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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.

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.

•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.

Although reference dependence plays a central role in explaining behavior, little is known about the way that reference points are selected. This paper identifies empirically which reference point people use in decision under risk. We assume a comprehensive reference-dependent model that nests the main reference-dependent theories, including prospect theory, and that allows for isolating the reference point rule from other behavioral parameters. Our experiment involved high stakes with payoffs up to a week’s salary. We used an optimal design to select the choices in the experiment and Bayesian hierarchical modeling for estimation. The most common reference points were the status quo and a security level (the maximum of the minimal outcomes of the prospects in a choice). We found little support for the use of expectations-based reference points. This paper was accepted by David Simchi-Levi, decision analysis.

A hierarchical Bayesian method is proposed that can be used to fit multiple psychometric functions (PFs) simultaneously across conditions and subjects. The method incorporates the generalized linear model and allows easy reparameterization of the parameters of the PFs, for example, to constrain parameter values across conditions or to code for experimental effects (e.g., main effects and interactions in a factorial design). Simulations indicate that fitting PFs for multiple conditions and observers simultaneously using the hierarchical structure effectively eliminates bias and improves precision in parameter estimates relative to fitting PFs individually in each condition. The method is further validated by analyzing human psychophysical data obtained in an experiment investigating the effect of attention on correspondence matching in an ambiguous long-range motion display. The method converges successfully, even for experiments that use a low number of trials per subject, without the need for fine-tuning by the user and while using the default essentially uninformative priors. The latter may make the method more acceptable to those critical of applying informative priors. The method is implemented in the freely downloadable Palamedes Toolbox, which also includes routines that graphically display the fitted psychometric functions alongside the data, and derive and display posterior distributions of parameters, summary statistics, and diagnostic measures. Overall, these features make hierarchical Bayesian modeling of PFs easily available to researchers who wish to use Bayesian statistics but lack the expertise to implement these methods themselves.

Snow is highly sensitive to atmospheric warming. However, because of the lack of sufficiently long snow avalanche time series and statistical techniques capable of accounting for the numerous biases inherent to sparse and incomplete avalanche records, the evolution of process activity in a warming climate remains little known. Filling this gap requires innovative approaches that put avalanche activity into a long-term context. Here, we combine extensive historical records and Bayesian techniques to construct a 240-y chronicle of snow avalanching in the Vosges Mountains (France). We show evidence that the transition from the late Little Ice Age to the early twentieth century (i.e., 1850 to 1920 CE) was not only characterized by local winter warming in the order of +1.35 °C but that this warming also resulted in a more than sevenfold reduction in yearly avalanche numbers, a severe shrinkage of avalanche size, and shorter avalanche seasons as well as in a reduction of the extent of avalanche-prone terrain. Using a substantial corpus of snow and climate proxy sources, we explain this abrupt shift with increasingly scarcer snow conditions with the low-to-medium elevations of the Vosges Mountains (600 to 1,200 m above sea level [a.s.l.]). As a result, avalanches migrated upslope, with only a relict activity persisting at the highest elevations (release areas >1,200 m a.s.l.). This abrupt, unambiguous response of snow avalanche activity to warming provides valuable information to anticipate likely changes in avalanche behavior in higher mountain environments under ongoing and future warming.

The domain of cognitive control has been a major focus of experimental, neuroscience, and individual differences research. Currently, however, no theory of cognitive control successfully unifies both experimental and individual differences findings. Some perspectives deny that there even exists a unified psychometric cognitive control construct to be measured at all. These shortcomings of the current literature may reflect the fact that current cognitive control paradigms are optimized for the detection of within-subject experimental effects rather than individual differences. In the current study, we examine the psychometric properties of the Dual Mechanisms of Cognitive Control (DMCC) task battery, which was designed in accordance with a theoretical framework that postulates common sources of within-subject and individual differences variation. We evaluated both internal consistency and test–retest reliability, and for the latter, utilized both classical test theory measures (i.e., split-half methods, intraclass correlation) and newer hierarchical Bayesian estimation of generative models. Although traditional psychometric measures suggested poor reliability, the hierarchical Bayesian models indicated a different pattern, with good to excellent test–retest reliability in almost all tasks and conditions examined. Moreover, within-task, between-condition correlations were generally increased when using the Bayesian model-derived estimates, and these higher correlations appeared to be directly linked to the higher reliability of the measures. In contrast, between-task correlations remained low regardless of theoretical manipulations or estimation approach. Together, these findings highlight the advantages of Bayesian estimation methods, while also pointing to the important role of reliability in the search for a unified theory of cognitive control.

There is a growing realization that experimental tasks that produce reliable effects in group comparisons can simultaneously provide unreliable assessments of individual differences. Proposed solutions to this “reliability paradox” range from collecting more test trials to modifying the tasks and/or the way in which effects are measured from these tasks. Here, we systematically compare two proposed modeling solutions in a cognitive conflict task. Using the ratio of individual variability of the conflict effect (i.e., signal) and the trial-by-trial variation in the data (i.e., noise) obtained from Bayesian hierarchical modeling, we examine whether improving statistical modeling may improve the reliability of individual differences assessment in four Stroop datasets. The proposed improvements are (1) increasing the descriptive adequacy of the statistical models from which conflict effects are derived, and (2) using psychologically motivated measures from cognitive measurement models. Our results show that the type of model does not have a consistent effect on the signal-to-noise ratio: the proposed solutions improved reliability in only one of the four datasets. We provide analytical and simulation-based approaches to compute the signal-to-noise ratio for a range of models of varying sophistication and discuss their potential to aid in developing and comparing new measurement solutions to the reliability paradox.

Forecasting productivity and stress across an ecosystem is complicated by the multiple interactions between competing species, the unknown levels of intra- and interspecific trait plasticity, and the dependencies between those traits within individuals. Integrating these features into a trait-based quantitative framework requires a conceptual and quantitative synthesis of how multiple species and their functional traits interact and respond to changing environments, a challenge known in community ecology as the \"fourth-corner problem.\" We propose such a novel synthesis, implemented as an integrated Bayesian hierarchical model. This allows us to (1) simultaneously model trait–trait and trait–environment relationships by explicitly accounting for both intra- and interspecific trait variabilities in a single analysis using all available data types, (2) quantify the strength of the trait–environment relationships, (3) identify trade-offs between multiple traits in multiple species, and (4) faithfully propagate our modeling uncertainties when making species-specific and community-wide trait predictions, reducing false confidence in our spatial prediction results. We apply this integrated approach to the world's largest mangrove forest, the Sundarbans, a sentinel ecosystem impacted simultaneously by both climate change and multiple types of human exploitation. The Sundarbans presents extensive variability in environmental variables, such as salinity and siltation, driven by changing seawater levels from the south and freshwater damming from the north. We find that tree species growing under stress have a typical functional response to the environmental drivers with inter-specific variability around this average, and the amount of variability is further contingent upon the nature and magnitude of the environmental drivers. Our model captures the retreat in traits related to resource acquisition and a plastic enhancement of traits related to resource conservation, both clear indications of stress. We predict that, if historical increases in salinity and siltation are maintained, one-third of whole-ecosystem productivity will be lost by 2050. Our integrated modeling approach bridges community and ecosystem ecology through simultaneously modeling trait–environment correlations and trait–trait tradeoffs at organismal, community, and ecosystem levels; provides a generalizable foundation for powerful modeling of trait-environment linkages under changing environments to predict their consequences on ecosystem functioning and services; and is readily applicable across the Earth's ecosystems.

Mechanics-based dynamic models are commonly used in the design and performance assessment of structural systems, and their accuracy can be improved by integrating models with measured data. This paper provides an overview of hierarchical Bayesian model updating which has been recently developed for probabilistic integration of models with measured data, while accounting for different sources of uncertainties and modeling errors. The proposed hierarchical Bayesian framework allows one to explicitly account for pertinent sources of variability such as ambient temperatures and/or excitation amplitudes, as well as modeling errors, and therefore yields more realistic predictions. The paper reports observations from applications of hierarchical approach to three full-scale civil structural systems, namely (1) a footbridge, (2) a 10-story reinforced concrete (RC) building, and (3) a damaged 2-story RC building. The first application highlights the capability of accounting for temperature effects within the hierarchical framework, while the second application underlines the effects of considering bias for prediction error. Finally, the third application considers the effects of excitation amplitude on structural response. The findings underline the importance and capabilities of the hierarchical Bayesian framework for structural identification. Discussions of its advantages and performance over classical deterministic and Bayesian model updating methods are provided.