Pub Date : 2023-04-03DOI: 10.1080/00401706.2023.2201126
S. Lipovetsky
This section will review those books whose content and level reflect the general editorial policy of Technometrics. Publishers should send books for review to Ejaz Ahmed, Department of Mathematics and Sciences, Brock University, St. Catharines, ON L2S 3A1 (dean.fms@brocku.ca). The opinions expressed in this section are those of the reviewers. These opinions do not represent positions of the reviewers’ organization and may not reflect those of the editors or the sponsoring societies. Listed prices reflect information provided by the publisher and may not be current. The book purchase programs of the American Society for Quality can provide some of these books at reduced prices for members. For information, contact the American Society for Quality at 1 (800) 248-1946.
{"title":"Introduction to Math Olympiad Problems","authors":"S. Lipovetsky","doi":"10.1080/00401706.2023.2201126","DOIUrl":"https://doi.org/10.1080/00401706.2023.2201126","url":null,"abstract":"This section will review those books whose content and level reflect the general editorial policy of Technometrics. Publishers should send books for review to Ejaz Ahmed, Department of Mathematics and Sciences, Brock University, St. Catharines, ON L2S 3A1 (dean.fms@brocku.ca). The opinions expressed in this section are those of the reviewers. These opinions do not represent positions of the reviewers’ organization and may not reflect those of the editors or the sponsoring societies. Listed prices reflect information provided by the publisher and may not be current. The book purchase programs of the American Society for Quality can provide some of these books at reduced prices for members. For information, contact the American Society for Quality at 1 (800) 248-1946.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":"65 1","pages":"296 - 296"},"PeriodicalIF":2.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49518960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00401706.2023.2201128
N. Khan
{"title":"The Effect: An Introduction to Research Design and Causality","authors":"N. Khan","doi":"10.1080/00401706.2023.2201128","DOIUrl":"https://doi.org/10.1080/00401706.2023.2201128","url":null,"abstract":"","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":"65 1","pages":"297 - 298"},"PeriodicalIF":2.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46257903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00401706.2023.2201132
Firdous Ahmad Mala
{"title":"Number Systems: A Path into Rigorous Mathematics","authors":"Firdous Ahmad Mala","doi":"10.1080/00401706.2023.2201132","DOIUrl":"https://doi.org/10.1080/00401706.2023.2201132","url":null,"abstract":"","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135674705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00401706.2023.2201129
P. Wludyka
to produce data that we can evaluate with a given method. Simulation can be used to rule out bad estimators and prove the value of good estimators to ourselves. Chapter 16, Fixed Effects, is about fixed effects, random effects, and fixed effects in the non-linear model and regression estimators. Fixed effects are methods of controlling for all variables whether they are observed or not, as long as they stay constant within some layer category. Chapter 17, Event Studies, is about event studies and how they work. The event study is probably the oldest and simplest causal inference research design. Event studies and performed in the stock market, event studies with regression, and event studies with multiple affected groups. Chapter 18, Differences-in-Differences, is about a method, a quasi-experimental approach that is concerned with comparing the changes in outcomes over time between a population enrolled in a program (the treatment group) and a population that is not (the comparison group). Its usefulness in data analysis has already been felt and appreciated. Chapter 19, Instrumental Variables, is about the working of instrumental variables and isolating variation instrumental variables designs seize directly on the concept of randomized control experiment. For work on instrumental variables, we must satisfy two assumptions: relevance of the instrument and validity of the instrument. Chapter 20, Regression Discontinuity, is about regression discontinuity. Regression discontinuity focuses on treatment that is assigned at a cutoff. It also focuses on the concept of running variable or forcing variable, cutoff, bandwidth, regression discontinuity with ordinary least squares, and the density discontinuity test. Chapter 21, A Gallery of Rogues: Other Methods, shows that the world of research design is too wide to be accommodated in a single book. There are methods and designs, both old and new, both tested and untested. This chapter demonstrates that there is a world of other methods that are new and yet developing. Among such exotic methods, the chapter talks about synthetic control, matrix completion, causal discovery, double machine learning, modeling of heterogeneous effects, causal forests, sorted effects, and structural estimation. This chapter could be inaccessible at the first reading, as the content of the chapter is either too advanced or too new to be grasped and understood. Chapter 22, Under the Rug, is all about the assumptions and concerns that are a part of pretty much any causal inference research study, but which often gets ignored or at least brushed aside. Overall, this book, though very voluminous, is an excellent addition to the world of literature. The book contains a good number of examples and wonderfully drawn diagrams, that facilitate a clearer understanding of the concepts. It is a wonderful exhibition of the parts and parcels of research design and causality.
{"title":"Principles of Biostatistics","authors":"P. Wludyka","doi":"10.1080/00401706.2023.2201129","DOIUrl":"https://doi.org/10.1080/00401706.2023.2201129","url":null,"abstract":"to produce data that we can evaluate with a given method. Simulation can be used to rule out bad estimators and prove the value of good estimators to ourselves. Chapter 16, Fixed Effects, is about fixed effects, random effects, and fixed effects in the non-linear model and regression estimators. Fixed effects are methods of controlling for all variables whether they are observed or not, as long as they stay constant within some layer category. Chapter 17, Event Studies, is about event studies and how they work. The event study is probably the oldest and simplest causal inference research design. Event studies and performed in the stock market, event studies with regression, and event studies with multiple affected groups. Chapter 18, Differences-in-Differences, is about a method, a quasi-experimental approach that is concerned with comparing the changes in outcomes over time between a population enrolled in a program (the treatment group) and a population that is not (the comparison group). Its usefulness in data analysis has already been felt and appreciated. Chapter 19, Instrumental Variables, is about the working of instrumental variables and isolating variation instrumental variables designs seize directly on the concept of randomized control experiment. For work on instrumental variables, we must satisfy two assumptions: relevance of the instrument and validity of the instrument. Chapter 20, Regression Discontinuity, is about regression discontinuity. Regression discontinuity focuses on treatment that is assigned at a cutoff. It also focuses on the concept of running variable or forcing variable, cutoff, bandwidth, regression discontinuity with ordinary least squares, and the density discontinuity test. Chapter 21, A Gallery of Rogues: Other Methods, shows that the world of research design is too wide to be accommodated in a single book. There are methods and designs, both old and new, both tested and untested. This chapter demonstrates that there is a world of other methods that are new and yet developing. Among such exotic methods, the chapter talks about synthetic control, matrix completion, causal discovery, double machine learning, modeling of heterogeneous effects, causal forests, sorted effects, and structural estimation. This chapter could be inaccessible at the first reading, as the content of the chapter is either too advanced or too new to be grasped and understood. Chapter 22, Under the Rug, is all about the assumptions and concerns that are a part of pretty much any causal inference research study, but which often gets ignored or at least brushed aside. Overall, this book, though very voluminous, is an excellent addition to the world of literature. The book contains a good number of examples and wonderfully drawn diagrams, that facilitate a clearer understanding of the concepts. It is a wonderful exhibition of the parts and parcels of research design and causality.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":"65 1","pages":"298 - 299"},"PeriodicalIF":2.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45511296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00401706.2023.2201134
S. Lipovetsky
chapter ends with a surprisingly-long account of modular arithmetic. Chapter 6 is devoted to rational numbers, which are the natural and legitimate successors to integers. The chapter discusses the denumerability of rationals after defining rational numbers and explaining their addition and multiplication. An interesting fact proved in the chapter is that rational numbers are countable, which means they are only as many as integers. The chapter concludes with a lovely but succinct presentation of sequences and series. Chapter 7 is about real numbers. It begins with the intriguing question of the completeness of the set of rational numbers and proceeds to state the well-known Axiom of Completeness of Real Numbers. Dedekind cuts are also discussed and demonstrated. The uncountability of reals refers to the fact that there are more reals than rationals. The famous diagonal argument is used in the chapter to demonstrate this fact. Finally, the chapter discusses algebraic and transcendental numbers. Quadratic extensions are discussed in Chapters 8 and 9. The subject matter covered in these two chapters is relatively complex, necessitating greater maturity and concentration on the part of the readers. Chapter 10 attempts to convince readers that the world of numbers is vaster and more immense than they realize. It is divided into two sections: one on constructible numbers and one on hypercomplex numbers, which includes accounts of Hilbert’s quaternions and John Graves’ octonions. Chapter 11 is a two-page guide to which readers should refer for a more comprehensive and advanced understanding of number systems. It implies that, in addition to abstract algebra, analysis is an excellent field for producing more elegant and unexpected results. In all, the book is a great attempt to introduce number systems to an undergraduate audience with the main focus on the rigor of mathematics. While, on the one hand, it provides detailed but accessible explanations of theorems and their proof, on the other hand, it is an attempt to provide the level of explanation needed for a first-year mathematics course on the subject that most others fail to do.
{"title":"Handbook of Measurement Error Models","authors":"S. Lipovetsky","doi":"10.1080/00401706.2023.2201134","DOIUrl":"https://doi.org/10.1080/00401706.2023.2201134","url":null,"abstract":"chapter ends with a surprisingly-long account of modular arithmetic. Chapter 6 is devoted to rational numbers, which are the natural and legitimate successors to integers. The chapter discusses the denumerability of rationals after defining rational numbers and explaining their addition and multiplication. An interesting fact proved in the chapter is that rational numbers are countable, which means they are only as many as integers. The chapter concludes with a lovely but succinct presentation of sequences and series. Chapter 7 is about real numbers. It begins with the intriguing question of the completeness of the set of rational numbers and proceeds to state the well-known Axiom of Completeness of Real Numbers. Dedekind cuts are also discussed and demonstrated. The uncountability of reals refers to the fact that there are more reals than rationals. The famous diagonal argument is used in the chapter to demonstrate this fact. Finally, the chapter discusses algebraic and transcendental numbers. Quadratic extensions are discussed in Chapters 8 and 9. The subject matter covered in these two chapters is relatively complex, necessitating greater maturity and concentration on the part of the readers. Chapter 10 attempts to convince readers that the world of numbers is vaster and more immense than they realize. It is divided into two sections: one on constructible numbers and one on hypercomplex numbers, which includes accounts of Hilbert’s quaternions and John Graves’ octonions. Chapter 11 is a two-page guide to which readers should refer for a more comprehensive and advanced understanding of number systems. It implies that, in addition to abstract algebra, analysis is an excellent field for producing more elegant and unexpected results. In all, the book is a great attempt to introduce number systems to an undergraduate audience with the main focus on the rigor of mathematics. While, on the one hand, it provides detailed but accessible explanations of theorems and their proof, on the other hand, it is an attempt to provide the level of explanation needed for a first-year mathematics course on the subject that most others fail to do.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":"65 1","pages":"302 - 304"},"PeriodicalIF":2.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46472727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-24DOI: 10.1080/00401706.2023.2190770
B. Weaver, S. V. Wiel
Abstract In some systems lowering any one of several stress variables limits the extent to which the others are able to accelerate random event times. That is, each stress variable can cap acceleration of the time to failure distribution, independent of the others. For example, repeated electrostatic shocks will set off a high-explosive detonator within the first few attempts only if voltage and energy are both sufficiently large. This article presents a class of time-to-event models with soft thresholds on multiple stressors. These models are fit to data obtained from an experiment performed at Los Alamos National Laboratory to estimate probabilities that detonators will fire from accidental electrostatic discharge. The models include a limited failure component to account for the possibility that a fraction of units is completely unable to produce the event of interest regardless of how long one waits or how many trials are attempted.
{"title":"Accelerated Event Times with Multiple Thresholds","authors":"B. Weaver, S. V. Wiel","doi":"10.1080/00401706.2023.2190770","DOIUrl":"https://doi.org/10.1080/00401706.2023.2190770","url":null,"abstract":"Abstract In some systems lowering any one of several stress variables limits the extent to which the others are able to accelerate random event times. That is, each stress variable can cap acceleration of the time to failure distribution, independent of the others. For example, repeated electrostatic shocks will set off a high-explosive detonator within the first few attempts only if voltage and energy are both sufficiently large. This article presents a class of time-to-event models with soft thresholds on multiple stressors. These models are fit to data obtained from an experiment performed at Los Alamos National Laboratory to estimate probabilities that detonators will fire from accidental electrostatic discharge. The models include a limited failure component to account for the possibility that a fraction of units is completely unable to produce the event of interest regardless of how long one waits or how many trials are attempted.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45292129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-15DOI: 10.1080/00401706.2023.2190779
Xin Wang, Xin Zhang, Zhengyuan Zhu
Abstract Motivated by a product warranty claims dataset, we propose clustered coefficient regression models in a nonhomogeneous Poisson process for recurrent event data. The proposed method, referred as CLUPP, can estimate the group structure and parameters simultaneously. In our proposed method, a penalized regression approach is used to identify the group structure. Numerical studies show that the proposed approach can identify the group structure well, and outperforms traditional methods such as hierarchical clustering and K-means. We also establish theoretical properties, which show that the proposed estimators can converge to true parameters in high probability. In the end, we apply our proposed methods to the product warranty claims dataset, which achieve better prediction than the state-of-the-art methods.
{"title":"Clustered coefficient regression models for Poisson process with an application to seasonal warranty claim data","authors":"Xin Wang, Xin Zhang, Zhengyuan Zhu","doi":"10.1080/00401706.2023.2190779","DOIUrl":"https://doi.org/10.1080/00401706.2023.2190779","url":null,"abstract":"Abstract Motivated by a product warranty claims dataset, we propose clustered coefficient regression models in a nonhomogeneous Poisson process for recurrent event data. The proposed method, referred as CLUPP, can estimate the group structure and parameters simultaneously. In our proposed method, a penalized regression approach is used to identify the group structure. Numerical studies show that the proposed approach can identify the group structure well, and outperforms traditional methods such as hierarchical clustering and K-means. We also establish theoretical properties, which show that the proposed estimators can converge to true parameters in high probability. In the end, we apply our proposed methods to the product warranty claims dataset, which achieve better prediction than the state-of-the-art methods.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48423748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-23DOI: 10.1080/00401706.2023.2174601
Dennis K. J. Lin, Jianbin Chen
Abstract The order-of-addition (OofA) experiment has received a great deal of attention in the recent literature. The primary goal of the OofA experiment is to identify the optimal order in a sequence of m components. All the existing methods are model-dependent and are limited to small number of components. The appropriateness of the resulting optimal order heavily depends on (a) the correctness of the underlying assumed model, and (b) the goodness of model fitting. Moreover, these methods are not applicable to deal with large m (e.g., ). With this in mind, this article proposes an efficient adaptive methodology, building upon the quick-sort algorithm, to explore the optimal order without any model specification. Compared to the existing work, the run sizes of the proposed method needed to achieve the optimal order are much smaller. Theoretical supports are given to illustrate the effectiveness of the proposed method. The proposed method is able to obtain the optimal order for large m (e.g., ). Numerical experiments are used to demonstrate the effectiveness of the proposed method.
{"title":"Adaptive Order-of-Addition Experiments via the Quick-Sort Algorithm","authors":"Dennis K. J. Lin, Jianbin Chen","doi":"10.1080/00401706.2023.2174601","DOIUrl":"https://doi.org/10.1080/00401706.2023.2174601","url":null,"abstract":"Abstract The order-of-addition (OofA) experiment has received a great deal of attention in the recent literature. The primary goal of the OofA experiment is to identify the optimal order in a sequence of m components. All the existing methods are model-dependent and are limited to small number of components. The appropriateness of the resulting optimal order heavily depends on (a) the correctness of the underlying assumed model, and (b) the goodness of model fitting. Moreover, these methods are not applicable to deal with large m (e.g., ). With this in mind, this article proposes an efficient adaptive methodology, building upon the quick-sort algorithm, to explore the optimal order without any model specification. Compared to the existing work, the run sizes of the proposed method needed to achieve the optimal order are much smaller. Theoretical supports are given to illustrate the effectiveness of the proposed method. The proposed method is able to obtain the optimal order for large m (e.g., ). Numerical experiments are used to demonstrate the effectiveness of the proposed method.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":"65 1","pages":"396 - 405"},"PeriodicalIF":2.5,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42512146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-21DOI: 10.1080/00401706.2023.2182366
Feng Xu, L. Shu, Yanting Li, Binhui Wang
Abstract Apart from the quick detection of abnormal changes in a process, it is also critical to pinpoint faulty variables after an out-of-control signal. The existing diagnostic procedures mainly focus on the diagnosis of changes in the process mean. This article investigates the joint diagnosis of high-dimensional process mean and covariance matrix based on Bayesian model selection with nonlocal priors. The proposed procedure enjoys two promising features. First, in addition to the isolation of shifted components, it can also provide a probability that the identified components are true, which is very useful for elimination of root causes of abnormal changes. Second, it possesses the model consistency property in the sense that the probability of identifying the true components with shifts approaches one as the sample size increases. The performance comparisons favor the proposed procedure. A real example based on the urban waste water treatment process is provided to illustrate the implementation of the proposed method.
{"title":"Joint Diagnosis of High-dimensional Process Mean and Covariance Matrix based on Bayesian Model Selection","authors":"Feng Xu, L. Shu, Yanting Li, Binhui Wang","doi":"10.1080/00401706.2023.2182366","DOIUrl":"https://doi.org/10.1080/00401706.2023.2182366","url":null,"abstract":"Abstract Apart from the quick detection of abnormal changes in a process, it is also critical to pinpoint faulty variables after an out-of-control signal. The existing diagnostic procedures mainly focus on the diagnosis of changes in the process mean. This article investigates the joint diagnosis of high-dimensional process mean and covariance matrix based on Bayesian model selection with nonlocal priors. The proposed procedure enjoys two promising features. First, in addition to the isolation of shifted components, it can also provide a probability that the identified components are true, which is very useful for elimination of root causes of abnormal changes. Second, it possesses the model consistency property in the sense that the probability of identifying the true components with shifts approaches one as the sample size increases. The performance comparisons favor the proposed procedure. A real example based on the urban waste water treatment process is provided to illustrate the implementation of the proposed method.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44234090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-16DOI: 10.1080/00401706.2023.2197471
Shuo Chen, Kejun He, Shiyuan He, Yang Ni, Raymond K. W. Wong
Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with unknown shapes and discontinuous jumps on the boundaries. Moreover, the relationship between the response and the tensor covariates can be nonlinear. In this article, we develop a nonlinear Bayesian tensor additive regression model to accommodate such spatial structure. A functional fused elastic net prior is proposed over the additive component functions to comprehensively model the nonlinearity and spatial smoothness, detect the discontinuous jumps, and simultaneously identify the active regions. The great flexibility and interpretability of the proposed method against the alternatives are demonstrated by a simulation study and an analysis on facial feature data.
{"title":"Bayesian Nonlinear Tensor Regression with Functional Fused Elastic Net Prior","authors":"Shuo Chen, Kejun He, Shiyuan He, Yang Ni, Raymond K. W. Wong","doi":"10.1080/00401706.2023.2197471","DOIUrl":"https://doi.org/10.1080/00401706.2023.2197471","url":null,"abstract":"Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with unknown shapes and discontinuous jumps on the boundaries. Moreover, the relationship between the response and the tensor covariates can be nonlinear. In this article, we develop a nonlinear Bayesian tensor additive regression model to accommodate such spatial structure. A functional fused elastic net prior is proposed over the additive component functions to comprehensively model the nonlinearity and spatial smoothness, detect the discontinuous jumps, and simultaneously identify the active regions. The great flexibility and interpretability of the proposed method against the alternatives are demonstrated by a simulation study and an analysis on facial feature data.","PeriodicalId":22208,"journal":{"name":"Technometrics","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47714991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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