Pub Date : 2023-06-22DOI: 10.3389/fams.2023.1155356
Jorin Dornemann
Vehicle routing problems are a class of NP-hard combinatorial optimization problems which attract a lot of attention, as they have many practical applications. In recent years there have been new developments solving vehicle routing problems with the help of machine learning, since learning how to automatically solve optimization problems has the potential to provide a big leap in optimization technology. Prior work on solving vehicle routing problems using machine learning has mainly focused on auto-regressive models, which are connected to high computational costs when combined with classical exact search methods as the model has to be evaluated in every search step. This paper proposes a new method for approximately solving the capacitated vehicle routing problem with time windows (CVRPTW) via a supervised deep learning-based approach in a non-autoregressive manner. The model uses a deep neural network to assist finding solutions by providing a probability distribution which is used to guide a tree search, resulting in a machine learning assisted heuristic. The model is built upon a new neural network architecture, called graph convolutional network, which is particularly suited for deep learning tasks. Furthermore, a new formulation for the CVRPTW in form of a quadratic unconstrained binary optimization (QUBO) problem is presented and solved via quantum-inspired computing in cooperation with Fujitsu, where a learned problem reduction based upon the proposed neural network is applied to circumvent limitations concerning the usage of quantum computing for large problem instances. Computational results show that the proposed models perform very well on small and medium sized instances compared to state-of-the-art solution methods in terms of computational costs and solution quality, and outperform commercial solvers for large instances.
{"title":"Solving the capacitated vehicle routing problem with time windows via graph convolutional network assisted tree search and quantum-inspired computing","authors":"Jorin Dornemann","doi":"10.3389/fams.2023.1155356","DOIUrl":"https://doi.org/10.3389/fams.2023.1155356","url":null,"abstract":"Vehicle routing problems are a class of NP-hard combinatorial optimization problems which attract a lot of attention, as they have many practical applications. In recent years there have been new developments solving vehicle routing problems with the help of machine learning, since learning how to automatically solve optimization problems has the potential to provide a big leap in optimization technology. Prior work on solving vehicle routing problems using machine learning has mainly focused on auto-regressive models, which are connected to high computational costs when combined with classical exact search methods as the model has to be evaluated in every search step. This paper proposes a new method for approximately solving the capacitated vehicle routing problem with time windows (CVRPTW) via a supervised deep learning-based approach in a non-autoregressive manner. The model uses a deep neural network to assist finding solutions by providing a probability distribution which is used to guide a tree search, resulting in a machine learning assisted heuristic. The model is built upon a new neural network architecture, called graph convolutional network, which is particularly suited for deep learning tasks. Furthermore, a new formulation for the CVRPTW in form of a quadratic unconstrained binary optimization (QUBO) problem is presented and solved via quantum-inspired computing in cooperation with Fujitsu, where a learned problem reduction based upon the proposed neural network is applied to circumvent limitations concerning the usage of quantum computing for large problem instances. Computational results show that the proposed models perform very well on small and medium sized instances compared to state-of-the-art solution methods in terms of computational costs and solution quality, and outperform commercial solvers for large instances.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45696986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-16DOI: 10.3389/fams.2023.1160250
P. Schulze
We discuss structure-preserving model order reduction for port-Hamiltonian systems based on a nonlinear approximation ansatz which is linear with respect to a part of the state variables of the reduced-order model. In recent years, such nonlinear approximation ansatzes have gained more and more attention especially due to their effectiveness in the context of model reduction for transport-dominated systems which are challenging for classical linear model reduction techniques. We demonstrate that port-Hamiltonian reduced-order models can often be obtained by a residual minimization approach where a suitable weighted norm is used for the residual. Moreover, we discuss sufficient conditions for the resulting reduced-order models to be stable. Finally, the methodology is illustrated by means of two transport-dominated numerical test cases, where the ansatz functions are determined based on snapshot data of the full-order state.
{"title":"Structure-preserving model reduction for port-Hamiltonian systems based on separable nonlinear approximation ansatzes","authors":"P. Schulze","doi":"10.3389/fams.2023.1160250","DOIUrl":"https://doi.org/10.3389/fams.2023.1160250","url":null,"abstract":"We discuss structure-preserving model order reduction for port-Hamiltonian systems based on a nonlinear approximation ansatz which is linear with respect to a part of the state variables of the reduced-order model. In recent years, such nonlinear approximation ansatzes have gained more and more attention especially due to their effectiveness in the context of model reduction for transport-dominated systems which are challenging for classical linear model reduction techniques. We demonstrate that port-Hamiltonian reduced-order models can often be obtained by a residual minimization approach where a suitable weighted norm is used for the residual. Moreover, we discuss sufficient conditions for the resulting reduced-order models to be stable. Finally, the methodology is illustrated by means of two transport-dominated numerical test cases, where the ansatz functions are determined based on snapshot data of the full-order state.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45059578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-16DOI: 10.3389/fams.2023.1122410
M. Maliyoni, H. Gaff, K. Govinder, F. Chirove
Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the largest patch reproduction number and for connected patches it lies between the minimum and maximum of the patch reproduction numbers. Numerical simulations for a two-patch deterministic and stochastic differential equation models are performed to illustrate the dynamics of the disease for varying migration rates. Our results show that the probability of eliminating or minimizing the disease in both patches is high when there is no migration unlike when it is present. The results imply that the probability of disease extinction can be increased if deer and tick movement are controlled or even prohibited especially when there is an outbreak in one or both patches since movement can introduce a disease in an area that was initially disease-free. Thus, screening of infectives in protected areas such as deer farms, private game parks or reserves, etc. before they migrate to other areas can be one of the intervention strategies for controlling and preventing disease spread.
{"title":"Multipatch stochastic epidemic model for the dynamics of a tick-borne disease","authors":"M. Maliyoni, H. Gaff, K. Govinder, F. Chirove","doi":"10.3389/fams.2023.1122410","DOIUrl":"https://doi.org/10.3389/fams.2023.1122410","url":null,"abstract":"Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the largest patch reproduction number and for connected patches it lies between the minimum and maximum of the patch reproduction numbers. Numerical simulations for a two-patch deterministic and stochastic differential equation models are performed to illustrate the dynamics of the disease for varying migration rates. Our results show that the probability of eliminating or minimizing the disease in both patches is high when there is no migration unlike when it is present. The results imply that the probability of disease extinction can be increased if deer and tick movement are controlled or even prohibited especially when there is an outbreak in one or both patches since movement can introduce a disease in an area that was initially disease-free. Thus, screening of infectives in protected areas such as deer farms, private game parks or reserves, etc. before they migrate to other areas can be one of the intervention strategies for controlling and preventing disease spread.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45850023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-15DOI: 10.3389/fams.2023.1201043
S. Abarzhi
Non-equilibrium dynamics is omnipresent in nature and technology and can exhibit symmetries and order. In idealistic systems this universality is well-captured by traditional models of dynamical systems. Realistic processes are often more complex. This work considers two paradigmatic complexities—canonical Kolmogorov turbulence and interfacial Rayleigh-Taylor mixing. We employ symmetries and invariant forms to assess very different properties and characteristics of these processes. We inter-link, for the first time, to our knowledge, the scaling laws and spectral shapes of Kolmogorov turbulence and Rayleigh-Taylor mixing. We reveal the decisive role of the control dimensional parameters in their respective dynamics. We find that the invariant forms and the control parameters provide the key insights into the attributes of the non-equilibrium dynamics, thus expanding the range of applicability of dynamical systems well-beyond traditional frameworks.
{"title":"Invariant forms and control dimensional parameters in complexity quantification","authors":"S. Abarzhi","doi":"10.3389/fams.2023.1201043","DOIUrl":"https://doi.org/10.3389/fams.2023.1201043","url":null,"abstract":"Non-equilibrium dynamics is omnipresent in nature and technology and can exhibit symmetries and order. In idealistic systems this universality is well-captured by traditional models of dynamical systems. Realistic processes are often more complex. This work considers two paradigmatic complexities—canonical Kolmogorov turbulence and interfacial Rayleigh-Taylor mixing. We employ symmetries and invariant forms to assess very different properties and characteristics of these processes. We inter-link, for the first time, to our knowledge, the scaling laws and spectral shapes of Kolmogorov turbulence and Rayleigh-Taylor mixing. We reveal the decisive role of the control dimensional parameters in their respective dynamics. We find that the invariant forms and the control parameters provide the key insights into the attributes of the non-equilibrium dynamics, thus expanding the range of applicability of dynamical systems well-beyond traditional frameworks.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43060114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-14DOI: 10.3389/fams.2023.1126511
Elisa Dong, R. Shcherbakov, K. Goda
The Epidemic Type Aftershock Sequence (ETAS) model and the modified Omori law (MOL) are two aftershock rate models that are used for operational earthquake/aftershock forecasting. Previous studies have investigated the relative performance of the two models for specific case studies. However, a rigorous comparative evaluation of the forecasting performance of the basic aftershock rate models for several different earthquake sequences has not been done before. In this study, forecasts of five prominent aftershock sequences from multiple catalogs are computed using the Bayesian predictive distribution, which fully accounts for the uncertainties in the model parameters. This is done by the Markov Chain Monte Carlo (MCMC) sampling of the model parameters and forward simulation of the ETAS or MOL models to compute the aftershock forecasts. The forecasting results are evaluated using five different statistical tests, including two comparison tests. The forecasting skill tests indicate that the ETAS model tends to perform consistently well on the first three tests. The MOL fails the same tests for certain forecasting time intervals. However, in the comparison tests, it is not definite whether the ETAS model is the better performing model. This work demonstrates the use of forecast testing for different catalogs, which is also applicable to catalogs with a higher magnitude of completeness.
{"title":"Testing the forecasting skills of aftershock models using a Bayesian framework","authors":"Elisa Dong, R. Shcherbakov, K. Goda","doi":"10.3389/fams.2023.1126511","DOIUrl":"https://doi.org/10.3389/fams.2023.1126511","url":null,"abstract":"The Epidemic Type Aftershock Sequence (ETAS) model and the modified Omori law (MOL) are two aftershock rate models that are used for operational earthquake/aftershock forecasting. Previous studies have investigated the relative performance of the two models for specific case studies. However, a rigorous comparative evaluation of the forecasting performance of the basic aftershock rate models for several different earthquake sequences has not been done before. In this study, forecasts of five prominent aftershock sequences from multiple catalogs are computed using the Bayesian predictive distribution, which fully accounts for the uncertainties in the model parameters. This is done by the Markov Chain Monte Carlo (MCMC) sampling of the model parameters and forward simulation of the ETAS or MOL models to compute the aftershock forecasts. The forecasting results are evaluated using five different statistical tests, including two comparison tests. The forecasting skill tests indicate that the ETAS model tends to perform consistently well on the first three tests. The MOL fails the same tests for certain forecasting time intervals. However, in the comparison tests, it is not definite whether the ETAS model is the better performing model. This work demonstrates the use of forecast testing for different catalogs, which is also applicable to catalogs with a higher magnitude of completeness.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44173474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-10DOI: 10.3389/fams.2023.1193191
Giulia Chiari, Giada Fiandaca, M. Delitala
In the study of therapeutic strategies for the treatment of cancer, eco-evolutionary dynamics are of particular interest, since characteristics of the tumor population, interaction with the environment and effects of the treatment, influence the geometric and epigenetic characterization of the tumor with direct consequences on the efficacy of the therapy and possible relapses. In particular, when considering radiotherapy, oxygen concentration plays a central role both in determining the effectiveness of the treatment and the selective pressure due to hypoxia.We propose a mathematical model, settled in the framework of epigenetically structured population dynamics and formulated in terms of systems of coupled non-linear integro-differential equations that aims to catch these phenomena and to provide a predictive tool for the tumor mass evolution and therapeutic effects.The outcomes of the simulations show how the model is able to explain the impact of environmental selection and therapies on the evolution of the mass, motivating observed dynamics such as relapses and therapeutic failures.This novel modeling framework, together with the experimental results obtained so far, offers a first hint for the development of therapies which can be adapted to overcome problems of resistance and relapses. Further studies, based on a quantification of medical data, could include the development of a mathematical tool for medical support in optimizing therapeutic protocols.
{"title":"Hypoxia-related radiotherapy resistance in tumors: treatment efficacy investigation in an eco-evolutionary perspective","authors":"Giulia Chiari, Giada Fiandaca, M. Delitala","doi":"10.3389/fams.2023.1193191","DOIUrl":"https://doi.org/10.3389/fams.2023.1193191","url":null,"abstract":"In the study of therapeutic strategies for the treatment of cancer, eco-evolutionary dynamics are of particular interest, since characteristics of the tumor population, interaction with the environment and effects of the treatment, influence the geometric and epigenetic characterization of the tumor with direct consequences on the efficacy of the therapy and possible relapses. In particular, when considering radiotherapy, oxygen concentration plays a central role both in determining the effectiveness of the treatment and the selective pressure due to hypoxia.We propose a mathematical model, settled in the framework of epigenetically structured population dynamics and formulated in terms of systems of coupled non-linear integro-differential equations that aims to catch these phenomena and to provide a predictive tool for the tumor mass evolution and therapeutic effects.The outcomes of the simulations show how the model is able to explain the impact of environmental selection and therapies on the evolution of the mass, motivating observed dynamics such as relapses and therapeutic failures.This novel modeling framework, together with the experimental results obtained so far, offers a first hint for the development of therapies which can be adapted to overcome problems of resistance and relapses. Further studies, based on a quantification of medical data, could include the development of a mathematical tool for medical support in optimizing therapeutic protocols.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42013725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-08DOI: 10.3389/fams.2023.1133349
C. Sisimayi, C. Harley, F. Nyabadza, Maria Vivien V. Visaya
Introduction The utility of non-contact technologies for screening infectious diseases such as COVID-19 can be enhanced by improving the underlying Artificial Intelligence (AI) models and integrating them into data visualization frameworks. AI models that are a fusion of different Machine Learning (ML) models where one has leveraged the different positive attributes of these models have the potential to perform better in detecting infectious diseases such as COVID-19. Furthermore, integrating other patient data such as clinical, socio-demographic, economic and environmental variables with the image data (e.g., chest X-rays) can enhance the detection capacity of these models. Methods In this study, we explore the use of chest X-ray data in training an optimized hybrid AI model based on a real-world dataset with limited sample size to screen patients with COVID-19. We develop a hybrid Convolutional Neural Network (CNN) and Random Forest (RF) model based on image features extracted through a CNN and EfficientNet B0 Transfer Learning Model and applied to an RF classifier. Our approach includes an intermediate step of using the RF's wrapper function, the Boruta Algorithm, to select important variable features and further reduce the number of features prior to using the RF model. Results and discussion The new model obtained an accuracy and recall of 96% for both and outperformed the base CNN model and four other experimental models that combined transfer learning and alternative options for dimensionality reduction. The performance of the model fares closely to relatively similar models previously developed, which were trained on large datasets drawn from different country contexts. The performance of the model is very close to that of the “gold standard” PCR tests, which demonstrates the potential for use of this approach to efficiently scale-up surveillance and screening capacities in resource limited settings.
{"title":"AI-enabled case detection model for infectious disease outbreaks in resource-limited settings","authors":"C. Sisimayi, C. Harley, F. Nyabadza, Maria Vivien V. Visaya","doi":"10.3389/fams.2023.1133349","DOIUrl":"https://doi.org/10.3389/fams.2023.1133349","url":null,"abstract":"Introduction The utility of non-contact technologies for screening infectious diseases such as COVID-19 can be enhanced by improving the underlying Artificial Intelligence (AI) models and integrating them into data visualization frameworks. AI models that are a fusion of different Machine Learning (ML) models where one has leveraged the different positive attributes of these models have the potential to perform better in detecting infectious diseases such as COVID-19. Furthermore, integrating other patient data such as clinical, socio-demographic, economic and environmental variables with the image data (e.g., chest X-rays) can enhance the detection capacity of these models. Methods In this study, we explore the use of chest X-ray data in training an optimized hybrid AI model based on a real-world dataset with limited sample size to screen patients with COVID-19. We develop a hybrid Convolutional Neural Network (CNN) and Random Forest (RF) model based on image features extracted through a CNN and EfficientNet B0 Transfer Learning Model and applied to an RF classifier. Our approach includes an intermediate step of using the RF's wrapper function, the Boruta Algorithm, to select important variable features and further reduce the number of features prior to using the RF model. Results and discussion The new model obtained an accuracy and recall of 96% for both and outperformed the base CNN model and four other experimental models that combined transfer learning and alternative options for dimensionality reduction. The performance of the model fares closely to relatively similar models previously developed, which were trained on large datasets drawn from different country contexts. The performance of the model is very close to that of the “gold standard” PCR tests, which demonstrates the potential for use of this approach to efficiently scale-up surveillance and screening capacities in resource limited settings.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47662913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-08DOI: 10.3389/fams.2023.1195810
J. Breeden, Ye. A. Leonova
Machine learning models have been used extensively for credit scoring, but the architectures employed suffer from a significant loss in accuracy out-of-sample and out-of-time. Further, the most common architectures do not effectively integrate economic scenarios to enable stress testing, cash flow, or yield estimation. The present research demonstrates that providing lifecycle and environment functions from Age-Period-Cohort analysis can significantly improve out-of-sample and out-of-time performance as well as enabling the model's use in both scoring and stress testing applications. This method is demonstrated for behavior scoring where account delinquency is one of the provided inputs, because behavior scoring has historically presented the most difficulties for combining credit scoring and stress testing. Our method works well in both origination and behavior scoring. The results are also compared to multihorizon survival models, which share the same architectural design with Age-Period-Cohort inputs and coefficients that vary with forecast horizon, but using a logistic regression estimation of the model. The analysis was performed on 30-year prime conforming US mortgage data. Nonlinear problems involving large amounts of alternate data are best at highlighting the advantages of machine learning. Data from Fannie Mae and Freddie Mac is not such a test case, but it serves the purpose of comparing these methods with and without Age-Period-Cohort inputs. In order to make a fair comparison, all models are given a panel structure where each account is observed monthly to determine default or non-default.
{"title":"Stabilizing machine learning models with Age-Period-Cohort inputs for scoring and stress testing","authors":"J. Breeden, Ye. A. Leonova","doi":"10.3389/fams.2023.1195810","DOIUrl":"https://doi.org/10.3389/fams.2023.1195810","url":null,"abstract":"Machine learning models have been used extensively for credit scoring, but the architectures employed suffer from a significant loss in accuracy out-of-sample and out-of-time. Further, the most common architectures do not effectively integrate economic scenarios to enable stress testing, cash flow, or yield estimation. The present research demonstrates that providing lifecycle and environment functions from Age-Period-Cohort analysis can significantly improve out-of-sample and out-of-time performance as well as enabling the model's use in both scoring and stress testing applications. This method is demonstrated for behavior scoring where account delinquency is one of the provided inputs, because behavior scoring has historically presented the most difficulties for combining credit scoring and stress testing. Our method works well in both origination and behavior scoring. The results are also compared to multihorizon survival models, which share the same architectural design with Age-Period-Cohort inputs and coefficients that vary with forecast horizon, but using a logistic regression estimation of the model. The analysis was performed on 30-year prime conforming US mortgage data. Nonlinear problems involving large amounts of alternate data are best at highlighting the advantages of machine learning. Data from Fannie Mae and Freddie Mac is not such a test case, but it serves the purpose of comparing these methods with and without Age-Period-Cohort inputs. In order to make a fair comparison, all models are given a panel structure where each account is observed monthly to determine default or non-default.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47077486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-05DOI: 10.3389/fams.2023.1187878
R. Maraia, Sebastian Springer, Teemu Härkönen, M. Simon, H. Haario
We present a Bayesian synthetic likelihood method to estimate both the parameters and their uncertainty in systems of stochastic differential equations. Together with novel summary statistics the method provides a generic and model-agnostic estimation procedure and is shown to perform well even for small observational data sets and biased observations of latent processes. Moreover, a strategy for assessing the goodness of the model fit to the observational data is provided. The combination of the aforementioned features differentiates our approach from other well-established estimation methods. We would like to stress the fact that the algorithm is pleasingly parallel and thus well suited for implementation on modern computing hardware. We test and compare the method to maximum likelihood, filtering and transition density estimation methods on a number of practically relevant examples from mathematical finance. Additionally, we analyze how to treat the lack-of-fit in situations where the model is biased due to the necessity of using proxies in place of unobserved volatility.
{"title":"Bayesian synthetic likelihood for stochastic models with applications in mathematical finance","authors":"R. Maraia, Sebastian Springer, Teemu Härkönen, M. Simon, H. Haario","doi":"10.3389/fams.2023.1187878","DOIUrl":"https://doi.org/10.3389/fams.2023.1187878","url":null,"abstract":"We present a Bayesian synthetic likelihood method to estimate both the parameters and their uncertainty in systems of stochastic differential equations. Together with novel summary statistics the method provides a generic and model-agnostic estimation procedure and is shown to perform well even for small observational data sets and biased observations of latent processes. Moreover, a strategy for assessing the goodness of the model fit to the observational data is provided. The combination of the aforementioned features differentiates our approach from other well-established estimation methods. We would like to stress the fact that the algorithm is pleasingly parallel and thus well suited for implementation on modern computing hardware. We test and compare the method to maximum likelihood, filtering and transition density estimation methods on a number of practically relevant examples from mathematical finance. Additionally, we analyze how to treat the lack-of-fit in situations where the model is biased due to the necessity of using proxies in place of unobserved volatility.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46446836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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