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Our ability to understand and predict the response of ecosystems to a changing environment depends on quantifying vegetation functional diversity. However, representing this diversity at the global scale is challenging. Typically, in Earth system models, characterization of plant diversity has been limited to grouping related species into plant functional types (PFTs), with all trait variation in a PFT collapsed into a single mean value that is applied globally. Using the largest global plant trait database and state of the art Bayesian modeling, we created fine-grained global maps of plant trait distributions that can be applied to Earth system models. Focusing on a set of plant traits closely coupled to photosynthesis and foliar respiration-specific leaf area (SLA) and dry mass-based concentrations of leaf nitrogen (N-m) and phosphorus (P-m), we characterize how traits vary within and among over 50,000 similar to 50 x 50-km cells across the entire vegetated land surface. We do this in several ways-without defining the PFT of each grid cell and using 4 or 14 PFTs; each model's predictions are evaluated against out-of-sample data. This endeavor advances prior trait mapping by generating global maps that preserve variability across scales by using modern Bayesian spatial statistical modeling in combination with a database over three times larger than that in previous analyses. Our maps reveal that the most diverse grid cells possess trait variability close to the range of global PFT means.

Multi-trait and multi-environment data are common in animal and plant breeding programs. However, what is lacking are more powerful statistical models that can exploit the correlation between traits to improve prediction accuracy in the context of genomic selection (GS). Multi-trait models are more complex than univariate models and usually require more computational resources, but they are preferred because they can exploit the correlation between traits, which many times helps improve prediction accuracy. For this reason, in this paper we explore the power of multi-trait deep learning (MTDL) models in terms of prediction accuracy. The prediction performance of MTDL models was compared to the performance of the Bayesian multi-trait and multi-environment (BMTME) model proposed by Montesinos-López et al. (2016), which is a multi-trait version of the genomic best linear unbiased prediction (GBLUP) univariate model. Both models were evaluated with predictors with and without the genotype×environment interaction term. The prediction performance of both models was evaluated in terms of Pearson’s correlation using cross-validation. We found that the best predictions in two of the three data sets were found under the BMTME model, but in general the predictions of both models, BTMTE and MTDL, were similar. Among models without the genotype×environment interaction, the MTDL model was the best, while among models with genotype×environment interaction, the BMTME model was superior. These results indicate that the MTDL model is very competitive for performing predictions in the context of GS, with the important practical advantage that it requires less computational resources than the BMTME model.

Artificial intelligence (AI) and machine learning models are being increasingly deployed in real-world applications. In many of these applications, there is strong motivation to develop hybrid systems in which humans and AI algorithms can work together, leveraging their complementary strengths and weaknesses. We develop a Bayesian framework for combining the predictions and different types of confidence scores from humans and machines. The framework allows us to investigate the factors that influence complementarity, where a hybrid combination of human and machine predictions leads to better performance than combinations of human or machine predictions alone. We apply this framework to a large-scale dataset where humans and a variety of convolutional neural networks perform the same challenging image classification task. We show empirically and theoretically that complementarity can be achieved even if the human and machine classifiers perform at different accuracy levels as long as these accuracy differences fall within a bound determined by the latent correlation between human and machine classifier confidence scores. In addition, we demonstrate that hybrid human–machine performance can be improved by differentiating between the errors that humans and machine classifiers make across different class labels. Finally, our results show that eliciting and including human confidence ratings improve hybrid performance in the Bayesian combination model. Our approach is applicable to a wide variety of classification problems involving human and machine algorithms.

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.

•Development and presentation of normative modeling approach based on hierarchical Bayesian modeling that can be applied to large multi-site neuroimaging data sets.•Comparison of performance of hierarchical Bayesian model including site as covariate to several common ways to harmonize for multi-site effects.•Presentation of normative modeling as site correction tool. The potential of normative modeling to make individualized predictions from neuroimaging data has enabled inferences that go beyond the case-control approach. However, site effects are often confounded with variables of interest in a complex manner and can bias estimates of normative models, which has impeded the application of normative models to large multi-site neuroimaging data sets. In this study, we suggest accommodating for these site effects by including them as random effects in a hierarchical Bayesian model. We compared the performance of a linear and a non-linear hierarchical Bayesian model in modeling the effect of age on cortical thickness. We used data of 570 healthy individuals from the ABIDE (autism brain imaging data exchange) data set in our experiments. In addition, we used data from individuals with autism to test whether our models are able to retain clinically useful information while removing site effects. We compared the proposed single stage hierarchical Bayesian method to several harmonization techniques commonly used to deal with additive and multiplicative site effects using a two stage regression, including regressing out site and harmonizing for site with ComBat, both with and without explicitly preserving variance caused by age and sex as biological variation of interest, and with a non-linear version of ComBat. In addition, we made predictions from raw data, in which site has not been accommodated for. The proposed hierarchical Bayesian method showed the best predictive performance according to multiple metrics. Beyond that, the resulting z-scores showed little to no residual site effects, yet still retained clinically useful information. In contrast, performance was particularly poor for the regression model and the ComBat model in which age and sex were not explicitly modeled. In all two stage harmonization models, predictions were poorly scaled, suffering from a loss of more than 90% of the original variance. Our results show the value of hierarchical Bayesian regression methods for accommodating site variation in neuroimaging data, which provides an alternative to harmonization techniques. While the approach we propose may have broad utility, our approach is particularly well suited to normative modeling where the primary interest is in accurate modeling of inter-subject variation and statistical quantification of deviations from a reference model.

Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covariates are partially (or totally) different than those of the observed locations and those in which we want to predict. As a result, we present two different models depending on the fact that there is uncertainty on the covariates or not. In both cases, Bayesian inference on the parameters and prediction of presence/absence in new locations are made by considering the model as a latent Gaussian model, which allows the use of the integrated nested Laplace approximation. In particular, the spatial effect is implemented with the stochastic partial differential equation approach. The methodology is evaluated on the presence of the Fasciola hepatica in Galicia, a North-West region of Spain.

The concentration of radiocarbon (14C) differs between ocean and atmosphere. Radiocarbon determinations from samples which obtained their 14C in the marine environment therefore need a marine-specific calibration curve and cannot be calibrated directly against the atmospheric-based IntCal20 curve. This paper presents Marine20, an update to the internationally agreed marine radiocarbon age calibration curve that provides a non-polar global-average marine record of radiocarbon from 0–55 cal kBP and serves as a baseline for regional oceanic variation. Marine20 is intended for calibration of marine radiocarbon samples from non-polar regions; it is not suitable for calibration in polar regions where variability in sea ice extent, ocean upwelling and air-sea gas exchange may have caused larger changes to concentrations of marine radiocarbon. The Marine20 curve is based upon 500 simulations with an ocean/atmosphere/biosphere box-model of the global carbon cycle that has been forced by posterior realizations of our Northern Hemispheric atmospheric IntCal20 14C curve and reconstructed changes in CO2 obtained from ice core data. These forcings enable us to incorporate carbon cycle dynamics and temporal changes in the atmospheric 14C level. The box-model simulations of the global-average marine radiocarbon reservoir age are similar to those of a more complex three-dimensional ocean general circulation model. However, simplicity and speed of the box model allow us to use a Monte Carlo approach to rigorously propagate the uncertainty in both the historic concentration of atmospheric 14C and other key parameters of the carbon cycle through to our final Marine20 calibration curve. This robust propagation of uncertainty is fundamental to providing reliable precision for the radiocarbon age calibration of marine based samples. We make a first step towards deconvolving the contributions of different processes to the total uncertainty; discuss the main differences of Marine20 from the previous age calibration curve Marine13; and identify the limitations of our approach together with key areas for further work. The updated values for ΔR, the regional marine radiocarbon reservoir age corrections required to calibrate against Marine20, can be found at the data base http://calib.org/marine/.

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.

Recent work at Vinča-Belo Brdo has combined a total of more than 200 radiocarbon dates with an array of other information to construct much more precise narratives for the structural history of the site and the cultural materials recovered from it. In this paper, we present the results of a recent attempt to construct formal models for the chronology of the wider Vinča potscape, so that we can place our now detailed understanding of changes at Belo Brdo within their contemporary contexts. We present our methodology for assessing the potential of the existing corpus of more than 600 radiocarbon dates for refining the chronology of the five phases of Vinča ceramics proposed by Milojčić across their spatial ranges, including a total of 490 of them in a series of Bayesian chronological models. Then we outline our main results for the development of Vinča pottery. Finally, we discuss some of the major implications for our understanding of the source, character and tempo of material change.