cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.9876116
title: Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler

description: For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. Fast simulation from such MRF models is often an important consideration, particularly when repeated generation of large numbers of datasets is required. However, a standard Gibbs strategy for simulating from MRF models involves single-site updates, performed with the conditional univariate distribution of each observation in a sequential manner, whereby a complete Gibbs iteration may become computationally involved even for moderate samples. As an alternative, we describe a general way to simulate from MRF models using Gibbs sampling with “concliques” (i.e., groups of nonneighboring observations). Compared to standard Gibbs sampling, this simulation scheme can be much faster by reducing Gibbs steps and independently updating all observations per conclique at once. The speed improvement depends on the number of concliques relative to the sample size for simulation, and order-of-magnitude speed increases are possible with many MRF models (e.g., having appropriately bounded neighborhoods). We detail the simulation method, establish its validity, and assess its computational performance through numerical studies, where speed advantages are shown for several spatial and network examples. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9954989.v3
title: Heteroscedastic BART via Multiplicative Regression Trees

description: Bayesian additive regression trees (BART) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear response surfaces, its advantages include a matrix-free formulation and the lack of a requirement to prespecify a confining regression basis. Although flexible in fitting the mean, BART has been limited by its reliance on a constant variance error model. Alleviating this limitation, we propose HBART, a nonparametric heteroscedastic elaboration of BART. In BART, the mean function is modeled with a sum of trees, each of which determines an additive contribution to the mean. In HBART, the variance function is further modeled with a product of trees, each of which determines a multiplicative contribution to the variance. Like the mean model, this flexible, multidimensional variance model is entirely nonparametric with no need for the prespecification of a confining basis. Moreover, with this enhancement, HBART can provide insights into the potential relationships of the predictors with both the mean and the variance. Practical implementations of HBART with revealing new diagnostic plots are demonstrated with simulated and real data on used car prices and song year of release. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9786068
title: Solving Fused Penalty Estimation Problems via Block Splitting Algorithms

description: We propose a method for solving a penalized estimation problem in which the penalty function is a function of differences between pairs of parameter vectors. In most cases such a penalty function is not separable in terms of the parameter vectors. This undesirable property often makes large scale estimation difficult with the penalty function. To solve the estimation problem in a separable way, we introduce a set of equality constraints that connect each parameter vector to a group of auxiliary variables. These auxiliary variables allow us to reformulate the estimation problem that is separable either in terms of the parameter vectors or in terms of the auxiliary variables. This separable property further facilitates us to solve the problem with an iterative scheme in that tasks within each iteration can be carried out separately in parallel. Our simulation results show that the iterative scheme has advantages over its traditional counterpart in terms of computational time and memory usage. Additional theoretical analysis shows that the iterative scheme can make the objective function approach to the optimal value with a convergence rate O(r−1), where <i>r</i> is the iteration number. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9876116.v1
title: Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler

description: For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. Fast simulation from such MRF models is often an important consideration, particularly when repeated generation of large numbers of datasets is required. However, a standard Gibbs strategy for simulating from MRF models involves single-site updates, performed with the conditional univariate distribution of each observation in a sequential manner, whereby a complete Gibbs iteration may become computationally involved even for moderate samples. As an alternative, we describe a general way to simulate from MRF models using Gibbs sampling with “concliques” (i.e., groups of nonneighboring observations). Compared to standard Gibbs sampling, this simulation scheme can be much faster by reducing Gibbs steps and independently updating all observations per conclique at once. The speed improvement depends on the number of concliques relative to the sample size for simulation, and order-of-magnitude speed increases are possible with many MRF models (e.g., having appropriately bounded neighborhoods). We detail the simulation method, establish its validity, and assess its computational performance through numerical studies, where speed advantages are shown for several spatial and network examples. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9693164.v3
title: Scalable Bayesian Inference for Coupled Hidden Markov and Semi-Markov Models

description: Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of <i>Escherichia coli</i> O157:H7 in cattle. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9805286
title: The Rational SPDE Approach for Gaussian Random Fields With General Smoothness

description: A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form Lβu=W, where W is Gaussian white noise, <i>L</i> is a second-order differential operator, and β&gt;0 is a parameter that determines the smoothness of <i>u</i>. However, this approach has been limited to the case 2β∈N, which excludes several important models and makes it necessary to keep <i>β</i> fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension d∈N is applicable for any β&gt;d/4, and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function x−β to approximate <i>u</i>. For the resulting approximation, an explicit rate of convergence to <i>u</i> in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case 2β∈N. Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including <i>β</i>. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9954989.v2
title: Heteroscedastic BART via Multiplicative Regression Trees

description: Bayesian additive regression trees (BART) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear response surfaces, its advantages include a matrix-free formulation and the lack of a requirement to prespecify a confining regression basis. Although flexible in fitting the mean, BART has been limited by its reliance on a constant variance error model. Alleviating this limitation, we propose HBART, a nonparametric heteroscedastic elaboration of BART. In BART, the mean function is modeled with a sum of trees, each of which determines an additive contribution to the mean. In HBART, the variance function is further modeled with a product of trees, each of which determines a multiplicative contribution to the variance. Like the mean model, this flexible, multidimensional variance model is entirely nonparametric with no need for the prespecification of a confining basis. Moreover, with this enhancement, HBART can provide insights into the potential relationships of the predictors with both the mean and the variance. Practical implementations of HBART with revealing new diagnostic plots are demonstrated with simulated and real data on used car prices and song year of release. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9954926.v1
title: Longitudinal Principal Component Analysis with an Application to Marketing Data

description: We propose a longitudinal principal component analysis method for multivariate longitudinal data using a random-effects eigen-decomposition, where the eigen-decomposition utilizes longitudinal information through nonparametric splines and the multivariate random effects incorporate significant store-wise heterogeneity. Our method can effectively analyze large marketing data containing sales information for products from hundreds of stores over an 11-year time period. The proposed method leads to more accurate estimation and interpretation compared to existing approaches. We illustrate our method through simulation studies and an application to marketing data from IRI.
DOI: 10.6084/m9.figshare.9693164.v2
title: Scalable Bayesian Inference for Coupled Hidden Markov and Semi-Markov Models

description: Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of <i>Escherichia coli</i> O157:H7 in cattle. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9786068.v2
title: Solving Fused Penalty Estimation Problems via Block Splitting Algorithms

description: We propose a method for solving a penalized estimation problem in which the penalty function is a function of differences between pairs of parameter vectors. In most cases such a penalty function is not separable in terms of the parameter vectors. This undesirable property often makes large scale estimation difficult with the penalty function. To solve the estimation problem in a separable way, we introduce a set of equality constraints that connect each parameter vector to a group of auxiliary variables. These auxiliary variables allow us to reformulate the estimation problem that is separable either in terms of the parameter vectors or in terms of the auxiliary variables. This separable property further facilitates us to solve the problem with an iterative scheme in that tasks within each iteration can be carried out separately in parallel. Our simulation results show that the iterative scheme has advantages over its traditional counterpart in terms of computational time and memory usage. Additional theoretical analysis shows that the iterative scheme can make the objective function approach to the optimal value with a convergence rate O(r−1), where <i>r</i> is the iteration number. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9805286.v3
title: The Rational SPDE Approach for Gaussian Random Fields With General Smoothness

description: A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form Lβu=W, where W is Gaussian white noise, <i>L</i> is a second-order differential operator, and β&gt;0 is a parameter that determines the smoothness of <i>u</i>. However, this approach has been limited to the case 2β∈N, which excludes several important models and makes it necessary to keep <i>β</i> fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension d∈N is applicable for any β&gt;d/4, and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function x−β to approximate <i>u</i>. For the resulting approximation, an explicit rate of convergence to <i>u</i> in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case 2β∈N. Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including <i>β</i>. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9786068.v1
title: Solving Fused Penalty Estimation Problems via Block Splitting Algorithms

description: We propose a method for solving a penalized estimation problem in which the penalty function is a function of differences between pairs of parameter vectors. In most cases such a penalty function is not separable in terms of the parameter vectors. This undesirable property often makes large scale estimation difficult with the penalty function. To solve the estimation problem in a separable way, we introduce a set of equality constraints that connect each parameter vector to a group of auxiliary variables. These auxiliary variables allow us to reformulate the estimation problem that is separable either in terms of the parameter vectors or in terms of the auxiliary variables. This separable property further facilitates us to solve the problem with an iterative scheme in that tasks within each iteration can be carried out separately in parallel. Our simulation results show that the iterative scheme has advantages over its traditional counterpart in terms of computational time and memory usage. Additional theoretical analysis shows that the iterative scheme can make the objective function approach to the optimal value with a convergence rate O(r−1), where <i>r</i> is the iteration number. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.9805286.v2
title: The Rational SPDE Approach for Gaussian Random Fields With General Smoothness

description: A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form Lβu=W, where W is Gaussian white noise, <i>L</i> is a second-order differential operator, and β&gt;0 is a parameter that determines the smoothness of <i>u</i>. However, this approach has been limited to the case 2β∈N, which excludes several important models and makes it necessary to keep <i>β</i> fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension d∈N is applicable for any β&gt;d/4, and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function x−β to approximate <i>u</i>. For the resulting approximation, an explicit rate of convergence to <i>u</i> in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case 2β∈N. Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including <i>β</i>. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11929461.v1
title: Testing for Equivalence of Network Distribution Using Subgraph Counts

description: We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this by deriving the joint asymptotic properties of average subgraph counts as the number of observed networks increases but the number of nodes in each network remains finite. In doing so, we do not require that each observed network contains the same number of nodes, or is drawn from the same distribution. Our results yield joint confidence regions for subgraph counts, and therefore methods for testing whether the observations in a network sample are drawn from: a specified distribution, a specified model, or from the same model as another network sample. We present simulation experiments and an illustrative example on a sample of brain networks where we find that highly creative individuals’ brains present significantly more short cycles than found in less creative people.
DOI: 10.6084/m9.figshare.11594178
title: Calendar-Based Graphics for Visualizing People’s Daily Schedules

description: Calendars are broadly used in society to display temporal information and events. This article describes a new calendar display for plotting data that include a layout algorithm with many options, and faceting functionality. The functions use modular arithmetic on the date variable to restructure the data into a calendar format. The user can apply the grammar of graphics to create plots inside each calendar cell, and thus the displays synchronize neatly with <i>ggplot2</i> graphics. The motivating application is studying pedestrian behavior in Melbourne, Australia, based on counts which are captured at hourly intervals by sensors scattered around the city. Faceting by the usual features such as day and month is insufficient to examine the behavior. Making displays on a monthly calendar format helps to understand pedestrian patterns relative to events such as work days, weekends, holidays, and special events. The functions for the calendar algorithm are available in the R package <i>sugrrants</i>. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11594178.v2
title: Calendar-Based Graphics for Visualizing People’s Daily Schedules

description: Calendars are broadly used in society to display temporal information and events. This article describes a new calendar display for plotting data that include a layout algorithm with many options, and faceting functionality. The functions use modular arithmetic on the date variable to restructure the data into a calendar format. The user can apply the grammar of graphics to create plots inside each calendar cell, and thus the displays synchronize neatly with <i>ggplot2</i> graphics. The motivating application is studying pedestrian behavior in Melbourne, Australia, based on counts which are captured at hourly intervals by sensors scattered around the city. Faceting by the usual features such as day and month is insufficient to examine the behavior. Making displays on a monthly calendar format helps to understand pedestrian patterns relative to events such as work days, weekends, holidays, and special events. The functions for the calendar algorithm are available in the R package <i>sugrrants</i>. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11114498.v2
title: Classification With the Matrix-Variate-<i>t</i> Distribution

description: Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal, or repeated measures. This article develops an expectation-maximization algorithm for discriminant analysis and classification with matrix-variate <i>t</i>-distributions. The methodology shows promise on simulated datasets or when applied to the forensic matching of fractured surfaces or to the classification of functional magnetic resonance, satellite, or hand gestures images. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.11811999.v2
title: Generalized Link-Based Additive Survival Models with Informative Censoring

description: Time to event data differ from other types of data because they are censored. Most of the related estimation techniques assume that the censoring mechanism is noninformative while in many applications it can actually be informative. The aim of this work is to introduce a class of flexible survival models which account for the information provided by the censoring times. The baseline functions are estimated non-parametrically by monotonic P-splines, whereas covariate effects are flexibly determined using additive predictors. Parameter estimation is reliably carried out within a penalized maximum likelihood framework with integrated automatic multiple smoothing parameter selection. We derive the n-consistency and asymptotic normality of the noninformative and informative estimators, and shed light on the efficiency gains produced by the newly introduced informative estimator when compared to its non-informative counterpart. The finite sample properties of the estimators are investigated via a Monte Carlo simulation study which highlights the good empirical performance of the proposal. The modeling framework is illustrated on data about infants hospitalized for pneumonia. The models and methods discussed in the article have been implemented in the R package GJRM to allow for transparent and reproducible research. Supplementary materials for this article are available online.