cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.963479.v3
title: On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

description: Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.
DOI: 10.6084/m9.figshare.963480.v2
title: Functional Generalized Additive Models

description: We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to <i>t</i> of <i>F</i>{<i>X</i>(<i>t</i>), <i>t</i>} where <i>F</i>(·, ·) is an unknown regression function and <i>X</i>(<i>t</i>) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate <i>F</i>(·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where <i>X</i>(<i>t</i>) is a signal from diffusion tensor imaging at position, <i>t</i>, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.
DOI: 10.6084/m9.figshare.963481.v3
title: Robust Parametric Classification and Variable Selection by a Minimum Distance Criterion

description: We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, that is, shrink toward the zero vector. Thus, using LASSO-like penalties to perform variable selection in the presence of outliers can result in missed detections of relevant covariates. We show that by choosing a minimum distance criterion together with an elastic net penalty, we can simultaneously find a parsimonious model and avoid estimation implosion even in the presence of many outliers in the important small <i>n</i> large <i>p</i> situation. Minimizing the penalized minimum distance criterion is a challenging problem due to its nonconvexity. To meet the challenge, we develop a simple and efficient MM (majorization–minimization) algorithm that can be adapted gracefully to the small <i>n</i> large <i>p</i> context. Performance of our algorithm is evaluated on simulated and real datasets. This article has supplementary materials available online.
DOI: 10.6084/m9.figshare.963476
title: The Bayesian Change Point and Variable Selection Algorithm: Application to the δ<sup>18</sup>O Proxy Record of the Plio-Pleistocene

description: In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.
DOI: 10.6084/m9.figshare.963478.v3
title: Approximate Bayesian Computation and Bayes’ Linear Analysis: Toward High-Dimensional ABC

description: Bayes’ linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article, we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first- and second-order moment summaries approximate adjusted expectation and variance for a Bayes’ linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using Markov chain Monte Carlo for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963479.v2
title: On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

description: Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.
DOI: 10.6084/m9.figshare.963475
title: Shape-Constrained Estimation Using Nonnegative Splines

description: We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.
DOI: 10.6084/m9.figshare.963478.v2
title: Approximate Bayesian Computation and Bayes’ Linear Analysis: Toward High-Dimensional ABC

description: Bayes’ linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article, we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first- and second-order moment summaries approximate adjusted expectation and variance for a Bayes’ linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using Markov chain Monte Carlo for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.963481.v2
title: Robust Parametric Classification and Variable Selection by a Minimum Distance Criterion

description: We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, that is, shrink toward the zero vector. Thus, using LASSO-like penalties to perform variable selection in the presence of outliers can result in missed detections of relevant covariates. We show that by choosing a minimum distance criterion together with an elastic net penalty, we can simultaneously find a parsimonious model and avoid estimation implosion even in the presence of many outliers in the important small <i>n</i> large <i>p</i> situation. Minimizing the penalized minimum distance criterion is a challenging problem due to its nonconvexity. To meet the challenge, we develop a simple and efficient MM (majorization–minimization) algorithm that can be adapted gracefully to the small <i>n</i> large <i>p</i> context. Performance of our algorithm is evaluated on simulated and real datasets. This article has supplementary materials available online.
DOI: 10.6084/m9.figshare.963476.v1
title: The Bayesian Change Point and Variable Selection Algorithm: Application to the δ<sup>18</sup>O Proxy Record of the Plio-Pleistocene

description: In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.
DOI: 10.6084/m9.figshare.963470
title: A glacial geomorphological map of the southernmost ice lobes of Patagonia: the Bahía Inútil – San Sebastián, Magellan, Otway, Skyring and Río Gallegos lobes

description: This paper presents a glacial geomorphological map of the landforms created by five large ice lobes that extended eastwards from the southernmost reaches of the Patagonian Ice Sheet during the Quaternary period. The study is focussed on Tierra del Fuego, but also updates previous mapping of the Skyring and Otway lobes, and the resulting level of detail and extent is a significant advance on previous work in the region. The map has been created as the necessary precursor for an improved understanding of the glacial history of the region, and to underpin a programme of dating glacial limits in the region. It was produced using Landsat ETM+ and ASTER satellite imagery and vertical aerial photography, supplemented by Google Earth™ imagery and field-checking. Eleven landform types were mapped: moraine ridges, subdued moraine topography, kettle-kame topography, glacial lineations, irregular and regular hummocky terrain, irregular dissected ridges, eskers, meltwater channels, former shorelines and outwash plains. The map reveals three important characteristics of the glacial geomorphology. First, the geomorphic systems are largely dominated by landforms associated with meltwater (channels, outwash plains and kettle-kame topography). Second, there is a difference in the nature of landforms associated with the northern three ice lobes, where limits are generally marked by numerous clear moraine ridges, compared to those to the south, where hummocky terrain and drift limits prevail. Finally, cross-cutting landforms offer evidence of multiple advances, in places, which has implications for the timing of limit deposition, and thus for the design and interpretation of a dating programme.
DOI: 10.6084/m9.figshare.963475.v1
title: Shape-Constrained Estimation Using Nonnegative Splines

description: We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.
DOI: 10.6084/m9.figshare.963476.v3
title: The Bayesian Change Point and Variable Selection Algorithm: Application to the δ<sup>18</sup>O Proxy Record of the Plio-Pleistocene

description: In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.
DOI: 10.6084/m9.figshare.963475.v3
title: Shape-Constrained Estimation Using Nonnegative Splines

description: We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.
DOI: 10.6084/m9.figshare.963476.v2
title: The Bayesian Change Point and Variable Selection Algorithm: Application to the δ<sup>18</sup>O Proxy Record of the Plio-Pleistocene

description: In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.