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Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, so proxy observations from natural archives are often considered. We describe a model-based approach to reconstructing climate defined in terms of raw tree-ring measurement data that simultaneously accounts for nonclimatic and climatic variability. In this approach, we specify a joint model for the tree-ring data and climate variable that we fit using Bayesian inference. We consider a range of prior densities and compare the modeling approach to current methodology using an example case of Scots pine from Torneträsk, Sweden, to reconstruct growing season temperature. We describe how current approaches translate into particular model assumptions. We explore how changes to various components in the model-based approach affect the resulting reconstruction. We show that minor changes in model specification can have little effect on model fit but lead to large changes in the predictions. In particular, the periods of relatively warmer and cooler temperatures are robust between models, but the magnitude of the resulting temperatures is highly model dependent. Such sensitivity may not be apparent with traditional approaches because the underlying statistical model is often hidden or poorly described. Supplementary materials for this article are available online.

This study analyzed the reporting of multilevel modeling applications of a sample of 99 articles from 13 peer-reviewed journals in education and the social sciences. A checklist, derived from the methodological literature on multilevel modeling and focusing on the issues of model development and specification, data considerations, estimation, and inference, was used to analyze the articles. The most common applications were two-level models where individuals were nested within contexts. Most studies were non-experimental and used nonprobability samples. The amount of data at each level varied widely across studies, as did the number of models examined. Analyses of reporting practices indicated some clear problems, with many articles not reporting enough information for a reader to critique the reported analyses. For example, in many articles, one could not determine how many models were estimated, what covariance structure was assumed, what type of centering if any was used, whether the data were consistent with assumptions, whether outliers were present, or how the models were estimated. Guidelines for researchers reporting multilevel analyses are provided.

The purpose of this mixed-methods experimental study was to investigate the effects and social validity of a text structure intervention for reading and writing in upper elementary grades. Fourth- and fifth-grade teachers (N = 11) in three elementary schools were randomly assigned to implement the text structure intervention or a comprehension strategies intervention. The student sample (N = 351) comprised 160 students who received the text structure intervention and 191 students who received the comprehension strategies intervention, across grades 4 and 5. Quantitative measures of text structure awareness, reading comprehension, and writing quality were analyzed using three-level hierarchical linear modeling. Qualitative interviews were analyzed typologically to assess upper elementary teachers’ perceptions of the social validity of each intervention. Quantitative results indicated that students who received the text structure intervention outperformed the students who received the comprehension strategies intervention on a measure of text structure awareness, a graphic organizer task, and use of ideas and details in informational writing. Qualitative findings indicated that teachers found the goals, procedures, and effects of the text structure intervention to be socially valid for upper elementary grades.

The effectiveness of mask wearing at controlling severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission has been unclear. While masks are known to substantially reduce disease transmission in healthcare settings [D. K. Chu et al., Lancet 395, 1973–1987 (2020); J. Howard et al., Proc. Natl. Acad. Sci. U.S.A. 118, e2014564118 (2021); Y. Cheng et al., Science eabg6296 (2021)], studies in community settings report inconsistent results [H. M. Ollila et al., medRxiv (2020); J. Brainard et al., Eurosurveillance 25, 2000725 (2020); T. Jefferson et al., Cochrane Database Syst. Rev. 11, CD006207 (2020)]. Most such studies focus on how masks impact transmission, by analyzing how effective government mask mandates are. However, we find that widespread voluntary mask wearing, and other data limitations, make mandate effectiveness a poor proxy for mask-wearing effectiveness. We directly analyze the effect of mask wearing on SARS-CoV-2 transmission, drawing on several datasets covering 92 regions on six continents, including the largest survey of wearing behavior (n = 20 million) [F. Kreuter et al., https://gisumd.github.io/COVID-19-API-Documentation (2020)]. Using a Bayesian hierarchical model, we estimate the effect of mask wearing on transmission, by linking reported wearing levels to reported cases in each region, while adjusting for mobility and nonpharmaceutical interventions (NPIs), such as bans on large gatherings. Our estimates imply that the mean observed level of mask wearing corresponds to a 19% decrease in the reproduction number R. We also assess the robustness of our results in 60 tests spanning 20 sensitivity analyses. In light of these results, policy makers can effectively reduce transmission by intervening to increase mask wearing.

Assays using ELISA measurements on serially diluted serum samples have been heavily used to measure serum reactivity to SARS-CoV-2 antigens and are widely used in virology and elsewhere in biology. We test a method using Bayesian hierarchical modelling to reduce the workload of these assays and measure reactivity of SARS-CoV-2 and HCoV antigens to human serum samples collected before and during the COVID-19 pandemic. Inflection titers for SARS-CoV-2 full-length spike protein (S1S2), spike protein receptor-binding domain (RBD), and nucleoprotein (N) inferred from 3 spread-out dilutions correlated with those inferred from 8 consecutive dilutions with an R2 value of 0.97 or higher. We confirm existing findings showing a small proportion of pre-pandemic human serum samples contain cross-reactive antibodies to SARS-CoV-2 S1S2 and N, and that SARS-CoV-2 infection increases serum reactivity to the beta-HCoVs OC43 and HKU1 S1S2. In serial dilution assays, large savings in resources and/or increases in throughput can be achieved by reducing the number of dilutions measured and using Bayesian hierarchical modelling to infer inflection or endpoint titers. We have released software for conducting these types of analysis.

Automated Writing Evaluation (AWE) provides automatic writing feedback and scoring to support student writing and revising. The purpose of the present study was to analyze a statewide implementation of an AWE software (n=114,582) in grades 4-11. The goals of the study were to evaluate (a) to what extent AWE features were used, (b) if equity and access issues influenced AWE usage, and (c) if AWE usage was associated with writing performance on a large-scale state writing assessment. Descriptive statistics and hierarchical linear modeling were used to answer the research questions. Results indicated that the main feature of AWE (i.e., writing and revising essays) were used but some features (peer review and independent lessons) were underutilized. School and student level demographic variables explained little variance in AWE usage. AWE usage was statistically and positively associated with performance on a large-scale state writing assessment when controlling for prior performance and demographics. The study presents evidence that AWE can positively influence writing on a distal measure when implemented at-scale. Implications for large-scale AWE implementation are discussed.

Gerard et al. highlight several issues encountered when genotyping polyploid organisms from next-generation sequencing data, including allelic bias, overdispersion, and outlying observations. They present modeling solutions and software to account for these issues... Detecting and quantifying the differences in individual genomes (i.e., genotyping), plays a fundamental role in most modern bioinformatics pipelines. Many scientists now use reduced representation next-generation sequencing (NGS) approaches for genotyping. Genotyping diploid individuals using NGS is a well-studied field, and similar methods for polyploid individuals are just emerging. However, there are many aspects of NGS data, particularly in polyploids, that remain unexplored by most methods. Our contributions in this paper are fourfold: (i) We draw attention to, and then model, common aspects of NGS data: sequencing error, allelic bias, overdispersion, and outlying observations. (ii) Many datasets feature related individuals, and so we use the structure of Mendelian segregation to build an empirical Bayes approach for genotyping polyploid individuals. (iii) We develop novel models to account for preferential pairing of chromosomes, and harness these for genotyping. (iv) We derive oracle genotyping error rates that may be used for read depth suggestions. We assess the accuracy of our method in simulations, and apply it to a dataset of hexaploid sweet potato (Ipomoea batatas). An R package implementing our method is available at https://cran.r-project.org/package=updog.

In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient-but at the same time intuitive-framework for the resolution of perceptual uncertainty in behaving agents.

Recently, a challenge in defence modelling and simulation is that simulating a satisfactory number of scenarios often requires an infeasible runtime. This paper resolves this challenge by utilizing a tabulation technique that encourages reuses of the previous simulation results in hierarchical models. For example, a mission-level model may contain a number of similar engagement scenarios that must be executed multiple times by an engagement-level model. Therefore, we collapse the multiple similar executions into a single simulation run while verifying the statistical stability in the output distribution. This reuse is supported by adapting the tabulation technique to hierarchical models with the extension of an interpolation in matching the lower abstractions. An application in the naval air defence domain shows that the simulation is speeded up a maximum of seven times, while producing statistically identical simulation results with few increments in the variance.

The ongoing global change and the increased interest in macroecological processes call for the analysis of spatially extensive data on species communities to understand and forecast distributional changes of biodiversity. Recently developed joint species distribution models can deal with numerous species efficiently, while explicitly accounting for spatial structure in the data. However, their applicability is generally limited to relatively small spatial data sets because of their severe computational scaling as the number of spatial locations increases. In this work, we propose a practical alleviation of this scalability constraint for joint species modeling by exploiting two spatial-statistics techniques that facilitate the analysis of large spatial data sets: Gaussian predictive process and nearest-neighbor Gaussian process. We devised an efficient Gibbs posterior sampling algorithm for Bayesian model fitting that allows us to analyze community data sets consisting of hundreds of species sampled from up to hundreds of thousands of spatial units. The performance of these methods is demonstrated using an extensive plant data set of 30,955 spatial units as a case study. We provide an implementation of the presented methods as an extension to the hierarchical modeling of species communities framework.