Bayesian Hierarchical Modeling Approach Research Articles

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.

Dorsolateral prefrontal cortex plays causal role in probability weighting during risky choice

In this study, we provide causal evidence that the dorsolateral prefrontal cortex (DLPFC) supports the computation of subjective value in choices under risk via its involvement in probability weighting. Following offline continuous theta-burst transcranial magnetic stimulation (cTBS) of the DLPFC subjects (N = 30, mean age 23.6, 56% females) completed a computerized task consisting of 96 binary lottery choice questions presented in random order. Using the hierarchical Bayesian modeling approach, we then estimated the structural parameters of risk preferences (the degree of risk aversion and the curvature of the probability weighting function) and analyzed the obtained posterior distributions to determine the effect of stimulation on model parameters. On a behavioral level, temporary downregulation of the left DLPFC excitability through cTBS decreased the likelihood of choosing an option with higher expected reward while the probability of choosing a riskier lottery did not significantly change. Modeling the stimulation effects on risk preference parameters showed anecdotal evidence as assessed by Bayes factors that probability weighting parameter increased after the left DLPFC TMS compared to sham.

Random-Parameter Bayesian Hierarchical Extreme Value Modeling Approach with Heterogeneity in Means and Variances for Traffic Conflict–Based Crash Estimation

Random-Parameter Bayesian Hierarchical Extreme Value Modeling Approach with Heterogeneity in Means and Variances for Traffic Conflict–Based Crash Estimation

Sedimentation supports life-cycle CH4 production and accumulation in a river valley reservoir: A hierarchical Bayesian modeling approach

Reservoirs have been recognized as a source of methane (CH4). With the gradual increase in the number of the world's reservoirs, predicting the long-term variation of reservoir CH4 emissions is important to understand the global change in carbon cycling due to reservoir creation and operation. Here, we first categorized the origins and transport of organic carbon (OC) by reservoir creation and operation into the following four aspects: a) the decomposition of flooded organic matter, b) the sedimentation of OC from upstream sediment inputs, c) the transition of the aquatic ecosystem from lotic to lentic type, stimulating the production of autochthonous OC; and d) reservoir as the collector of anthropogenic OC inputs from surrounding communities. It was assumed that OC from the four aspects jointly determined the production and accumulation of reservoir CH4 concentration, supporting life-cycle reservoir CH4 emissions. A hierarchical Bayesian model of reservoir CH4 concentration was established and calibrated by observed monthly datasets in 2018 in the Xiangjiaba Reservoir (XJB), a river valley dammed reservoir in the upper Yangtze River, China. The model explained the relative contributions of the four aspects to reservoir CH4 production and accumulation. Approximately 78% of the CH4 concentration was contributed by the decomposition of flooded organic matter during the first 10 years after impoundment. However, the contribution of flooding faded away after 10 years of impoundment. With the increase in reservoir age, sedimentation of OC dominantly determined the reservoir CH4 production and accumulation. Scenario analysis of the XJB's life cycle demostrated that the CH4 concentration in the XJB would reach its peak approximately 70 - 80 years after impoundment. In the cascade system, the upstream reservoir will help to reduce sediment OC input, and to mitigate downstream reservoir CH4 production and accumulation. Our effort provided a new modeling approach for long-term management strategies to reduce reservoir CH4 emissions under global change.

The effect of weather and climate on dengue outbreak risk in Peru, 2000-2018: A time-series analysis.

BackgroundDengue fever is the most common arboviral disease in humans, with an estimated 50-100 million annual infections worldwide. Dengue fever cases have increased substantially in the past four decades, driven largely by anthropogenic factors including climate change. More than half the population of Peru is at risk of dengue infection and due to its geography, Peru is also particularly sensitive to the effects of El Niño Southern Oscillation (ENSO). Determining the effect of ENSO on the risk for dengue outbreaks is of particular public health relevance and may also be applicable to other Aedes-vectored viruses.MethodsWe conducted a time-series analysis at the level of the district-month, using surveillance data collected from January 2000 to September 2018 from all districts with a mean elevation suitable to survival of the mosquito vector (<2,500m), and ENSO and weather data from publicly-available datasets maintained by national and international agencies. We took a Bayesian hierarchical modeling approach to address correlation in space, and B-splines with four knots per year to address correlation in time. We furthermore conducted subgroup analyses by season and natural region.ResultsWe detected a positive and significant effect of temperature (°C, RR 1.14, 95% CI 1.13, 1.15, adjusted for precipitation) and ENSO (ICEN index: RR 1.17, 95% CI 1.15, 1.20; ONI index: RR 1.04, 95% CI 1.02, 1.07) on outbreak risk, but no evidence of a strong effect for precipitation after adjustment for temperature. Both natural region and season were found to be significant effect modifiers of the ENSO-dengue effect, with the effect of ENSO being stronger in the summer and the Selva Alta and Costa regions, compared with winter and Selva Baja and Sierra regions.ConclusionsOur results provide strong evidence that temperature and ENSO have significant effects on dengue outbreaks in Peru, however these results interact with region and season, and are stronger for local ENSO impacts than remote ENSO impacts. These findings support optimization of a dengue early warning system based on local weather and climate monitoring, including where and when to deploy such a system and parameterization of ENSO events, and provide high-precision effect estimates for future climate and dengue modeling efforts.

A flexible Bayesian nonconfounding spatial model for analysis of dispersed count data.

In employing spatial regression models for counts, we usually meet two issues. First, the possible inherent collinearity between covariates and the spatial effect could lead to misleading inferences. Second, real count data usually reveal over- or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining nonconfounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data based on the gamma distribution assumption for waiting times. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation by using the integrated nested Laplace approximation method. We examine different popular approaches for handling spatial confounding and compare their performances in the presence of dispersion. Two real applications from a crime study against women in India as well as stomach cancer incidences in Slovenia motivate the suggested methods. We also perform a simulation study to understand the proposed approach's merits better. Supplementary Materials for this article areavailable.

Linking Climate Variables to Large-Scale Spatial Pattern and Risk of Citrus Huanglongbing: A Hierarchical Bayesian Modeling Approach.

Huanglongbing (HLB) is one of the most important diseases affecting citriculture in the world. Knowledge of climatic factors linked to HLB risk at large spatial scales is limited. We gathered HLB presence and absence data from official surveys conducted in the state of Minas Gerais, Brazil, over 13 years. The total count of orange and mandarin orchards, and mean orchard area, normalized to a spatial grid of 60 cells (55 × 55 km), were derived from the same database. Monthly climate normals (1984 to 2013) of rainfall, mean temperature, and wind speed split into rainy (September to April) and dry (May to August) seasons (annual summary was retained) were obtained for each grid cell. Two hierarchical Bayesian modeling approaches were evaluated, both based on the integrated nested Laplace approximation method. The first, the climate covariates model (CC model), used orchard, climate, and the spatial effect as covariates. The second, principal components (PC model), used the first three components from a principal component analysis of all variables and the spatial effect as covariates. Both models showed an inverse relationship between posterior prevalence and grid cell mean temperature during the dry season. Annual wind speed, as well as annual and rainy season rainfall, contributed to HLB risk in the CC and PC models, respectively. A partial influence of neighboring regions on HLB risk was observed. The results should assist policymakers in defining regions at HLB risk and guide monitoring strategies to mitigate further spread of HLB in the state of Minas Gerais.