Bayesian Hierarchical Modeling Approach Research Articles

The evolution of thermal performance curves in fungi farmed by attine ant mutualists in aboveground or belowground microclimates.

Fungi are abundant and ecologically important at a global scale, but little is known about whether their thermal adaptations are shaped by biochemical constraints (i.e. the Hotter is Better Model, HBM) or evolutionary tradeoffs (i.e., the Specialist Generalist Model, SGM). We tested these hypotheses by generating thermal performance curves (TPCs) of fungal cultivars farmed by six species of Panamanian fungus-farming 'attine' ants. These fungi represent evolutionary transitions in farming strategies as four cultivars are farmed by ants belowground at stable temperatures near 25°C and two cultivars are farmed aboveground at variable temperatures. We generated TPCs using a common garden experiment confining fungal isolates to different temperatures and then used a Bayesian hierarchical modeling approach to compare competing temperature sensitivity models. Some thermal performance traits differed consistently across farming strategies, with aboveground cultivars having: 1) higher tolerance to low temperatures (CTLmin) and 2) higher maximum growth rate at the optimal temperature (rmax). However, two core assumptions shared by the HBM or SGM were not supported as aboveground cultivars did not show systematic increases in either their optimal temperature (Topt) or thermal tolerance breadth. These results harness ant farming systems as long-term natural experiments to decouple the effects of environmental thermal variation and innate physiological temperature sensitivity on fungal thermal evolution. The results have clear implications for predicting climate warming induced breaking points in animal-microbe mutualisms.

Mapping Forest Carbon Stock Distribution in a Subtropical Region with the Integration of Airborne Lidar and Sentinel-2 Data

Forest carbon stock is an important indicator reflecting a forest ecosystem’s structures and functions. Its spatial distribution is valuable for managing natural resources, protecting ecosystems and biodiversity, and further promoting sustainability, but accurately mapping the forest carbon stock distribution in a large area is a challenging task. This study selected Changting County, Fujian Province, as a case study to explore a method to map the forest carbon stock distribution using the integration of airborne Lidar, Sentinel-2, and ancillary data in 2022. The Bayesian hierarchical modeling approach was used to estimate the local forest carbon stock based on airborne Lidar data and field measurements, and then the random forest approach was used to develop a regional forest carbon stock estimation model based on the Sentinel-2 and ancillary data. The results indicated that the Lidar-based carbon stock distribution effectively provided sample plots with good spatial representativeness for modeling regional carbon stock with a coefficient of determination (R2) of 0.7 and root mean square error (RMSE) of 12.94 t/ha. The average carbon stocks were 48.55 t/ha, 55.51 t/ha, and 57.04 t/ha for Masson pine, Chinese fir, and broadleaf forests, respectively. The carbon stock in non-conservation regions was 15.2–16.1 t/ha higher than that in conservation regions. This study provides a promising method through the use of airborne Lidar data as a linkage between sample plots and Sentinel-2 data to map the regional carbon stock distribution in those subtropical regions where serious soil erosion has led to a relatively sparse forest canopy density. The results are valuable for local government to make scientific decisions for promoting ecosystem restoration due to water and soil erosion.

Evaluating the direct effect of vaccination and non-pharmaceutical interventions during the COVID-19 pandemic in Europe

BackgroundAcross Europe, countries have responded to the COVID-19 pandemic with a combination of non-pharmaceutical interventions and vaccination. Evaluating the effectiveness of such interventions is of particular relevance to policy-makers.MethodsWe leverage almost three years of available data across 38 European countries to evaluate the effectiveness of governmental responses in controlling the pandemic. We developed a Bayesian hierarchical model that flexibly relates daily COVID-19 incidence to past levels of vaccination and non-pharmaceutical interventions as summarised in the Stringency Index. Specifically, we use a distributed lag approach to temporally weight past intervention values, a tensor-product smooth to capture non-linearities and interactions between both types of interventions, and a hierarchical approach to parsimoniously address heterogeneity across countries.ResultsWe identify a pronounced negative association between daily incidence and the strength of non-pharmaceutical interventions, along with substantial heterogeneity in effectiveness among European countries. Similarly, we observe a strong but more consistent negative association with vaccination levels. Our results show that non-linear interactions shape the effectiveness of interventions, with non-pharmaceutical interventions becoming less effective under high vaccination levels. Finally, our results indicate that the effects of interventions on daily incidence are most pronounced at a lag of 14 days after being in place.ConclusionsOur Bayesian hierarchical modelling approach reveals clear negative and lagged effects of non-pharmaceutical interventions and vaccination on confirmed COVID-19 cases across European countries.

Statistical considerations for the platform trial in COVID-19 vaccine priming and boosting

The Platform trial In COVID-19 priming and BOOsting (PICOBOO) is a multi-site, adaptive platform trial designed to generate evidence of the immunogenicity, reactogenicity, and cross-protection of different booster vaccination strategies against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its variants, specific for the Australian context. The PICOBOO trial randomises participants to receive one of three COVID-19 booster vaccine brands (Pfizer, Moderna, Novavax) available for use in Australia, where the vaccine brand subtypes vary over time according to the national vaccine roll out strategy, and employs a Bayesian hierarchical modelling approach to efficiently borrow information across consecutive booster doses, age groups and vaccine brand subtypes. Here, we briefly describe the PICOBOO trial structure and report the statistical considerations for the estimands, statistical models and decision making for trial adaptations. This paper should be read in conjunction with the PICOBOO Core Protocol and PICOBOO Sub-Study Protocol 1: Booster Vaccination. PICOBOO was registered on 10 February 2022 with the Australian and New Zealand Clinical Trials Registry ACTRN12622000238774.

Syrian refugee young adults as community mental health workers implementing problem management plus: Protocol for a pilot randomized controlled trial to measure the mechanisms of effect on their own wellbeing, stress and coping

This pilot randomized controlled trial protocol aims to (1) assess the impact on the wellbeing of Syrian refugee young adults (18–24 years) of being a community mental health worker (CMHW) implementing WHO's evidence-based psychosocial intervention - Problem Management Plus (PM+) - with adults in their community, and (2) identify the mechanisms associated with the outcomes of enhanced wellbeing and coping, and reduced stress among these CMHWs. Over 108 million people have been forcibly displaced as of the end of 2022. Mental health consequences of these displacements are significant, yet human resources for health are not sufficient to meet the needs. A large proportion of refugee populations are youth and young adults (YA). Evidence indicates their engagement in supporting their communities leads to their own enhanced wellbeing and that of their community. This trial trains Syrian refugees to serve their communities as CMHW (n=19) or tutors (n=19) and compare wellbeing, stress and coping outcomes between these two groups and a control group (n = 40). We will also assess 7 mechanisms as potential pathways for the interventions to influence outcomes. Surveys will assess outcomes and mechanisms, hair samples will measure stress cortisol. The primary analysis will use a Bayesian Hierarchical Model approach to model the trajectories of the mechanisms and primary study endpoints over time for individuals in each of the arms. Our results will elucidate critical mechanisms in which engagement of young adults to support their community enhances their own wellbeing. Trial registrationNational Institutes of Mental Health, NCT05265611, Registered prospectively in 2021. Lebanon clinical trials registry #LBCTR2023015206, Registered in 2023.

Predicting Abiotic TCE Transformation Rate Constants—A Bayesian Hierarchical Approach

AbstractFe(II) minerals can mediate the abiotic reduction of trichloroethylene (TCE), a widespread groundwater contaminant. If reaction rates are sufficiently fast for natural attenuation, the process holds potential for mitigating TCE pollution in groundwater. To assess the variability of abiotic TCE reduction rate constants, we collected pseudo‐first‐order rate constants for natural sediments and rocks from the literature, as well as intrinsic (surface‐area‐normalized) rate constants of individual minerals. Using a Bayesian hierarchical modeling approach, we were able to differentiate the contributions of natural variability and experimental error to the total variance. Applying the model, we also predicted rate constants at new sites, revealing a considerable uncertainty of several orders of magnitude. We investigated whether incorporating additional information about sediment composition could reduce this uncertainty. We tested two sets of predictors: reactive mineral content (measured by X‐ray diffraction) combined with surface areas and intrinsic rate constants, or the extractable Fe(II) content. Knowledge of the mineral composition only marginally reduced the uncertainty of predicted rate constants. We attribute the low information gain to the inability to measure the (reactive) surface areas of individual minerals in sediments or rocks, which are subject to environmental factors like aqueous geochemistry and redox potential. In contrast, knowing the Fe(II) content reduced the uncertainty about the first‐order rate constant by nearly two orders of magnitude, because the relationship between Fe(II) content and rate constants is approximately log–log‐linear. We demonstrate how our approach provides estimates for the range of cleanup times for a simple example of diffusion‐controlled transport in a contaminated aquitard.

Coarsened Mixtures of Hierarchical Skew Normal Kernels for Flow and Mass Cytometry Analyses

Cytometry is the standard multi-parameter assay for measuring single cell phenotype and functionality. It is commonly used for quantifying the relative frequencies of cell subsets in blood and disaggregated tissues. A typical analysis of cytometry data involves cell classification—that is, the identification of cell subgroups in the sample—and comparisons of the cell subgroups across samples or conditions. While modern experiments often necessitate the collection and processing of samples in multiple batches, analysis of cytometry data across batches is challenging because differences across samples may occur due to either true biological variation or technical reasons such as antibody lot effects or instrument optics across batches. Thus a critical step in comparative analyses of multi-sample cytometry data—yet missing in existing automated methods for analyzing such data—is cross-sample calibration, whose goal is to align corresponding cell subsets across multiple samples in the presence of technical variations, so that biological variations can be meaningfully compared. We introduce a Bayesian nonparametric hierarchical modeling approach for accomplishing both calibration and cell classification simultaneously in a unified probabilistic manner. Three important features of our method make it particularly effective for analyzing multi-sample cytometry data: a nonparametric mixture avoids prespecifying the number of cell clusters; a hierarchical skew normal kernel that allows flexibility in the shapes of the cell subsets and cross-sample variation in their locations; and finally the “coarsening” strategy makes inference robust to departures from the model not captured by the skew normal kernels. We demonstrate the merits of our approach in simulated examples and carry out a case study in the analysis of a multi-sample cytometry data set. We provide an R package for our method.

A generalized calibrated Bayesian hierarchical modeling approach to basket trials with multiple endpoints.

A basket trial simultaneously evaluates a treatment in multiple cancer subtypes, offering an effective way to accelerate drug development in multiple indications. Many basket trials are designed and monitored based on a single efficacy endpoint, primarily the tumor response. For molecular targeted or immunotherapy agents, however, a single efficacy endpoint cannot adequately characterize the treatment effect. It is increasingly important to use more complex endpoints to comprehensively assess the risk-benefit profile of such targeted therapies. We extend the calibrated Bayesian hierarchical modeling approach to monitor phase II basket trials with multiple endpoints. We propose two generalizations, one based on the latent variable approach and the other based on the multinomial-normal hierarchical model, to accommodate different types of endpoints and dependence assumptions regarding information sharing. We introduce shrinkage parameters as functions of statistics measuring homogeneity among subgroups and propose a general calibration approach to determine the functional forms. Theoretical properties of the generalized hierarchical models are investigated. Simulation studies demonstrate that the monitoring procedure based on the generalized approach yields desirable operatingcharacteristics.

Parsing memory and nonmemory contributions to age-related declines in mnemonic discrimination performance: a hierarchical Bayesian diffusion decision modeling approach.

The mnemonic discrimination task (MDT) is a widely used cognitive assessment tool. Performance in this task is believed to indicate an age-related deficit in episodic memory stemming from a decreased ability to pattern-separate among similar experiences. However, cognitive processes other than memory ability might impact task performance. In this study, we investigated whether nonmnemonic decision-making processes contribute to the age-related deficit in the MDT. We applied a hierarchical Bayesian version of the Ratcliff diffusion model to the MDT performance of 26 younger and 31 cognitively normal older adults. It allowed us to decompose decision behavior in the MDT into different underlying cognitive processes, represented by specific model parameters. Model parameters were compared between groups, and differences were evaluated using the Bayes factor. Our results suggest that the age-related decline in MDT performance indicates a predominantly mnemonic deficit rather than differences in nonmnemonic decision-making processes. In addition, this mnemonic deficit might also involve a slowing in processes related to encoding and retrieval strategies, which are relevant for successful memory as well. These findings help to better understand what cognitive processes contribute to the age-related decline in MDT performance and may help to improve the diagnostic value of this popular task.

Chemical Oxygen Demand as a Measure of Fluvial Organic Matter Oxidation State

AbstractThe oxidative ratio (OR) of the terrestrial biosphere is directly related to the size of the terrestrial biosphere carbon sink. In turn, OR of naturally occurring organic matter can be directly related to the oxidation state of the carbon in naturally occurring organic matter (Cox). Chemical oxygen demand (COD) is a widely measured water quality parameter that has been used as a short‐term substitute for the biochemical oxygen demand (BOD). Here, we propose that if the concentration of reduced species is known, then COD measurement can be used to assess the oxidation state (Cox) of fluvial organic C. Using a Bayesian hierarchical modeling approach, this study analyzed 21 years of water quality monitoring across England to calculate Cox of fluvial organic matter. The study showed that (a) COD could not be considered separately from the reduced species (e.g., NH4) commonly occurring in freshwater water samples, but it was still possible to calculate the Cox of dissolved organic carbon (DOC) and particulate organic carbon (POC). (b) The median Cox of DOC was 0.23 with a 95th percentile range of −0.1 to 0.4. (c) The median Cox of POC was 0.20 with a 95th percentile range of 0.03–0.37. (d) The estimated Cox in fluvial systems confirms that BOD is decoupled from the production of CO2. Including new Cox estimates in the global estimate of OR gives a new median value of 1.059 with a 95th percentile range of 1.047–1.071, giving the annual flux of CO2 to land (fland) of 1.45 ± 0.1 Gt C/year.

An Australian convective wind gust climatology using Bayesian hierarchical modelling

To quantify the hazard or risks associated with severe convective wind gusts, it is necessary to have a reliable and spatially complete climatology of these events. The coupling of observational and global reanalysis (ERA-Interim) data over the period 2005–2015 is used here to facilitate the development of a spatially complete convective wind gust climatology for Australia. This is done through the development of Bayesian Hierarchical models that use both weather station-based wind gust observations and seasonally averaged severe weather indices (SWI), calculated using reanalysis data, to estimate seasonal gust frequencies across the country while correcting for observational biases specifically, the sparse observational network to record events. Different SWI combinations were found to explain event counts for different seasons. For example, combinations of Lifted Index and low level wind shear were found to generate the best results for autumn and winter. While for spring and summer, the composite Microburst Index and the combination of most unstable CAPE and 0–1 km wind shear were found to be most successful. Results from these models showed a minimum in event counts during the winter months, with events that do occur mainly doing so along the southwest coast of Western Australia or along the coasts of Tasmania and Victoria. Summer is shown to have the largest event counts across the country, with the largest number of gusts occurring in northern Western Australia extending east into the Northern Territory with another maximum over northeast New South Wales. Similar trends were found with an extended application of the models to the period 1979–2015 when utilizing only reanalysis data as input. This implementation of the models highlights the versatility of the Bayesian hierarchical modelling approach and its ability, when trained, to be used in the absence of observations.

Combining aggregate and individual-level data to estimate individual-level associations between air pollution and COVID-19 mortality in the United States.

Imposing stricter regulations for PM2.5 has the potential to mitigate damaging health and climate change effects. Recent evidence establishing a link between exposure to air pollution and COVID-19 outcomes is one of many arguments for the need to reduce the National Ambient Air Quality Standards (NAAQS) for PM2.5. However, many studies reporting a relationship between COVID-19 outcomes and PM2.5 have been criticized because they are based on ecological regression analyses, where area-level counts of COVID-19 outcomes are regressed on area-level exposure to air pollution and other covariates. It is well known that regression models solely based on area-level data are subject to ecological bias, i.e., they may provide a biased estimate of the association at the individual-level, due to within-area variability of the data. In this paper, we augment county-level COVID-19 mortality data with a nationally representative sample of individual-level covariate information from the American Community Survey along with high-resolution estimates of PM2.5 concentrations obtained from a validated model and aggregated to the census tract for the contiguous United States. We apply a Bayesian hierarchical modeling approach to combine county-, census tract-, and individual-level data to ultimately draw inference about individual-level associations between long-term exposure to PM2.5 and mortality for COVID-19. By analyzing data prior to the Emergency Use Authorization for the COVID-19 vaccines we found that an increase of 1 μg/m3 in long-term PM2.5 exposure, averaged over the 17-year period 2000-2016, is associated with a 3.3% (95% credible interval, 2.8 to 3.8%) increase in an individual's odds of COVID-19 mortality. Code to reproduce our study is publicly available at https://github.com/NSAPH/PM_COVID_ecoinference. The results confirm previous evidence of an association between long-term exposure to PM2.5 and COVID-19 mortality and strengthen the case for tighter regulations on harmful air pollution and greenhouse gas emissions.

Repetition learning is neither a continuous nor an implicit process

Learning advances through repetition. A classic paradigm for studying this process is the Hebb repetition effect: Immediate serial recall performance improves for lists presented repeatedly as compared to nonrepeated lists. Learning in the Hebb paradigm has been described as a slow but continuous accumulation of long-term memory traces over repetitions [e.g., Page & Norris, Phil. Trans. R. Soc. B 364, 3737-3753 (2009)]. Furthermore, it has been argued that Hebb repetition learning requires no awareness of the repetition, thereby being an instance of implicit learning [e.g., Guérard etal., Mem. Cogn. 39, 1012-1022 (2011); McKelvie, J. Gen. Psychol.114, 75-88 (1987)]. While these assumptions match the data from a group-level perspective, another picture emerges when analyzing data on the individual level. We used a Bayesian hierarchical mixture modeling approach to describe individual learning curves. In two preregistered experiments, using a visual and a verbal Hebb repetition task, we demonstrate that 1) individual learning curves show an abrupt onset followed by rapid growth, with a variable time for the onset of learning across individuals, and that 2) learning onset was preceded by, or coincided with, participants becoming aware of the repetition. These results imply that repetition learning is not implicit and that the appearance of a slow and gradual accumulation of knowledge is an artifact of averaging over individual learning curves.

Bayesian Spatial Modelling of HIV Prevalence in Jimma Zone, Ethiopia.

Background: Although the human immunodeficiency virus (HIV) is spatially heterogeneous in Ethiopia, current regional estimates of HIV prevalence hide the epidemic's heterogeneity. A thorough examination of the prevalence of HIV infection using district-level data could assist to develop HIV prevention strategies. The aims of this study were to examine the spatial clustering of HIV prevalence in Jimma Zone at district level and assess the effects of patient characteristics on the prevalence of HIV infection. Methods: The 8440 files of patients who underwent HIV testing in the 22 Districts of Jimma Zone between September 2018 and August 2019 were the source of data for this study. The global Moran's index, Getis-Ord Gi* local statistic, and Bayesian hierarchical spatial modelling approach were applied to address the research objectives. Results: Positive spatial autocorrelation was observed in the districts and the local indicators of spatial analysis using the Getis-Ord statistic also identified three districts, namely Agaro, Gomma and Nono Benja, as hotspots, and two districts, namely Mancho and Omo Beyam, as coldspots with 95% and 90% confidence levels, respectively, for HIV prevalence. The results also showed eight patient-related characteristics that were considered in the study were associated with HIV prevalence in the study area. Furthermore, after accounting for these characteristics in the fitted model, there was no spatial clustering of HIV prevalence suggesting the patient characteristics had explained most of the heterogeneity in HIV prevalence in Jimma Zone for the study data. Conclusions: The identification of hotspot districts and the spatial dynamic of HIV infection in Jimma Zone at district level may allow health policymakers in the zone or Oromiya region or at national level to develop geographically specific strategies to prevent HIV transmission. Because clinic register data were used in the study, it is important to use caution when interpreting the results. The results are restricted to Jimma Zone districts and may not be generalizable to Ethiopia or the Oromiya region.

Estimating phosphorus retention capacity of flow-through wetlands

A Bayesian hierarchical modeling approach is introduced to pool data properly from multiple flow-through wetlands to estimate wetland-specific long-term phosphorus retention capacity. By pooling data from multiple wetlands, we overcome the difficulties in estimating the effectiveness of using constructed and natural wetlands for nutrient reduction. The Bayesian hierarchical modeling approach reduces estimation uncertainty by shrinking wetland-specific estimates towards the overall average of the same quantity from multiple wetlands, facilitating information sharing across sites, thereby reducing the demand on sample sizes from individual wetlands and avoiding several common pitfalls of using large data (i.e., from multiple systems) induced by Simpson's paradox. In this paper, we develop a sequential updating framework to alleviate the computational burden of compiling and modeling data from multiple wetlands. We then demonstrate the sequential updating process to estimate retention capacity of a suite of wetlands in Ohio, USA. A total of four wetlands, representing both natural and constructed wetlands, were used. The estimated total phosphorus retention capacities range less than 0.01 to well over 1 ton per year per system. As wetland restoration initiatives expand around the Laurentian Great Lakes and nationally, this model serves as an important initial step in developing tools to meet nutrient reduction goals and standards. Extending this work, we have developed a publicly accessible on-line open computation platform that can help natural resource specialists better plan for wetland efficacy in the future.

Combining Continuous and Categorical Data Modeling in Developmental Age Estimation Using Hierarchical Bayes

Residual correlations (correlations that persist after accounting for the effect of chronological age) between variables can have a significant impact on final age estimates. Such correlations can result in overly narrow age intervals and high error rates when not accounted for. Modeling correlations can be mathematically problematic across mixed data types. Hierarchical modeling can incorporate continuous and categorical traits into a single model that accounts for correlated variables while reducing computationally expensive calculations. This paper demonstrates a Bayesian hierarchical modeling approach in which trait variables were grouped by data type or bodily system and used to produce separate age estimates with any appropriate model. These age estimates were combined into a single estimate using a multivariate normal model via nested cross-validation. The data used included nine diaphyseal length measurements and 29 epiphyseal fusion and ossification sites from 179 individuals in the publicly available U.S. Subadult Virtual Anthropology Database. Diaphyseal ages were modeled with linear regression and epiphyseal ages with random forest regression. Age estimates from the hierarchical model had reduced bias relative to diaphyseal or epiphyseal maximum likelihood estimates alone. Combined-indicator age intervals from 95% highest density regions (HDRs) were on average 15% narrower than those from diaphyseal 95% HDRs while success rates were 2% lower (91% vs. 93%). Functional example code is provided. A general hierarchical modeling approach may be applicable to other areas of skeletal analysis that employ correlated variables of mixed data types including adult age estimation and ancestry estimation.

MSR46 A Bayesian Hierarchical Modelling Approach for Indirect Comparison of Response Outcomes in Histology-Independent Therapies

MSR46 A Bayesian Hierarchical Modelling Approach for Indirect Comparison of Response Outcomes in Histology-Independent Therapies

Field-based physical inference from peculiar velocity tracers

ABSTRACT We present a proof-of-concept Bayesian hierarchical modelling approach to reconstruct the initial cosmic matter density field constrained by peculiar velocity observations. Using a model for the gravitational evolution of dark matter to connect the initial conditions to late-time observations, it reconstructs the late-time density and velocity fields as natural byproducts. We implement this field-based physical inference approach by adapting the Bayesian Origin Reconstruction from Galaxies ($\small {\rm BORG}$) algorithm, which explores the high-dimensional posterior through the use of Hamiltonian Monte Carlo sampling. We test the self-consistency of the method using random sets of tracers, and assess its accuracy in a more complex scenario where peculiar velocity tracers are mock haloes drawn from $\small {\rm GADGET2}$ N-body simulations. We find that our framework self-consistently infers the initial conditions, density and velocity fields, and shows some robustness to model mis-specification. Compared with the approach of constrained Gaussian random fields/Wiener filtering, the hierarchical model produces more accurate final density and velocity field reconstructions. It also allows us to constrain the initial conditions by peculiar velocity observations, complementing in this aspect other field-based approaches based on alternative cosmological observables such as galaxy clustering or weak lensing.

Spatiotemporal Bayesian estimation of the number of under-reported COVID-19 cases in Victoria Australia.

Having an estimate of the number of under-reported cases is crucial in determining the true burden of a disease. In the COVID-19 pandemic, there is a great need to quantify the true disease burden by capturing the true incidence rate to establish appropriate measures and strategies to combat the disease. This study investigates the under-reporting of COVID-19 cases in Victoria, Australia, during the third wave of the pandemic as a result of variation in geographic area and time. It is aimed to determine potential under-reported areas and generate the true picture of the disease in terms of the number of cases. A two-tiered Bayesian hierarchical model approach is employed to estimate the true incidence and detection rates through Bayesian model averaging. The proposed model goes beyond testing inequality across areas by looking into other covariates such as weather, vaccination rates, and access to vaccination and testing centres, including interactions and variations between space and time. This model aims for parsimony yet allows a broader range of scope to capture the underlying dynamic of the reported COVID-19 cases. Moreover, it is a data-driven, flexible, and generalisable model to a global context such as cross-country estimation and across time points under strict pandemic conditions.

A hierarchical Bayesian regression model that reduces uncertainty in material demand predictions

AbstractPredictions of metal consumption are vital for criticality assessments and sustainability analyses. Although demand for a material varies strongly by region and end‐use sector, statistical models of demand typically predict demand using regression analyses at an aggregated global level (“fully pooled models”). “Un‐pooled” regression models that predict demand at a disaggregated country or regional level face challenges due to limited data availability and large uncertainty. In this paper, we propose a Bayesian hierarchical model that can simultaneously identify heterogeneous demand parameters (like price and income elasticities) for individual regions and sectors, as well as global parameters. We demonstrate the model's value by estimating income and price elasticity of copper demand in five sectors (Transportation, Electrical, Construction, Manufacturing, and Other) and five regions (North America, Europe, Japan, China, and Rest of World). To validate the benefits of the Bayesian approach, we compare the model to both a “fully pooled” and an “un‐pooled” model. The Bayesian model can predict global demand with similar uncertainty as a fully pooled regression model, while additionally capturing regional heterogeneity in income elasticity of demand. Compared to un‐pooled models that predict demand for individual countries and sectors separately, our model reduces the uncertainty of parameter estimates by more than 50%. The hierarchical Bayesian modeling approach we propose can be used for various commodities, improving material demand projections used to study the impact of policies on mining sector emissions and informing investment in critical material production.