing a mathematical model to optimize the friction stir welding process. Furthermore, we are interested in exploring how these methods may be applied to problems in other unrelated domains such as health, energy materials, and/or nanophotonics.
Pulmonary Ventilator Perfusion Mismatch
Develop a mathematical model and methodologies for evaluating pulmonary ventilation perfusion mismatch. Ventilation/perfusion mismatch occurs in pulmonary diseases such as ARDS and COPD. While low tidal volume ventilator strategy has shown a reduction in mortality rate of ARDS, there is no consensus among clinicians on other ventilator settings for ARDS patients. Mathematical models or ARDS provide useful insights into the condition but they are not readily applicable to investigate ventilation/perfusion mismatch. We are interested in deriving a measurement of the intrapulmonary shunt of a lung by using inhale and exhale gas fractions. We would like to be able to identify differences in ventilation/perfusion mismatch induced by dead space and/or intrapulmonary shunt in the lung.
Publications
Habib, Faisal; Huang, Huaxiong; Gupta, Arvind; Wright, Tom
MERCI: A Machine Learning Approach to Identifying Hydroxychloroquine Retinopathy using mfERG Journal Article
In: Documenta Ophthalmologica, vol. 145, pp. 53-63, 2022, ISSN: 1573-2622.
@article{Habib2022,
title = {MERCI: A Machine Learning Approach to Identifying Hydroxychloroquine Retinopathy using mfERG},
author = {Faisal Habib and Huaxiong Huang and Arvind Gupta and Tom Wright},
url = {https://doi.org/10.1007/s10633-022-09879-7},
doi = {10.1007/s10633-022-09879-7},
issn = {1573-2622},
year = {2022},
date = {2022-08-01},
urldate = {2022-08-01},
journal = {Documenta Ophthalmologica},
volume = {145},
pages = {53-63},
abstract = {Hydroxychloroquine (HCQ) is an anti-inflammatory drug in widespread use for the treatment of systemic auto-immune diseases. Vision loss caused by retinal toxicity is a significant risk associated with long term HCQ therapy. Identifying patients at risk of developing retinal toxicity can help prevent vision loss and improve the quality of life for patients. This paper presents updated reference thresholds and examines the diagnostic accuracy of a machine learning approach for identifying retinal toxicity using the multifocal Electroretinogram (mfERG).},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Hydroxychloroquine (HCQ) is an anti-inflammatory drug in widespread use for the treatment of systemic auto-immune diseases. Vision loss caused by retinal toxicity is a significant risk associated with long term HCQ therapy. Identifying patients at risk of developing retinal toxicity can help prevent vision loss and improve the quality of life for patients. This paper presents updated reference thresholds and examines the diagnostic accuracy of a machine learning approach for identifying retinal toxicity using the multifocal Electroretinogram (mfERG).
Li, Shixuan; Pan, Ruiqi; Gupta, Arvind; Xu, Shixin; Fang, Yibin; Huang, Huaxiong
Predicting the risk of rupture for vertebral aneurysm based on geometric features of blood vessels Journal Article
In: Royal Society Open Science, vol. 8, no. 8, 2021, ISSN: 2054-5703.
@article{Li2021,
title = {Predicting the risk of rupture for vertebral aneurysm based on geometric features of blood vessels},
author = {Shixuan Li and Ruiqi Pan and Arvind Gupta and Shixin Xu and Yibin Fang and Huaxiong Huang},
url = {https://royalsocietypublishing.org/doi/10.1098/rsos.210392},
doi = {10.1098/rsos.210392},
issn = {2054-5703},
year = {2021},
date = {2021-08-11},
urldate = {2021-08-11},
journal = {Royal Society Open Science},
volume = {8},
number = {8},
abstract = {A significant proportion of the adult population worldwide suffers from cerebral aneurysms. If left untreated, aneurysms may rupture and lead to fatal massive internal bleeding. On the other hand, treatment of aneurysms also involve significant risks. It is desirable, therefore, to have an objective tool that can be used to predict the risk of rupture and assist in surgical decision for operating on the aneurysms. Currently, such decisions are made mostly based on medical expertise of the healthcare team. In this paper, we investigate the possibility of using machine learning algorithms to predict rupture risk of vertebral artery fusiform aneurysms based on geometric features of the blood vessels surrounding but excluding the aneurysm. For each of the aneurysm images (12 ruptured and 25 unruptured), the vessel is segmented into distal and proximal parts by cross-sectional area and 382 non-aneurysm-related geometric features extracted. The decision tree model using two of the features (standard deviation of eccentricity of proximal vessel, and diameter at the distal endpoint) achieved 83.8% classification accuracy. Additionally, with support vector machine and logistic regression, we also achieved 83.8% accuracy with another set of two features (ratio of mean curvature between distal and proximal parts, and diameter at the distal endpoint). Combining the aforementioned three features with integration of curvature of proximal vessel and also ratio of mean cross-sectional area between distal and proximal parts, these models achieve an impressive 94.6% accuracy. These results strongly suggest the usefulness of geometric features in predicting the risk of rupture.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A significant proportion of the adult population worldwide suffers from cerebral aneurysms. If left untreated, aneurysms may rupture and lead to fatal massive internal bleeding. On the other hand, treatment of aneurysms also involve significant risks. It is desirable, therefore, to have an objective tool that can be used to predict the risk of rupture and assist in surgical decision for operating on the aneurysms. Currently, such decisions are made mostly based on medical expertise of the healthcare team. In this paper, we investigate the possibility of using machine learning algorithms to predict rupture risk of vertebral artery fusiform aneurysms based on geometric features of the blood vessels surrounding but excluding the aneurysm. For each of the aneurysm images (12 ruptured and 25 unruptured), the vessel is segmented into distal and proximal parts by cross-sectional area and 382 non-aneurysm-related geometric features extracted. The decision tree model using two of the features (standard deviation of eccentricity of proximal vessel, and diameter at the distal endpoint) achieved 83.8% classification accuracy. Additionally, with support vector machine and logistic regression, we also achieved 83.8% accuracy with another set of two features (ratio of mean curvature between distal and proximal parts, and diameter at the distal endpoint). Combining the aforementioned three features with integration of curvature of proximal vessel and also ratio of mean cross-sectional area between distal and proximal parts, these models achieve an impressive 94.6% accuracy. These results strongly suggest the usefulness of geometric features in predicting the risk of rupture.
Chen, Yu; Cheng, Jin; Gupta, Arvind; Huang, Huaxiong; Xu, Shixin
Numerical Method for Parameter Inference of Nonlinear ODEs with Partial Observations Journal Article
In: Royal Society Open Science, vol. 8, no. 7, 2021, ISSN: 2054-5703.
@article{chen2019numerical,
title = {Numerical Method for Parameter Inference of Nonlinear ODEs with Partial Observations},
author = {Yu Chen and Jin Cheng and Arvind Gupta and Huaxiong Huang and Shixin Xu},
url = {https://royalsocietypublishing.org/doi/10.1098/rsos.210171},
doi = {10.1098/rsos.210171},
issn = {2054-5703},
year = {2021},
date = {2021-07-28},
urldate = {2021-07-28},
journal = {Royal Society Open Science},
volume = {8},
number = {7},
abstract = {Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ordinary differential equations with partial observations. Our method combines fast Gaussian process-based gradient matching and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate, robust and efficient with partial observations and large noise.},
keywords = {},
pubstate = {published},
tppubtype = {article}
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Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ordinary differential equations with partial observations. Our method combines fast Gaussian process-based gradient matching and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate, robust and efficient with partial observations and large noise.
McCarthy, Zachary; Xu, Shixin; Rahman, Ashrafur; Bragazzi, Nicola Luigi; Corrales-Medina, Vicente F.; Lee, Jason; Seet, Bruce T.; Neame, Dion; Thommes, Edward; Heffernan, Jane; Chit, Ayman; Wu, Jianhong
Modelling the linkage between influenza infection and cardiovascular events via thrombosis Journal Article
In: Scientific Reports, vol. 10, 2020.
@article{McCarthy2020,
title = {Modelling the linkage between influenza infection and cardiovascular events via thrombosis},
author = {Zachary McCarthy and Shixin Xu and Ashrafur Rahman and Nicola Luigi Bragazzi and Vicente F. Corrales-Medina and Jason Lee and Bruce T. Seet and Dion Neame and Edward Thommes and Jane Heffernan and Ayman Chit and Jianhong Wu},
url = {https://doi.org/10.1038/s41598-020-70753-0},
doi = {10.1038/s41598-020-70753-0},
year = {2020},
date = {2020-08-31},
urldate = {2020-08-31},
journal = {Scientific Reports},
volume = {10},
abstract = {There is a heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza associated cardiac events have been linked to multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular thrombotic events, we develop a dynamic model which incorporates some key elements of the host immune response, inflammatory response, and blood coagulation. We formulate these biological systems and integrate them into a cohesive modelling framework to show how blood clotting may be connected to influenza virus infection. With blood clot formation inside an artery resulting from influenza virus infection as the primary outcome of this integrated model, we demonstrate how blood clot severity may depend on circulating prothrombin levels. We also utilize our model to leverage clinical data to inform the threshold level of the inflammatory cytokine TNFα which initiates tissue factor induction and subsequent blood clotting. Our model provides a tool to explore how individual biological components contribute to blood clotting events in the presence of influenza infection, to identify individuals at risk of clotting based on their circulating prothrombin levels, and to guide the development of future vaccines to optimally interact with the immune system.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
There is a heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza associated cardiac events have been linked to multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular thrombotic events, we develop a dynamic model which incorporates some key elements of the host immune response, inflammatory response, and blood coagulation. We formulate these biological systems and integrate them into a cohesive modelling framework to show how blood clotting may be connected to influenza virus infection. With blood clot formation inside an artery resulting from influenza virus infection as the primary outcome of this integrated model, we demonstrate how blood clot severity may depend on circulating prothrombin levels. We also utilize our model to leverage clinical data to inform the threshold level of the inflammatory cytokine TNFα which initiates tissue factor induction and subsequent blood clotting. Our model provides a tool to explore how individual biological components contribute to blood clotting events in the presence of influenza infection, to identify individuals at risk of clotting based on their circulating prothrombin levels, and to guide the development of future vaccines to optimally interact with the immune system.
Xu, Shixin; Chang, Joshua C.; Chow, Carson C.; Brennan, KC; Huang, Huaxiong
A mathematical model for persistent post-CSD vasoconstriction Journal Article
In: PLOS Computational Biology , vol. 16, no. 7, 2020.
@article{Xu2020,
title = {A mathematical model for persistent post-CSD vasoconstriction},
author = {Shixin Xu and Joshua C. Chang and Carson C. Chow and KC Brennan and Huaxiong Huang},
url = {https://doi.org/10.1371/journal.pcbi.1007996},
doi = {10.1371/journal.pcbi.1007996},
year = {2020},
date = {2020-07-15},
urldate = {2020-07-15},
journal = {PLOS Computational Biology },
volume = {16},
number = {7},
abstract = {Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.
Shen, Lingyue; Huang, Huaxiong; Lin, Ping; Song, Zilong; Xu, Shixin
An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density Journal Article
In: Journal of Computational Physics, vol. 405, 2020, ISSN: 0021-9991.
@article{nokey,
title = {An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density},
author = {Lingyue Shen and Huaxiong Huang and Ping Lin and Zilong Song and Shixin Xu},
url = {https://doi.org/10.1016/j.jcp.2019.109179},
doi = {10.1016/j.jcp.2019.109179},
issn = {0021-9991},
year = {2020},
date = {2020-03-15},
journal = {Journal of Computational Physics},
volume = {405},
abstract = {In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.
Liao, Mai-Jia; Wei, Ming-Tzo; Xu, Shixin; Ou-Yang, H Daniel; Sheng, Ping
Non-Stokes drag coefficient in single-particle electrophoresis: New insights on a classical problem Journal Article
In: Chinese Physics B, vol. 28, no. 8, 2019.
@article{Liao2019,
title = {Non-Stokes drag coefficient in single-particle electrophoresis: New insights on a classical problem},
author = {Mai-Jia Liao and Ming-Tzo Wei and Shixin Xu and H Daniel Ou-Yang and Ping Sheng},
url = {https://doi.org/10.1088/1674-1056/28/8/084701},
doi = {10.1088/1674-1056/28/8/084701},
year = {2019},
date = {2019-08-01},
urldate = {2019-08-01},
journal = {Chinese Physics B},
volume = {28},
number = {8},
abstract = {We measured the intrinsic electrophoretic drag coefficient of a single charged particle by optically trapping the particle and applying an AC electric field, and found it to be markedly different from that of the Stokes drag. The drag coefficient, along with the measured electrical force, yield a mobility-zeta potential relation that agrees with the literature. By using the measured mobility as input, numerical calculations based on the Poisson–Nernst–Planck equations, coupled to the Navier–Stokes equation, reveal an intriguing microscopic electroosmotic flow near the particle surface, with a well-defined transition between an inner flow field and an outer flow field in the vicinity of electric double layer's outer boundary. This distinctive interface delineates the surface that gives the correct drag coefficient and the effective electric charge. The consistency between experiments and theoretical predictions provides new insights into the classic electrophoresis problem, and can shed light on new applications of electrophoresis to investigate biological nanoparticles.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We measured the intrinsic electrophoretic drag coefficient of a single charged particle by optically trapping the particle and applying an AC electric field, and found it to be markedly different from that of the Stokes drag. The drag coefficient, along with the measured electrical force, yield a mobility-zeta potential relation that agrees with the literature. By using the measured mobility as input, numerical calculations based on the Poisson–Nernst–Planck equations, coupled to the Navier–Stokes equation, reveal an intriguing microscopic electroosmotic flow near the particle surface, with a well-defined transition between an inner flow field and an outer flow field in the vicinity of electric double layer's outer boundary. This distinctive interface delineates the surface that gives the correct drag coefficient and the effective electric charge. The consistency between experiments and theoretical predictions provides new insights into the classic electrophoresis problem, and can shed light on new applications of electrophoresis to investigate biological nanoparticles.
Zhu, Yi; Xu, Shixin; Eisenberg, Robert S.; Huang, Huaxiong
A Bidomain Model for Lens Microcirculation Journal Article
In: Biophysical Journal, vol. 116, no. 6, pp. 1171-1184, 2019, ISSN: 0006-3495.
@article{Zhu2019,
title = {A Bidomain Model for Lens Microcirculation},
author = {Yi Zhu and Shixin Xu and Robert S. Eisenberg and Huaxiong Huang},
url = {https://doi.org/10.1016/j.bpj.2019.02.007},
doi = {10.1016/j.bpj.2019.02.007},
issn = {0006-3495},
year = {2019},
date = {2019-03-19},
journal = {Biophysical Journal},
volume = {116},
number = {6},
pages = {1171-1184},
abstract = {There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the “brain.” Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the “brain.” Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.
Zhao, Xiukun; Gold, Nathan; Fang, Yibin; Xu, Shixin; Zhang, Yongxin; Liu, Jianmin; Gupta, Arvind; Huang, Huaxiong
Vertebral artery fusiform aneurysm geometry in predicting rupture risk Journal Article
In: Royal Society Open Science, vol. 5, no. 10, 2018, ISSN: 2054-5703.
@article{Zhao2018,
title = {Vertebral artery fusiform aneurysm geometry in predicting rupture risk},
author = {Xiukun Zhao and Nathan Gold and Yibin Fang and Shixin Xu and Yongxin Zhang and Jianmin Liu and Arvind Gupta and Huaxiong Huang},
url = {https://doi.org/10.1098/rsos.180780},
doi = {10.1098/rsos.180780},
issn = {2054-5703},
year = {2018},
date = {2018-10-31},
journal = {Royal Society Open Science},
volume = {5},
number = {10},
abstract = {Cerebral aneurysms affect a significant portion of the adult population worldwide. Despite significant progress, the development of robust techniques to evaluate the risk of aneurysm rupture remains a critical challenge. We hypothesize that vertebral artery fusiform aneurysm (VAFA) morphology may be predictive of rupture risk and can serve as a deciding factor in clinical management. To investigate the VAFA morphology, we use a combination of image analysis and machine learning techniques to study a geometric feature set computed from a depository of 37 (12 ruptured and 25 un-ruptured) aneurysm images. Of the 571 unique features we compute, we distinguish five features for use by our machine learning classification algorithm by an analysis of statistical significance. These machine learning methods achieve state-of-the-art classification performance (81.43 ± 13.08%) for the VAFA morphology, and identify five features (cross-sectional area change of aneurysm, maximum diameter of nearby distal vessel, solidity of aneurysm, maximum curvature of nearby distal vessel, and ratio of curvature between aneurysm and its nearby proximal vessel) as effective predictors of VAFA rupture risk. These results suggest that the geometric features of VAFA morphology may serve as useful non-invasive indicators for the prediction of aneurysm rupture risk in surgical settings.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Cerebral aneurysms affect a significant portion of the adult population worldwide. Despite significant progress, the development of robust techniques to evaluate the risk of aneurysm rupture remains a critical challenge. We hypothesize that vertebral artery fusiform aneurysm (VAFA) morphology may be predictive of rupture risk and can serve as a deciding factor in clinical management. To investigate the VAFA morphology, we use a combination of image analysis and machine learning techniques to study a geometric feature set computed from a depository of 37 (12 ruptured and 25 un-ruptured) aneurysm images. Of the 571 unique features we compute, we distinguish five features for use by our machine learning classification algorithm by an analysis of statistical significance. These machine learning methods achieve state-of-the-art classification performance (81.43 ± 13.08%) for the VAFA morphology, and identify five features (cross-sectional area change of aneurysm, maximum diameter of nearby distal vessel, solidity of aneurysm, maximum curvature of nearby distal vessel, and ratio of curvature between aneurysm and its nearby proximal vessel) as effective predictors of VAFA rupture risk. These results suggest that the geometric features of VAFA morphology may serve as useful non-invasive indicators for the prediction of aneurysm rupture risk in surgical settings.
Aroda, Pavan; Guergachi, Aziz; Huang, Huaxiong
Application of the convolution operator for scenario integration with loss data in operational risk modeling Journal Article
In: Journal of Operational Risk, vol. 10, no. 4, pp. 23-44, 2015, ISSN: 17552710.
@article{Aroda2015,
title = {Application of the convolution operator for scenario integration with loss data in operational risk modeling},
author = {Pavan Aroda and Aziz Guergachi and Huaxiong Huang},
url = {https://www.risk.net/journal-of-operational-risk/2434653/application-of-the-convolution-operator-for-scenario-integration-with-loss-data-in-operational-risk-modeling},
doi = {10.21314/JOP.2015.168},
issn = {17552710},
year = {2015},
date = {2015-11-13},
journal = {Journal of Operational Risk},
volume = {10},
number = {4},
pages = {23-44},
abstract = {When using the advanced measurement approach to determine required regulatory capital for operational risk, expert opinion is applied via scenario analysis to help quantify exposure to high-severity events. A methodology is presented that makes use of the convolution operator to integrate scenarios into a baseline model. Using a baseline loss distribution model calibrated on historical losses and a scenario-derived loss distribution calibrated on scenario data points, the addition of both random processes equates to the convolution of the corresponding densities. Using an analogy from digital signal processing, the commutative property of convolution allows one function to smooth and average the other. The inherent uncertainty in scenario analysis has caused concern amongst practitioners when too much emphasis has been placed on absolutes in terms of quantified frequency/severity estimates. This method addresses this uncertainty and produces a combined loss distribution that takes information from the entire domain of the calibrated scenario distribution. The necessary theory is provided within and an example is shown to provide context.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
When using the advanced measurement approach to determine required regulatory capital for operational risk, expert opinion is applied via scenario analysis to help quantify exposure to high-severity events. A methodology is presented that makes use of the convolution operator to integrate scenarios into a baseline model. Using a baseline loss distribution model calibrated on historical losses and a scenario-derived loss distribution calibrated on scenario data points, the addition of both random processes equates to the convolution of the corresponding densities. Using an analogy from digital signal processing, the commutative property of convolution allows one function to smooth and average the other. The inherent uncertainty in scenario analysis has caused concern amongst practitioners when too much emphasis has been placed on absolutes in terms of quantified frequency/severity estimates. This method addresses this uncertainty and produces a combined loss distribution that takes information from the entire domain of the calibrated scenario distribution. The necessary theory is provided within and an example is shown to provide context.