We propose a scalable Bayesian network learning algorithm based on sparse Cholesky decomposition. Our approach only requires observational data and user-specified confidence level as inputs and can estimate networks with thousands of variables. The computational complexity of the proposed method is $O({p^{3}})$ for a graph with p vertices. Extensive numerical experiments illustrate the usefulness of our method with promising results. In simulation, the initial step in our approach also improves an alternative Bayesian network structure estimation method that uses an undirected graph as an input.
{"title":"FROSTY: A High-Dimensional Scale-Free Bayesian Network Learning Method","authors":"Joshua Bang, Sang-Yun Oh","doi":"10.6339/23-jds1097","DOIUrl":"https://doi.org/10.6339/23-jds1097","url":null,"abstract":"We propose a scalable Bayesian network learning algorithm based on sparse Cholesky decomposition. Our approach only requires observational data and user-specified confidence level as inputs and can estimate networks with thousands of variables. The computational complexity of the proposed method is $O({p^{3}})$ for a graph with p vertices. Extensive numerical experiments illustrate the usefulness of our method with promising results. In simulation, the initial step in our approach also improves an alternative Bayesian network structure estimation method that uses an undirected graph as an input.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320996","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}
Analyzing “large p small n” data is becoming increasingly paramount in a wide range of application fields. As a projection pursuit index, the Penalized Discriminant Analysis ($mathrm{PDA}$) index, built upon the Linear Discriminant Analysis ($mathrm{LDA}$) index, is devised in Lee and Cook (2010) to classify high-dimensional data with promising results. Yet, there is little information available about its performance compared with the popular Support Vector Machine ($mathrm{SVM}$). This paper conducts extensive numerical studies to compare the performance of the $mathrm{PDA}$ index with the $mathrm{LDA}$ index and $mathrm{SVM}$, demonstrating that the $mathrm{PDA}$ index is robust to outliers and able to handle high-dimensional datasets with extremely small sample sizes, few important variables, and multiple classes. Analyses of several motivating real-world datasets reveal the practical advantages and limitations of individual methods, suggesting that the $mathrm{PDA}$ index provides a useful alternative tool for classifying complex high-dimensional data. These new insights, along with the hands-on implementation of the $mathrm{PDA}$ index functions in the R package classPP, facilitate statisticians and data scientists to make effective use of both sets of classification tools.
{"title":"Assessment of Projection Pursuit Index for Classifying High Dimension Low Sample Size Data in R","authors":"Zhaoxing Wu, Chunming Zhang","doi":"10.6339/23-jds1096","DOIUrl":"https://doi.org/10.6339/23-jds1096","url":null,"abstract":"Analyzing “large p small n” data is becoming increasingly paramount in a wide range of application fields. As a projection pursuit index, the Penalized Discriminant Analysis ($mathrm{PDA}$) index, built upon the Linear Discriminant Analysis ($mathrm{LDA}$) index, is devised in Lee and Cook (2010) to classify high-dimensional data with promising results. Yet, there is little information available about its performance compared with the popular Support Vector Machine ($mathrm{SVM}$). This paper conducts extensive numerical studies to compare the performance of the $mathrm{PDA}$ index with the $mathrm{LDA}$ index and $mathrm{SVM}$, demonstrating that the $mathrm{PDA}$ index is robust to outliers and able to handle high-dimensional datasets with extremely small sample sizes, few important variables, and multiple classes. Analyses of several motivating real-world datasets reveal the practical advantages and limitations of individual methods, suggesting that the $mathrm{PDA}$ index provides a useful alternative tool for classifying complex high-dimensional data. These new insights, along with the hands-on implementation of the $mathrm{PDA}$ index functions in the R package classPP, facilitate statisticians and data scientists to make effective use of both sets of classification tools.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320830","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}
High-Order Markov Chains (HOMC) are conventional models, based on transition probabilities, that are used by the United States Department of Agriculture (USDA) National Agricultural Statistics Service (NASS) to study crop-rotation patterns over time. However, HOMCs routinely suffer from sparsity and identifiability issues because the categorical data are represented as indicator (or dummy) variables. In fact, the dimension of the parametric space increases exponentially with the order of HOMCs required for analysis. While parsimonious representations reduce the number of parameters, as has been shown in the literature, they often result in less accurate predictions. Most parsimonious models are trained on big data structures, which can be compressed and efficiently processed using alternative algorithms. Consequently, a thorough evaluation and comparison of the prediction results obtain using a new HOMC algorithm and different types of Deep Neural Networks (DNN) across a range of agricultural conditions is warranted to determine which model is most appropriate for operational crop specific land cover prediction of United States (US) agriculture. In this paper, six neural network models are applied to crop rotation data between 2011 and 2021 from six agriculturally intensive counties, which reflect the range of major crops grown and a variety of crop rotation patterns in the Midwest and southern US. The six counties include: Renville, North Dakota; Perkins, Nebraska; Hale, Texas; Livingston, Illinois; McLean, Illinois; and Shelby, Ohio. Results show the DNN models achieve higher overall prediction accuracy for all counties in 2021. The proposed DNN models allow for the ingestion of long time series data, and robustly achieve higher accuracy values than a new HOMC algorithm considered for predicting crop specific land cover in the US.
{"title":"An Assessment of Crop-Specific Land Cover Predictions Using High-Order Markov Chains and Deep Neural Networks","authors":"L. Sartore, C. Boryan, Andrew Dau, P. Willis","doi":"10.6339/23-jds1098","DOIUrl":"https://doi.org/10.6339/23-jds1098","url":null,"abstract":"High-Order Markov Chains (HOMC) are conventional models, based on transition probabilities, that are used by the United States Department of Agriculture (USDA) National Agricultural Statistics Service (NASS) to study crop-rotation patterns over time. However, HOMCs routinely suffer from sparsity and identifiability issues because the categorical data are represented as indicator (or dummy) variables. In fact, the dimension of the parametric space increases exponentially with the order of HOMCs required for analysis. While parsimonious representations reduce the number of parameters, as has been shown in the literature, they often result in less accurate predictions. Most parsimonious models are trained on big data structures, which can be compressed and efficiently processed using alternative algorithms. Consequently, a thorough evaluation and comparison of the prediction results obtain using a new HOMC algorithm and different types of Deep Neural Networks (DNN) across a range of agricultural conditions is warranted to determine which model is most appropriate for operational crop specific land cover prediction of United States (US) agriculture. In this paper, six neural network models are applied to crop rotation data between 2011 and 2021 from six agriculturally intensive counties, which reflect the range of major crops grown and a variety of crop rotation patterns in the Midwest and southern US. The six counties include: Renville, North Dakota; Perkins, Nebraska; Hale, Texas; Livingston, Illinois; McLean, Illinois; and Shelby, Ohio. Results show the DNN models achieve higher overall prediction accuracy for all counties in 2021. The proposed DNN models allow for the ingestion of long time series data, and robustly achieve higher accuracy values than a new HOMC algorithm considered for predicting crop specific land cover in the US.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71321012","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}
Malignant mesotheliomas are aggressive cancers that occur in the thin layer of tissue that covers most commonly the linings of the chest or abdomen. Though the cancer itself is rare and deadly, early diagnosis will help with treatment and improve outcomes. Mesothelioma is usually diagnosed in the later stages. Symptoms are similar to other, more common conditions. As such, predicting and diagnosing mesothelioma early is essential to starting early treatment for a cancer that is often diagnosed too late. The goal of this comprehensive empirical comparison is to determine the best-performing model based on recall (sensitivity). We particularly wish to avoid false negatives, as it is costly to diagnose a patient as healthy when they actually have cancer. Model training will be conducted based on k-fold cross validation. Random forest is chosen as the optimal model. According to this model, age and duration of asbestos exposure are ranked as the most important features affecting diagnosis of mesothelioma.
{"title":"Binary Classification of Malignant Mesothelioma: A Comparative Study","authors":"Ted Si Yuan Cheng, Xiyue Liao","doi":"10.6339/23-jds1090","DOIUrl":"https://doi.org/10.6339/23-jds1090","url":null,"abstract":"Malignant mesotheliomas are aggressive cancers that occur in the thin layer of tissue that covers most commonly the linings of the chest or abdomen. Though the cancer itself is rare and deadly, early diagnosis will help with treatment and improve outcomes. Mesothelioma is usually diagnosed in the later stages. Symptoms are similar to other, more common conditions. As such, predicting and diagnosing mesothelioma early is essential to starting early treatment for a cancer that is often diagnosed too late. The goal of this comprehensive empirical comparison is to determine the best-performing model based on recall (sensitivity). We particularly wish to avoid false negatives, as it is costly to diagnose a patient as healthy when they actually have cancer. Model training will be conducted based on k-fold cross validation. Random forest is chosen as the optimal model. According to this model, age and duration of asbestos exposure are ranked as the most important features affecting diagnosis of mesothelioma.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320731","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}
Wenru Zhou, Miranda Kroehl, Maxene Meier, A. Kaizer
The use of error spending functions and stopping rules has become a powerful tool for conducting interim analyses. The implementation of an interim analysis is broadly desired not only in traditional clinical trials but also in A/B tests. Although many papers have summarized error spending approaches, limited work has been done in the context of large-scale data that assists in finding the “optimal” boundary. In this paper, we summarized fifteen boundaries that consist of five error spending functions that allow early termination for futility, difference, or both, as well as a fixed sample size design without interim monitoring. The simulation is based on a practical A/B testing problem comparing two independent proportions. We examine sample sizes across a range of values from 500 to 250,000 per arm to reflect different settings where A/B testing may be utilized. The choices of optimal boundaries are summarized using a proposed loss function that incorporates different weights for the expected sample size under a null experiment with no difference between variants, the expected sample size under an experiment with a difference in the variants, and the maximum sample size needed if the A/B test did not stop early at an interim analysis. The results are presented for simulation settings based on adequately powered, under-powered, and over-powered designs with recommendations for selecting the “optimal” design in each setting.
{"title":"Building a Foundation for More Flexible A/B Testing: Applications of Interim Monitoring to Large Scale Data","authors":"Wenru Zhou, Miranda Kroehl, Maxene Meier, A. Kaizer","doi":"10.6339/23-jds1099","DOIUrl":"https://doi.org/10.6339/23-jds1099","url":null,"abstract":"The use of error spending functions and stopping rules has become a powerful tool for conducting interim analyses. The implementation of an interim analysis is broadly desired not only in traditional clinical trials but also in A/B tests. Although many papers have summarized error spending approaches, limited work has been done in the context of large-scale data that assists in finding the “optimal” boundary. In this paper, we summarized fifteen boundaries that consist of five error spending functions that allow early termination for futility, difference, or both, as well as a fixed sample size design without interim monitoring. The simulation is based on a practical A/B testing problem comparing two independent proportions. We examine sample sizes across a range of values from 500 to 250,000 per arm to reflect different settings where A/B testing may be utilized. The choices of optimal boundaries are summarized using a proposed loss function that incorporates different weights for the expected sample size under a null experiment with no difference between variants, the expected sample size under an experiment with a difference in the variants, and the maximum sample size needed if the A/B test did not stop early at an interim analysis. The results are presented for simulation settings based on adequately powered, under-powered, and over-powered designs with recommendations for selecting the “optimal” design in each setting.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320881","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}
The reputation of the maximum pseudolikelihood estimator (MPLE) for Exponential Random Graph Models (ERGM) has undergone a drastic change over the past 30 years. While first receiving broad support, mainly due to its computational feasibility and the lack of alternatives, general opinions started to change with the introduction of approximate maximum likelihood estimator (MLE) methods that became practicable due to increasing computing power and the introduction of MCMC methods. Previous comparison studies appear to yield contradicting results regarding the preference of these two point estimators; however, there is consensus that the prevailing method to obtain an MPLE’s standard error by the inverse Hessian matrix generally underestimates standard errors. We propose replacing the inverse Hessian matrix by an approximation of the Godambe matrix that results in confidence intervals with appropriate coverage rates and that, in addition, enables examining for model degeneracy. Our results also provide empirical evidence for the asymptotic normality of the MPLE under certain conditions.
{"title":"Computing Pseudolikelihood Estimators for Exponential-Family Random Graph Models","authors":"Christian S. Schmid, David R. Hunter","doi":"10.6339/23-jds1094","DOIUrl":"https://doi.org/10.6339/23-jds1094","url":null,"abstract":"The reputation of the maximum pseudolikelihood estimator (MPLE) for Exponential Random Graph Models (ERGM) has undergone a drastic change over the past 30 years. While first receiving broad support, mainly due to its computational feasibility and the lack of alternatives, general opinions started to change with the introduction of approximate maximum likelihood estimator (MLE) methods that became practicable due to increasing computing power and the introduction of MCMC methods. Previous comparison studies appear to yield contradicting results regarding the preference of these two point estimators; however, there is consensus that the prevailing method to obtain an MPLE’s standard error by the inverse Hessian matrix generally underestimates standard errors. We propose replacing the inverse Hessian matrix by an approximation of the Godambe matrix that results in confidence intervals with appropriate coverage rates and that, in addition, enables examining for model degeneracy. Our results also provide empirical evidence for the asymptotic normality of the MPLE under certain conditions.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320816","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}
The least squares (LS) estimator of the autoregressive coefficient in the bifurcating autoregressive (BAR) model was recently shown to suffer from substantial bias, especially for small to moderate samples. This study investigates the impact of the bias in the LS estimator on the behavior of various types of bootstrap confidence intervals for the autoregressive coefficient and introduces methods for constructing bias-corrected bootstrap confidence intervals. We first describe several bootstrap confidence interval procedures for the autoregressive coefficient of the BAR model and present their bias-corrected versions. The behavior of uncorrected and corrected confidence interval procedures is studied empirically through extensive Monte Carlo simulations and two real cell lineage data applications. The empirical results show that the bias in the LS estimator can have a significant negative impact on the behavior of bootstrap confidence intervals and that bias correction can significantly improve the performance of bootstrap confidence intervals in terms of coverage, width, and symmetry.
{"title":"Impact of Bias Correction of the Least Squares Estimation on Bootstrap Confidence Intervals for Bifurcating Autoregressive Models","authors":"T. Elbayoumi, S. Mostafa","doi":"10.6339/23-jds1092","DOIUrl":"https://doi.org/10.6339/23-jds1092","url":null,"abstract":"The least squares (LS) estimator of the autoregressive coefficient in the bifurcating autoregressive (BAR) model was recently shown to suffer from substantial bias, especially for small to moderate samples. This study investigates the impact of the bias in the LS estimator on the behavior of various types of bootstrap confidence intervals for the autoregressive coefficient and introduces methods for constructing bias-corrected bootstrap confidence intervals. We first describe several bootstrap confidence interval procedures for the autoregressive coefficient of the BAR model and present their bias-corrected versions. The behavior of uncorrected and corrected confidence interval procedures is studied empirically through extensive Monte Carlo simulations and two real cell lineage data applications. The empirical results show that the bias in the LS estimator can have a significant negative impact on the behavior of bootstrap confidence intervals and that bias correction can significantly improve the performance of bootstrap confidence intervals in terms of coverage, width, and symmetry.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320777","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}
Vaccine efficacy is a key index to evaluate vaccines in initial clinical trials during the development of vaccines. In particular, it plays a crucial role in authorizing Covid-19 vaccines. It has been reported that Covid-19 vaccine efficacy varies with a number of factors, including demographics of population, time after vaccine administration, and virus strains. By examining clinical trial data of three Covid-19 vaccine studies, we find that current approach to evaluating vaccines with an overall efficacy does not provide desired accuracy. It requires no time frame during which a candidate vaccine is evaluated, and is subject to misuse, resulting in potential misleading information and interpretation. In particular, we illustrate with clinical trial data that the variability of vaccine efficacy is underestimated. We demonstrate that a new method may help to address these caveats. It leads to accurate estimation of the variation of efficacy, provides useful information to define a reasonable time frame to evaluate vaccines, and avoids misuse of vaccine efficacy and misleading information.
{"title":"Covid-19 Vaccine Efficacy: Accuracy Assessment, Comparison, and Caveats","authors":"Wenjiang J. Fu, Jieni Li, P. Scheet","doi":"10.6339/23-jds1089","DOIUrl":"https://doi.org/10.6339/23-jds1089","url":null,"abstract":"Vaccine efficacy is a key index to evaluate vaccines in initial clinical trials during the development of vaccines. In particular, it plays a crucial role in authorizing Covid-19 vaccines. It has been reported that Covid-19 vaccine efficacy varies with a number of factors, including demographics of population, time after vaccine administration, and virus strains. By examining clinical trial data of three Covid-19 vaccine studies, we find that current approach to evaluating vaccines with an overall efficacy does not provide desired accuracy. It requires no time frame during which a candidate vaccine is evaluated, and is subject to misuse, resulting in potential misleading information and interpretation. In particular, we illustrate with clinical trial data that the variability of vaccine efficacy is underestimated. We demonstrate that a new method may help to address these caveats. It leads to accurate estimation of the variation of efficacy, provides useful information to define a reasonable time frame to evaluate vaccines, and avoids misuse of vaccine efficacy and misleading information.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71320716","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}
Sameh Abdulah, Faten S. Alamri, Pratik Nag, Ying Sun, H. Ltaief, D. Keyes, M. Genton
In the last few decades, the size of spatial and spatio-temporal datasets in many research areas has rapidly increased with the development of data collection technologies. As a result, classical statistical methods in spatial statistics are facing computational challenges. For example, the kriging predictor in geostatistics becomes prohibitive on traditional hardware architectures for large datasets as it requires high computing power and memory footprint when dealing with large dense matrix operations. Over the years, various approximation methods have been proposed to address such computational issues, however, the community lacks a holistic process to assess their approximation efficiency. To provide a fair assessment, in 2021, we organized the first competition on spatial statistics for large datasets, generated by our ExaGeoStat software, and asked participants to report the results of estimation and prediction. Thanks to its widely acknowledged success and at the request of many participants, we organized the second competition in 2022 focusing on predictions for more complex spatial and spatio-temporal processes, including univariate nonstationary spatial processes, univariate stationary space-time processes, and bivariate stationary spatial processes. In this paper, we describe in detail the data generation procedure and make the valuable datasets publicly available for a wider adoption. Then, we review the submitted methods from fourteen teams worldwide, analyze the competition outcomes, and assess the performance of each team.
{"title":"The Second Competition on Spatial Statistics for Large Datasets","authors":"Sameh Abdulah, Faten S. Alamri, Pratik Nag, Ying Sun, H. Ltaief, D. Keyes, M. Genton","doi":"10.6339/22-jds1076","DOIUrl":"https://doi.org/10.6339/22-jds1076","url":null,"abstract":"In the last few decades, the size of spatial and spatio-temporal datasets in many research areas has rapidly increased with the development of data collection technologies. As a result, classical statistical methods in spatial statistics are facing computational challenges. For example, the kriging predictor in geostatistics becomes prohibitive on traditional hardware architectures for large datasets as it requires high computing power and memory footprint when dealing with large dense matrix operations. Over the years, various approximation methods have been proposed to address such computational issues, however, the community lacks a holistic process to assess their approximation efficiency. To provide a fair assessment, in 2021, we organized the first competition on spatial statistics for large datasets, generated by our ExaGeoStat software, and asked participants to report the results of estimation and prediction. Thanks to its widely acknowledged success and at the request of many participants, we organized the second competition in 2022 focusing on predictions for more complex spatial and spatio-temporal processes, including univariate nonstationary spatial processes, univariate stationary space-time processes, and bivariate stationary spatial processes. In this paper, we describe in detail the data generation procedure and make the valuable datasets publicly available for a wider adoption. Then, we review the submitted methods from fourteen teams worldwide, analyze the competition outcomes, and assess the performance of each team.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42045278","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}
We describe our implementation of the multivariate Matérn model for multivariate spatial datasets, using Vecchia’s approximation and a Fisher scoring optimization algorithm. We consider various pararameterizations for the multivariate Matérn that have been proposed in the literature for ensuring model validity, as well as an unconstrained model. A strength of our study is that the code is tested on many real-world multivariate spatial datasets. We use it to study the effect of ordering and conditioning in Vecchia’s approximation and the restrictions imposed by the various parameterizations. We also consider a model in which co-located nuggets are correlated across components and find that forcing this cross-component nugget correlation to be zero can have a serious impact on the other model parameters, so we suggest allowing cross-component correlation in co-located nugget terms.
{"title":"Vecchia Approximations and Optimization for Multivariate Matérn Models","authors":"Youssef A. Fahmy, J. Guinness","doi":"10.6339/22-jds1074","DOIUrl":"https://doi.org/10.6339/22-jds1074","url":null,"abstract":"We describe our implementation of the multivariate Matérn model for multivariate spatial datasets, using Vecchia’s approximation and a Fisher scoring optimization algorithm. We consider various pararameterizations for the multivariate Matérn that have been proposed in the literature for ensuring model validity, as well as an unconstrained model. A strength of our study is that the code is tested on many real-world multivariate spatial datasets. We use it to study the effect of ordering and conditioning in Vecchia’s approximation and the restrictions imposed by the various parameterizations. We also consider a model in which co-located nuggets are correlated across components and find that forcing this cross-component nugget correlation to be zero can have a serious impact on the other model parameters, so we suggest allowing cross-component correlation in co-located nugget terms.","PeriodicalId":73699,"journal":{"name":"Journal of data science : JDS","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44042544","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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