Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS478 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonstationary cross-covariance models for multivariate processes on a globe

ABSTRACT. In geophysical and environmental problems, it is common to have multiple variables of interest measured at the same location and time. These multiple variables typically have dependence over space (and/or time). As a consequence, there is a growing interest in developing models for multivariate spatial processes, in particular, the cross-covariance models. On the other hand, many data sets these days cover a large portion of the Earth such as satellite data, which require valid covariance models on a globe. We present a class of parametric covariance models for multivariate processes on a globe. The covariance models are flexible in capturing non-stationarity in the data yet computationally feasible and require moderate numbers of parameters. We apply our covariance model to surface temperature and precipitation data from an NCAR climate model output. We compare our model to the multivariate version of the Matérn cross-covariance function and models based on coregionalization and demonstrate the superior performance of our model in terms of AIC (and/or maximum loglikelihood values) and predictive skill. We also present some challenges in modelling the cross-covariance structure of the temperature and precipitation data. Based on the fitted results using full data, we give the estimated cross-correlation structure between the two variables

Flexible Spatio-Temporal Hawkes Process Models for Earthquake Occurrences

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space-time interactions between aftershocks with a non-separable spatio-temporal triggering structure. For model estimation, we extend the model-independent stochastic declustering (MISD) algorithm and suggest substituting its histogram-based estimators with kernel methods. We demonstrate the utility of the proposed methods by applying them to the seismicity data in regions with active seismic activities.Comment: 53 page

Local eigenvalue analysis of CMIP3 climate model errors

Of the two dozen or so global atmosphere—ocean general circulation models (AOGCMs), many share parameterizations, components or numerical schemes, and several are developed by the same institutions. Thus it is natural to suspect that some of the AOGCMs have correlated error patterns. Here we present a local eigenvalue analysis for the AOGCM errors based on statistically quantified correlation matrices for these errors. Our statistical method enables us to assess the significance of the result based on the simulated data under the assumption that all AOGCMs are independent. The result reveals interesting local features of the dependence structure of AOGCM errors. At least for the variable and the timescale considered here, the Coupled Model Intercomparison Project phase 3 (CMIP3) model archive cannot be treated as a collection of independent models.We use multidimensional scaling to visualize the similarity of AOGCMs and all-subsets regression to provide subsets of AOGCMs that are the best approximation to the variation among the full set of models.ISSN:0280-6495ISSN:1600-087

Nonstationary covariance models for global data

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS183 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

bizicount: Bivariate Zero-Inflated Count Copula Regression Using R

Two common issues arise in regression modelling of bivariate count data: (i) dependence across outcomes, and (ii) excess zero counts (i.e., zero inflation). However, there are currently few options to estimate bivariate zero-inflated count regression models in R. Therefore, we present an R package, bizicount, that enables researchers to easily estimate bivariate zero-inflated count copula regression models. By using copulas to model the dependence across outcomes, researchers do not have to make assumptions about the multivariate (and zero-inflated) structure relating their count variables to one another. Instead, they are only required to make familiar assumptions about the marginal distribution of each outcome variable, which should enable wider use of our approach. Below we present our proposed estimator, detail its advantages over existing alternatives, and demonstrate the use of the corresponding functions for bivariate modeling of terrorism data from Nigeria

Validation of CMIP5 multimodel ensembles through the smoothness of climate variables

Smoothness is an important characteristic of a spatial process that measures local variability. If climate model outputs are realistic, then not only the values at each grid pixel but also the relative variation over nearby pixels should represent the true climate. We estimate the smoothness of long-term averages for land surface temperature anomalies in the Coupled Model Intercomparison Project Phase 5 (CMIP5), and compare them by climate regions and seasons. We also compare the estimated smoothness of the climate outputs in CMIP5 with those of reanalysis data. The estimation is done through the composite likelihood approach for locally self-similar processes. The composite likelihood that we consider is a product of conditional likelihoods of neighbouring observations. We find that the smoothness of the surface temperature anomalies in CMIP5 depends primarily on the modelling institution and on the climate region. The seasonal difference in the smoothness is generally small, except for some climate regions where the average temperature is extremely high or low

Prediction of Tropical Pacific Rain Rates with Over-parameterized Neural Networks

The prediction of tropical rain rates from atmospheric profiles poses significant challenges, mainly due to the heavy-tailed distribution exhibited by tropical rainfall. This study introduces over-parameterized neural networks not only to forecast tropical rain rates, but also to explain their heavy-tailed distribution. The prediction is separately conducted for three rain types (stratiform, deep convective, and shallow convective) observed by the Global Precipitation Measurement satellite radar over the West and East Pacific regions. Atmospheric profiles of humidity, temperature, and zonal and meridional winds from the MERRA-2 reanalysis are considered as features. Although over-parameterized neural networks are well-known for their "double descent phenomenon," little has been explored about their applicability to climate data and capability of capturing the tail behavior of data. In our results, over-parameterized neural networks accurately predict the rain rate distributions and outperform other machine learning methods. Spatial maps show that over-parameterized neural networks also successfully describe spatial patterns of each rain type across the tropical Pacific. In addition, we assess the feature importance for each over-parameterized neural network to provide insight into the key factors driving the predictions, with low-level humidity and temperature variables being the overall most important. These findings highlight the capability of over-parameterized neural networks in predicting the distribution of the rain rate and explaining extreme values

Effects of ACT Out! Social Issue Theater on Social-Emotional Competence and Bullying in Youth and Adolescents: Cluster Randomized Controlled Trial

Background: Schools increasingly prioritize social-emotional competence and bullying and cyberbullying prevention, so the development of novel, low-cost, and high-yield programs addressing these topics is important. Further, rigorous assessment of interventions prior to widespread dissemination is crucial. Objective: This study assesses the effectiveness and implementation fidelity of the ACT Out! Social Issue Theater program, a 1-hour psychodramatic intervention by professional actors; it also measures students' receptiveness to the intervention. Methods: This study is a 2-arm cluster randomized control trial with 1:1 allocation that randomized either to the ACT Out! intervention or control (treatment as usual) at the classroom level (n=76 classrooms in 12 schools across 5 counties in Indiana, comprised of 1571 students at pretest in fourth, seventh, and tenth grades). The primary outcomes were self-reported social-emotional competence, bullying perpetration, and bullying victimization; the secondary outcomes were receptiveness to the intervention, implementation fidelity (independent observer observation), and prespecified subanalyses of social-emotional competence for seventh- and tenth-grade students. All outcomes were collected at baseline and 2-week posttest, with planned 3-months posttest data collection prevented due to the COVID-19 pandemic. Results: Intervention fidelity was uniformly excellent (>96% adherence), and students were highly receptive to the program. However, trial results did not support the hypothesis that the intervention would increase participants' social-emotional competence. The intervention's impact on bullying was complicated to interpret and included some evidence of small interaction effects (reduced cyberbullying victimization and increased physical bullying perpetration). Additionally, pooled within-group reductions were also observed and discussed but were not appropriate for causal attribution. Conclusions: This study found no superiority for a 1-hour ACT Out! intervention compared to treatment as usual for social-emotional competence or offline bullying, but some evidence of a small effect for cyberbullying. On the basis of these results and the within-group effects, as a next step, we encourage research into whether the ACT Out! intervention may engender a bystander effect not amenable to randomization by classroom. Therefore, we recommend a larger trial of the ACT Out! intervention that focuses specifically on cyberbullying, measures bystander behavior, is randomized by school, and is controlled for extant bullying prevention efforts at each school.Funding for this study was provided by Lilly Endowment Inc, grant no. 2019 0543, to Claude McNeal Productions. Funding was provided to Prevention Insights via a subaward from that grant. Claude McNeal Productions and their representatives own the rights to the ACT Out! Social Issue Theater program. No one from that organization was involved in preparing the study protocol, interpreting findings, conducting analyses, or writing this manuscript, both as a matter of practice and per written agreement in the subaward to Prevention Insights