Graphical modelling is an important branch of statistics that has been successfully applied in biology, social science, causal inference and so on. Graphical models illuminate connections between many variables and can even describe complex data structures or noisy data. Graphical models have been combined with supervised learning techniques such as regression modelling and classification analysis with multi-class responses. This paper first reviews some fundamental graphical modelling concepts, focusing on estimation methods and computational algorithms. Several advanced topics are then considered, delving into complex graphical structures and noisy data. Applications in regression and classification are considered throughout.
{"title":"Estimation of Graphical Models: An Overview of Selected Topics","authors":"Li-Pang Chen","doi":"10.1111/insr.12552","DOIUrl":"10.1111/insr.12552","url":null,"abstract":"<div>\u0000 \u0000 <p>Graphical modelling is an important branch of statistics that has been successfully applied in biology, social science, causal inference and so on. Graphical models illuminate connections between many variables and can even describe complex data structures or noisy data. Graphical models have been combined with supervised learning techniques such as regression modelling and classification analysis with multi-class responses. This paper first reviews some fundamental graphical modelling concepts, focusing on estimation methods and computational algorithms. Several advanced topics are then considered, delving into complex graphical structures and noisy data. Applications in regression and classification are considered throughout.</p>\u0000 </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"92 2","pages":"194-245"},"PeriodicalIF":1.7,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135591380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joshua S. North, Christopher K. Wikle, Erin M. Schliep
Many real‐world scientific processes are governed by complex non‐linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non‐linear dynamic systems using data‐driven approaches. In this paper, we review the current literature on data‐driven discovery for dynamic systems. We provide a categorisation to the different approaches for data‐driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data‐driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work.
{"title":"A Review of Data‐Driven Discovery for Dynamic Systems","authors":"Joshua S. North, Christopher K. Wikle, Erin M. Schliep","doi":"10.1111/insr.12554","DOIUrl":"https://doi.org/10.1111/insr.12554","url":null,"abstract":"Many real‐world scientific processes are governed by complex non‐linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non‐linear dynamic systems using data‐driven approaches. In this paper, we review the current literature on data‐driven discovery for dynamic systems. We provide a categorisation to the different approaches for data‐driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data‐driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work.","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135132140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cointegration has shown useful for modeling non-stationary data with long-run equilibrium relationships among variables, with applications in many fields such as econometrics, climate research and biology. However, the analyses of vector autoregressive models are becoming more difficult as data sets of higher dimensions are becoming available, in particular because the number of parameters is quadratic in the number of variables. This leads to lack of statistical robustness, and regularisation methods are paramount for obtaining valid estimates. In the last decade, many papers have appeared suggesting different penalisation approaches to the inference problem. Here, we make a comprehensive review of different penalisation methods adapted to the specific structure of vector cointegrated models suggested in the literature, with relevant references to software packages. The methods are evaluated and compared according to a range of error measures in a simulation study, considering combinations of low and high dimension of the system and small and large sample sizes.
{"title":"Penalisation Methods in Fitting High-Dimensional Cointegrated Vector Autoregressive Models: A Review","authors":"Marie Levakova, Susanne Ditlevsen","doi":"10.1111/insr.12553","DOIUrl":"10.1111/insr.12553","url":null,"abstract":"<p>Cointegration has shown useful for modeling non-stationary data with long-run equilibrium relationships among variables, with applications in many fields such as econometrics, climate research and biology. However, the analyses of vector autoregressive models are becoming more difficult as data sets of higher dimensions are becoming available, in particular because the number of parameters is quadratic in the number of variables. This leads to lack of statistical robustness, and regularisation methods are paramount for obtaining valid estimates. In the last decade, many papers have appeared suggesting different penalisation approaches to the inference problem. Here, we make a comprehensive review of different penalisation methods adapted to the specific structure of vector cointegrated models suggested in the literature, with relevant references to software packages. The methods are evaluated and compared according to a range of error measures in a simulation study, considering combinations of low and high dimension of the system and small and large sample sizes.</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"92 2","pages":"160-193"},"PeriodicalIF":1.7,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12553","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135014699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ziqing Dong, Yves Tille, Giovanni Maria Giorgi, Alessio Guandalini
This paper proposes a deep generalisation for income inequality indices. A generalised income inequality index that depends on two parameters and that involves a large set of income inequality indices in the same framework is proposed. The two parameters control the sensitivity of the generalised index to different levels of the income distribution. A thorough investigation of the generalised index paves the way for understanding the influence of the low, middle and high incomes on various income inequality indices and thereby facilitates the choice of multiple indices simultaneously for a better analysis of inequality as advocated by several recent studies. Moreover, two methods for estimating the generalised index in the case of finite populations are shown. A new method for estimating the inequality indices is proposed.
{"title":"Generalised Income Inequality Index","authors":"Ziqing Dong, Yves Tille, Giovanni Maria Giorgi, Alessio Guandalini","doi":"10.1111/insr.12551","DOIUrl":"10.1111/insr.12551","url":null,"abstract":"<p>This paper proposes a deep generalisation for income inequality indices. A generalised income inequality index that depends on two parameters and that involves a large set of income inequality indices in the same framework is proposed. The two parameters control the sensitivity of the generalised index to different levels of the income distribution. A thorough investigation of the generalised index paves the way for understanding the influence of the low, middle and high incomes on various income inequality indices and thereby facilitates the choice of multiple indices simultaneously for a better analysis of inequality as advocated by several recent studies. Moreover, two methods for estimating the generalised index in the case of finite populations are shown. A new method for estimating the inequality indices is proposed.</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"92 1","pages":"87-105"},"PeriodicalIF":2.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12551","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48981484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Number Savvy: From the Invention of Numbers to the Future of Data , George Sciadas Chapman & Hall/CRC, 2022, 312 pages, £56.99/$74.95, hardcover ISBN 9781032362151","authors":"Fabrizio Durante","doi":"10.1111/insr.12550","DOIUrl":"10.1111/insr.12550","url":null,"abstract":"","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"91 2","pages":"348"},"PeriodicalIF":2.0,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46364123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modern Applied Regressions: Bayesian and Frequentist Analysis of Categorical and Limited Response Variables with R and Stan , Jun Xu Chapman & Hall/CRC, 2023, xv + 281 pages, £80.99/$108, hardcover ISBN: 9780367173876 (hbk); 9781032376745 (pbk); 9780429056468 (ebk)","authors":"Shuangzhe Liu","doi":"10.1111/insr.12548","DOIUrl":"10.1111/insr.12548","url":null,"abstract":"","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"91 2","pages":"345-347"},"PeriodicalIF":2.0,"publicationDate":"2023-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46140403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anna Pajor, Justyna Wróblewska, Łukasz Kwiatkowski, Jacek Osiewalski
We compare predictive performance of a multitude of alternative Bayesian vector autoregression (VAR) models allowing for cointegration and time-varying conditional covariances, described by different multivariate stochastic volatility (MSV) models, including their hybrids with multivariate GARCH processes (MSV-MGARCH), as well as t-GARCH and Markov-switching structures. The forecast accuracy is evaluated mainly through predictive Bayes factors, but energy scores and the probability integral transform are also used. Two empirical studies, for the US and Polish economies, are based on a small model of monetary policy comprising inflation, unemployment and interest rate. The results indicate that capturing conditional heteroskedasticity by some MSV-MGARCH specifications contributes the most to the forecasting power of the VAR/VEC model.
{"title":"Hybrid SV-GARCH, t-GARCH and Markov-switching covariance structures in VEC models—Which is better from a predictive perspective?","authors":"Anna Pajor, Justyna Wróblewska, Łukasz Kwiatkowski, Jacek Osiewalski","doi":"10.1111/insr.12546","DOIUrl":"10.1111/insr.12546","url":null,"abstract":"<div>\u0000 \u0000 <p>We compare predictive performance of a multitude of alternative Bayesian vector autoregression (VAR) models allowing for cointegration and time-varying conditional covariances, described by different multivariate stochastic volatility (MSV) models, including their hybrids with multivariate GARCH processes (MSV-MGARCH), as well as <i>t</i>-GARCH and Markov-switching structures. The forecast accuracy is evaluated mainly through predictive Bayes factors, but energy scores and the probability integral transform are also used. Two empirical studies, for the US and Polish economies, are based on a small model of monetary policy comprising inflation, unemployment and interest rate. The results indicate that capturing conditional heteroskedasticity by some MSV-MGARCH specifications contributes the most to the forecasting power of the VAR/VEC model.</p>\u0000 </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"92 1","pages":"62-86"},"PeriodicalIF":2.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41819387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Effect: An Introduction to Research Design and Causality , Nick Huntington-Klein Chapman & Hall/CRC, 2022, xiv + 620 pages, $39.95, paperback. ISBN: 9781032125787","authors":"Brian W. Sloboda","doi":"10.1111/insr.12547","DOIUrl":"10.1111/insr.12547","url":null,"abstract":"","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"91 2","pages":"343-345"},"PeriodicalIF":2.0,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49021756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Patrick Toman, N. Ravishanker, S. Rajasekaran, Nathan Lally
The ‘Internet of Things’ (IoT) is a rapidly developing set of technologies that leverages large numbers of networked sensors, to relay data in an online fashion. Typically, knowledge of the sensor environment is incomplete and subject to changes over time. There is a need to employ classification algorithms to understand the data. We first review of existing time series classification (TSC) approaches, with emphasis on the well‐known k‐nearest neighbours (kNN) methods. We extend these to dynamical kNN classifiers, and discuss their shortcomings for handling the inherent uncertainty in IoT data. We next review evidential kNN ( EkNN ) classifiers that leverage the well‐known Dempster–Shafer theory to allow principled uncertainty quantification. We develop a dynamic EkNN approach for classifying IoT streams via algorithms that use evidential theoretic pattern rejection rules for (i) classifying incoming patterns into a set of oracle classes, (ii) automatically pruning ambiguously labelled patterns such as aberrant streams (due to malfunctioning sensors, say), and (iii) identifying novel classes that may emerge in new subsequences over time. While these methods have wide applicability in many domains, we illustrate the dynamic kNN and EkNN approaches for classifying a large, noisy IoT time series dataset from an insurance firm.
{"title":"Online Evidential Nearest Neighbour Classification for Internet of Things Time Series","authors":"Patrick Toman, N. Ravishanker, S. Rajasekaran, Nathan Lally","doi":"10.1111/insr.12540","DOIUrl":"https://doi.org/10.1111/insr.12540","url":null,"abstract":"The ‘Internet of Things’ (IoT) is a rapidly developing set of technologies that leverages large numbers of networked sensors, to relay data in an online fashion. Typically, knowledge of the sensor environment is incomplete and subject to changes over time. There is a need to employ classification algorithms to understand the data. We first review of existing time series classification (TSC) approaches, with emphasis on the well‐known k‐nearest neighbours (kNN) methods. We extend these to dynamical kNN classifiers, and discuss their shortcomings for handling the inherent uncertainty in IoT data. We next review evidential kNN ( EkNN ) classifiers that leverage the well‐known Dempster–Shafer theory to allow principled uncertainty quantification. We develop a dynamic EkNN approach for classifying IoT streams via algorithms that use evidential theoretic pattern rejection rules for (i) classifying incoming patterns into a set of oracle classes, (ii) automatically pruning ambiguously labelled patterns such as aberrant streams (due to malfunctioning sensors, say), and (iii) identifying novel classes that may emerge in new subsequences over time. While these methods have wide applicability in many domains, we illustrate the dynamic kNN and EkNN approaches for classifying a large, noisy IoT time series dataset from an insurance firm.","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45000249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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