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Bayesian synthetic likelihood for stochastic models with applications in mathematical finance 随机模型的贝叶斯综合似然及其在数学金融中的应用
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-06-05 DOI: 10.3389/fams.2023.1187878
R. Maraia, Sebastian Springer, Teemu Härkönen, M. Simon, H. Haario
{"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}
引用次数: 0
MAD (about median) vs. quantile-based alternatives for classical standard deviation, skewness, and kurtosis MAD(关于中位数)vs.基于分位数的经典标准差、偏度和峰度的替代方法
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-06-02 DOI: 10.3389/fams.2023.1206537
E. Pinsky, S. Klawansky
{"title":"MAD (about median) vs. quantile-based alternatives for classical standard deviation, skewness, and kurtosis","authors":"E. Pinsky, S. Klawansky","doi":"10.3389/fams.2023.1206537","DOIUrl":"https://doi.org/10.3389/fams.2023.1206537","url":null,"abstract":"In classical probability and statistics, one computes many measures of interest from mean and standard deviation. However, mean, and especially standard deviation, are overly sensitive to outliers. One way to address this sensitivity is by considering alternative metrics for deviation, skewness, and kurtosis using mean absolute deviations from the median (MAD). We show that the proposed measures can be computed in terms of the sub-means of the appropriate left and right sub-ranges. They can be interpreted in terms of average distances of values of these sub-ranges from their respective medians. We emphasize that these measures utilize only the first-order moment within each sub-range and, in addition, are invariant to translation or scaling. The obtained formulas are similar to the quantile measures of deviation, skewness, and kurtosis but involve computing sub-means as opposed to quantiles. While the classical skewness can be unbounded, both the MAD-based and quantile skewness always lies in the range [−1, 1]. In addition, while both the classical kurtosis and quantile-based kurtosis can be unbounded, the proposed MAD-based alternative for kurtosis lies in the range [0, 1]. We present a detailed comparison of MAD-based, quantile-based, and classical metrics for the six well-known theoretical distributions considered. We illustrate the practical utility of MAD-based metrics by considering the theoretical properties of the Pareto distribution with high concentrations of density in the upper tail, as might apply to the analysis of wealth and income. In summary, the proposed MAD-based alternatives provide a universal scale to compare deviation, skewness, and kurtosis across different distributions.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42514155","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}
引用次数: 0
Mathematical modeling for the control of fly-borne mastitis disease in cattle 牛蝇传乳腺炎疾病控制的数学模型
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-06-01 DOI: 10.3389/fams.2023.1171157
Moses Olayemi Adeyemi, T. O. Oluyo
{"title":"Mathematical modeling for the control of fly-borne mastitis disease in cattle","authors":"Moses Olayemi Adeyemi, T. O. Oluyo","doi":"10.3389/fams.2023.1171157","DOIUrl":"https://doi.org/10.3389/fams.2023.1171157","url":null,"abstract":"Several diseases cause losses in cattle farming, especially in the dairy industry among which mastitis disease (Bovine mastitis) is the leading cause of health and economic damages globally as it results in animals' ill health and reduced quality and quantity of milk produced by infected cows. Some mathematical studies have been conducted that focused on mastitis transmission from one udder-quarter to another in an infected cow, even though clinical studies established the cow–cow and flies–cow transmissions. The present study, therefore, proposed a mathematical model for the control of mastitis disease in cattle in the presence of flies as vectors. The formulated model was shown to have non-negative solutions in feasible regions for both cattle and flies populations. Furthermore, the model has a stable disease-free equilibrium if the sum of the effective reproduction numbers for cattle–cattle and fly–cattle transmissions (ℜch and ℜch) is less than unity, and there is a possibility of multiple endemic equilibria if otherwise. The numerical results indicated that the infectious populations can be reduced if the rates of the control parameters are increased, thereby curtailing or eradicating mastitis in the cattle population.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44638763","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}
引用次数: 0
Editorial: Advances in data-driven approaches and modeling of complex systems 社论：数据驱动方法和复杂系统建模的进展
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-25 DOI: 10.3389/fams.2023.1215077
M. H. Mohd, T. Nguyen-Huu, Junpyo Park, J. Addawe, H. Haga
{"title":"Editorial: Advances in data-driven approaches and modeling of complex systems","authors":"M. H. Mohd, T. Nguyen-Huu, Junpyo Park, J. Addawe, H. Haga","doi":"10.3389/fams.2023.1215077","DOIUrl":"https://doi.org/10.3389/fams.2023.1215077","url":null,"abstract":"COPYRIGHT © 2023 Mohd, Nguyen-Huu, Park, Addawe and Haga. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Editorial: Advances in data-driven approaches and modeling of complex systems","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48161168","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}
引用次数: 0
Editorial: Mathematical and empirical foundations of models of consciousness 社论:意识模型的数学和经验基础
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-22 DOI: 10.3389/fams.2023.1214939
X. Arsiwalla, Johannes Kleiner, S. Tull, Pedro Resende, Kobi Kremnitzer
{"title":"Editorial: Mathematical and empirical foundations of models of consciousness","authors":"X. Arsiwalla, Johannes Kleiner, S. Tull, Pedro Resende, Kobi Kremnitzer","doi":"10.3389/fams.2023.1214939","DOIUrl":"https://doi.org/10.3389/fams.2023.1214939","url":null,"abstract":"COPYRIGHT © 2023 Arsiwalla, Kleiner, Tull, Resende and Kremnitzer. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Editorial: Mathematical and empirical foundations of models of consciousness","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45541293","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}
引用次数: 0
Thermal Timoshenko beam system with suspenders and Kelvin–Voigt damping 带吊杆和Kelvin-Voigt阻尼的Timoshenko热梁系统
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-19 DOI: 10.3389/fams.2023.1153071
S. E. Mukiawa, Yasir Khan, Hamdan Al Sulaimani, M. Omaba, C. Enyi
{"title":"Thermal Timoshenko beam system with suspenders and Kelvin–Voigt damping","authors":"S. E. Mukiawa, Yasir Khan, Hamdan Al Sulaimani, M. Omaba, C. Enyi","doi":"10.3389/fams.2023.1153071","DOIUrl":"https://doi.org/10.3389/fams.2023.1153071","url":null,"abstract":"In the present study, we consider a thermal-Timoshenko-beam system with suspenders and Kelvin–Voigt damping type, where the heat is given by Cattaneo's law. Using the existing semi-group theory and energy method, we establish the existence and uniqueness of weak global solution, and an exponential stability result. The results are obtained without imposing the equal-wave speed of propagation condition. 2010 MSC: 35D30, 35D35, 35B35.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42966311","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}
引用次数: 2
Optimal vaccination control for COVID-19 in a metapopulation model: a case of the Philippines 集合人口模型中新冠肺炎疫苗接种的最佳控制：菲律宾的一例
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-18 DOI: 10.3389/fams.2023.1154634
Randy L. Caga-anan, Jead M. Macalisang, John Lemuel M. Dalisay, M. Raza, J. Martinez, J. P. Arcede
{"title":"Optimal vaccination control for COVID-19 in a metapopulation model: a case of the Philippines","authors":"Randy L. Caga-anan, Jead M. Macalisang, John Lemuel M. Dalisay, M. Raza, J. Martinez, J. P. Arcede","doi":"10.3389/fams.2023.1154634","DOIUrl":"https://doi.org/10.3389/fams.2023.1154634","url":null,"abstract":"We investigate a contextual problem of how to distribute a limited supply of vaccines over a period of time in a country where different regions have its own vaccination capacities. Considering that daily vaccination will affect future disease progression, we aim to find a distribution strategy over time that can minimize the total infection and implementation costs. Lagrangian and Eulerian migrations connect our multi-patch COVID-19 model, and vaccination is added as a control measure. An optimal control problem with an isoperimetric constraint is formulated and solved using the Adapted Forward–Backward Sweep Method. In distributing 5 million vaccines in 50 days, simulations showed that the optimal control strategy could lead to a difference of reducing two hundred thousand infections in just one region.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43979927","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}
引用次数: 0
Controllability of Hilfer fractional Langevin evolution equations Hilfer分数阶Langevin演化方程的可控性
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-18 DOI: 10.3389/fams.2023.1191661
Haihua Wang, Junhua Ku
{"title":"Controllability of Hilfer fractional Langevin evolution equations","authors":"Haihua Wang, Junhua Ku","doi":"10.3389/fams.2023.1191661","DOIUrl":"https://doi.org/10.3389/fams.2023.1191661","url":null,"abstract":"The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45316182","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}
引用次数: 0
Modeling visceral leishmaniasis and tuberculosis co-infection dynamics 模拟内脏利什曼病和肺结核合并感染动力学
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-15 DOI: 10.3389/fams.2023.1153666
O. Egbelowo, J. Munyakazi, P. Dlamini, F. Osaye, S. Simelane
{"title":"Modeling visceral leishmaniasis and tuberculosis co-infection dynamics","authors":"O. Egbelowo, J. Munyakazi, P. Dlamini, F. Osaye, S. Simelane","doi":"10.3389/fams.2023.1153666","DOIUrl":"https://doi.org/10.3389/fams.2023.1153666","url":null,"abstract":"The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42517867","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}
引用次数: 0
Data augmentation using generative adversarial networks for images and biomarkers in medicine and neuroscience 在医学和神经科学中使用生成对抗网络进行图像和生物标记物的数据增强
IF 1.4
Frontiers in Applied Mathematics and Statistics Pub Date : 2023-05-12 DOI: 10.3389/fams.2023.1162760
Maizan Syamimi Meor Yahaya, J. Teo
{"title":"Data augmentation using generative adversarial networks for images and biomarkers in medicine and neuroscience","authors":"Maizan Syamimi Meor Yahaya, J. Teo","doi":"10.3389/fams.2023.1162760","DOIUrl":"https://doi.org/10.3389/fams.2023.1162760","url":null,"abstract":"The fields of medicine and neuroscience often face challenges in obtaining a sufficient amount of diverse data for training machine learning models. Data augmentation can alleviate this issue by artificially synthesizing new data from existing data. Generative adversarial networks (GANs) provide a promising approach for data augmentation in the context of images and biomarkers. GANs can synthesize high-quality, diverse, and realistic data that can supplement real data in the training process. This study provides an overview of the use of GANs for data augmentation in medicine and neuroscience. The strengths and weaknesses of various GAN models, including deep convolutional GANs (DCGANs) and Wasserstein GANs (WGANs), are discussed. This study also explores the challenges and ways to address them when using GANs for data augmentation in the field of medicine and neuroscience. Future works on this topic are also discussed.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48210856","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}
引用次数: 0
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