Bayesian Hierarchical Modeling Approach Research Articles

Gas Turbine Health State Prognostics by Means of Bayesian Hierarchical Models

Abstract The prediction of time evolution of gas turbine (GT) performance is an emerging requirement of modern prognostics and health management (PHM), aimed at improving system reliability and availability, while reducing life cycle costs. In this work, a data-driven Bayesian hierarchical model (BHM) is employed to perform a probabilistic prediction of GT future behavior, thanks to its capability to deal with fleet data from multiple units. First, the theoretical background of the predictive methodology is outlined to highlight the inference mechanism and data processing for estimating BHM-predicted outputs. Then, the BHM approach is applied to both simulated and field data representative of GT degradation to assess its prediction reliability and grasp some rules of thumb for minimizing BHM prediction error. For the considered field data, the average values of the prediction errors are found to be lower than 1.0% or 1.7% for single- or multi-step prediction, respectively.

Dust properties and star formation of approximately a thousand local galaxies

Aims. We derived the dust properties for 753 local galaxies and examine how these relate to some of their physical properties. We present the derived dust emission properties, including model spectral energy distribution (SEDs), star formation rates (SFRs) and stellar masses, as well as their relations. Methods. We modelled the global dust-SEDs for 753 galaxies, treated statistically as an ensemble within a hierarchical Bayesian dust-SED modelling approach, so as to derive their infrared (IR) emission properties. To create the observed dust-SEDs, we used a multi-wavelength set of observations, ranging from near-IR to far-IR-to-submillimeter wavelengths. The model-derived properties are the dust masses (Mdust), the average interstellar radiation field intensities (Uav), the mass fraction of very small dust grains (“QPAH” fraction), as well as their standard deviations. In addition, we used mid-IR observations to derive SFR and stellar masses, quantities independent of the dust-SED modelling. Results. We derive distribution functions of the properties for the galaxy ensemble and as a function of galaxy type. The mean value of Mdust for the early-type galaxies (ETGs) is lower than that for the late-type and irregular galaxies (LTGs and Irs, respectively), despite ETGs and LTGs having stellar masses spanning across the whole range observed. The Uav and “QPAH” fraction show no difference among different galaxy types. When fixing Uav to the Galactic value, the derived “QPAH” fraction varies across the Galactic value (0.071). The specific SFR increases with galaxy type, while this is not the case for the dust-specific SFR (SFR/Mdust), showing an almost constant star formation efficiency per galaxy type. The galaxy sample is characterised by a tight relationship between the dust mass and the stellar mass for the LTGs and Irs, while ETGs scatter around this relation and tend towards smaller dust masses. While the relation indicates that Mdust may fundamentally be linked to M⋆, metallicity and Uav are the second parameter driving the scatter, which we investigate in a forthcoming work. We used the extended Kennicutt–Schmidt (KS) law to estimate the gas mass and the gas-to-dust mass ratio (GDR). The gas mass derived from the extended KS law is on average ∼20% higher than that derived from the KS law, and a large standard deviation indicates the importance of the average star formation present to regulate star formation and gas supply. The average GDR for the LTGs and Irs is 370, and including the ETGs gives an average of 550.

Comparative thermal performance of the reef-building coral Orbicella franksi at its latitudinal range limits

Temperature drives biological responses that scale from the cellular to ecosystem levels and thermal sensitivity will shape organismal functions and population dynamics as the world warms. Reef-building corals are sensitive to temperature due to their endosymbiotic relationship with single-celled dinoflagellates, with mass mortality events increasing in frequency and magnitude. The purpose of this study was to quantify the thermal sensitivity of important physiological functions of a Caribbean reef-building coral, Orbicella franksi, through the measurement of thermal performance curves (TPCs). We compared TPC metrics (thermal optimum, critical maximum, activation energy, deactivation energy, and rate at a standardized temperature) between two populations at the northern and southern extents of the geographic range of O. franksi. We further compared essential coral organismal processes (gross photosynthesis, respiration, and calcification) within a site to determine which function is most sensitive to thermal stress using a hierarchical Bayesian-modeling approach. We found evidence for differences in thermal performance, which could be due to thermal adaptation or acclimatization, with higher TPC metrics (thermal optimum and critical maximum) in warmer Panama, compared to cooler Bermuda. We also documented the hierarchy in thermal sensitivity of essential organismal functions within a population: respiration was less sensitive than photosynthesis, which was less sensitive than calcification. Understanding thermal performance of corals is essential for projecting coral reef futures, given that key biological functions necessary to sustain coral reef ecosystems are thermally mediated.

The implications of Simpson's paradox for cross-scale inference among lakes

Using cross-sectional data for making ecological inference started as a practical means of pooling data to enable meaningful empirical model development. For example, limnologists routinely use sample averages from numerous individual lakes to examine patterns across lakes. The basic assumption behind the use of cross-lake data is often that responses within and across lakes are identical. As data from multiple study units across a wide spatiotemporal scale are increasingly accessible for researchers, an assessment of this assumption is now feasible. In this study, we demonstrate that this assumption is usually unjustified, due largely to a statistical phenomenon known as the Simpson's paradox. Through comparisons of a commonly used empirical model of the effect of nutrients on algal growth developed using several data sets, we discuss the cognitive importance of distinguishing factors affecting lake eutrophication operating at different spatial and temporal scales. Our study proposes the use of the Bayesian hierarchical modeling approach to properly structure the data analysis when data from multiple lakes are employed.

A modelling approach for correcting reporting delays in disease surveillance data.

One difficulty for real‐time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistical problems, infrastructure difficulties, and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast due to the use of the integrated nested Laplace approximation. The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and severe acute respiratory infection data in the state of Paraná, Brazil.

Ignoring the spatial structure of the sea cucumber Isostichopus fuscus distribution when granting quotas can be costly

There is an increasing demand for fisheries resources worldwide. For example, the Asian markets have traditionally consumed sea cucumber as a delicacy and their buoyant economies have promoted demand for it in recent years. The brown sea cucumber Isostichopus fuscus is the most valuable species from the Eastern Pacific and it has been almost depleted due to overfishing. In this work, we analyzed data of sea cucumber abundance collected monthly (October 2014–December 2016) along the west coast of the Gulf of California (29.95 oN – 28.05 oN) in 1,107 swath (25 × 2 m) quadrats performed at 118 sites with the goal of determining if current fishing quotas are sustainable. We applied a Bayesian hierarchical modelling approach with integrated nested Laplace approximation (INLA) to this data to account for spatial structure in the data when calculating densities. The observed density ranged from a minimum of 0 to a maximum of 0.58 ind/m2, with an average of 0.03 ind/m2 in suitable habitat, defined as the habitat less than 30 m deep and with hard substrate. There are large spatial variations in abundance, but the overall mean suitable habitat is 15.7% (min = 7.8%, max = 28.8%) of the total fishing area. Current quotas are usually higher than 5% of the lower bounds of population density estimates. We propose, among other management measures, that quotas should be granted taking into account the spatial structure of sea cucumber densities as well as the proportion of suitable area within each estate. Given the high levels of illegal fishing within the Gulf of California, it is imperative that quotas are based on the lower bounds of spatially explicit density estimates – along with increased surveillance and enforcement – if the long-term commercial sustainability of the fishery is to be maintained.

Revealing the coral habitat effect on benthopelagic fauna diversity in the Santa Maria di Leuca cold‐water coral province using different devices and Bayesian hierarchical modelling

Abstract Data from two experimental longline surveys and two video inspections carried out in Santa Maria di Leuca cold‐water coral province (Mediterranean Sea) during spring–autumn 2010 were used in order to compare the benthopelagic abundance and diversity between coral and non‐coral habitats and between different devices. The sampling was carried out in two types of habitat: a coral habitat with carbonate mounds and a non‐coral habitat characterized by intermound sea floor. A Bayesian hierarchical modelling approach to accommodate factors influencing community assemblages was used considering the number of species, the Shannon–Wiener diversity index and the two most abundant species represented by the European conger (Conger conger) and blackbelly rosefish (Helicolenus dactylopterus). A relevant effect of the habitat factor was observed for both the number of species and the diversity index, showing a higher species number and diversity index in the coral habitat than in the non‐coral habitat. Concerning the relevance of fixed effects from the model on the probability of observing non‐zero (positive) abundances, the devices considered, longline and baited lander, did not show different influence for either C. conger or H. dactylopterus. In the case of positive abundance, a relevant device effect was only observed for H. dactylopterus, showing higher abundances for longline than for baited lander. A habitat effect was detected, with positive abundances for both species in the coral habitat. This study proves that structurally complex habitats generated by cold‐water corals influence the distribution and diversity of the benthopelagic fauna, and that the use of different devices can provide complementary useful results. Increased knowledge about the role of cold‐water corals in the associated benthopelagic fauna could lead to better conservation of one of the most important hot spots of biodiversity in the Mediterranean Sea.

Hierarchical Bayesian modeling for the spatial analysis of robberies in Toronto, Canada

This paper investigates the geographic variation of robbery risk in Toronto, Canada. A hierarchical Bayesian modeling approach is used for estimating the relative risk of robberies across Toronto’s 140 neighbourhood districts in 2017. The association between robbery risk and various socio-economic explanatory variables (i.e., business density, education and income levels) are analyzed using a Poisson-based spatial regression model. Markov Chain Monte Carlo model fitting is utilized for the estimation of relative risk and associated regression parameters. Results reveal that elevated levels of robbery risk are predominant in the eastern, north-western and southern neighbourhoods of Toronto whereas, lower risk areas are situated in the central neighbourhoods. Across all neighbourhoods, there was a geographical difference in robbery risk, ranging from 0.17 (95% CI 0.05–0.38) to 4.87 (95% CI 4.22–5.55). Education and income variables had a negative association with robberies at posterior probabilities of 96.9% and 85.5% respectively, whereas business density had a positive association with robberies at a posterior probability of 100%. Hence, neighbourhoods with higher amounts of businesses, lower education levels and lower household incomes tend to have a higher mean amount of robberies in Toronto and thus higher associated risks.

Bayesian hierarchical modeling of the non-stationary traffic conflict extremes for crash estimation

A Bayesian hierarchical modeling (BHM) approach is used to model non-stationary traffic conflict extremes of different sites together for crash estimation. The hierarchical structure has three layers, a data layer that is modeled with a generalized extreme value (GEV) distribution, a latent Gaussian process layer that relates parameters of GEV to covariates and the unobserved heterogeneity, and a prior layer with prior distributions to characterize the latent process. The proposed approach was applied to traffic conflicts collected at the signal cycle level from four intersections in the city of Surrey, British Columbia. Traffic conflicts were measured by the modified time to collision (MTTC) indicator while traffic volume, shock wave area, average shock wave speed, and platoon ration of each cycle were employed as covariates. Four BHM models were developed, including a stationary model (i.e., BHM_GEV(0,0,0)) with no covariates and three non-stationary models (i.e., BHM_GEV(1,0,0), BHM_GEV(0,1,0), and BHM_GEV(1,1,0)) with covariates added to the location parameter, scale parameter, and both parameters of the GEV distribution, respectively. Traditional at-site GEV models were also developed for individual sites for comparison purposes. The results show that the BHM_GEV(1,1,0) is the best fitted model among the four models since considering covariates and unobserved heterogeneity significantly improves the model performance in terms of goodness of fit. The BHM_GEV(1,1,0) also yields relatively accurate and more precise crash estimates compared to the at-site models. This is attributed to the BHM_GEV(1,1,0) allowing borrowing strength from other sites. It is also found that the traffic volume, shock wave area, and platoon ratio have significant influence on the safety of signalized intersections.

Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision song contest

The Eurovision Song Contest is a popular TV singing competition held annually among country members of the European Broadcasting Union. In this competition, each member can be both contestant and jury, as it can participate with a song and/or vote for other countries' tunes. Throughout the years, the voting system has repeatedly been accused of being biased by the presence of tactical voting, according to which votes would represent strategic interests rather than actual musical preferences of the voting countries. In this work, we develop a latent space model to investigate the presence of a latent structure underlying the exchange of votes. Focusing on the period from 1998 to 2015, we represent the vote exchange as a multivariate network: each edition is a network, where countries are the nodes and two countries are linked by an edge if one voted for the other. The different networks are taken to be independent replicates of a common latent space capturing the overall relationships among the countries. Proximity denotes similarity, and countries close in the latent space are assumed to be more likely to exchange votes. Therefore, if the exchange of votes depends on the similarity between countries, the quality of the competing songs might not be a relevant factor in the determination of the voting preferences, and this would suggest the presence of bias. A Bayesian hierarchical modelling approach is employed to model the probability of a connection between any two countries as a function of their distance in the latent space, and of network-specific parameters and edge-specific covariates. The inferred latent space is found to be relevant in the determination of edge probabilities, however, the positions of the countries in such space only partially correspond to their actual geographical positions.

A Bayesian Hierarchical Analysis of Geographical Patterns for Child Mortality in Nigeria

Background:In an epidemiological study, disease mapping models are commonly used to estimate the spatial (or temporal) patterns in disease risk and to identify high-risk clusters, allowing for health interventions and allocation of the resources. The present study proposes a hierarchical Bayesian modeling approach to simultaneously capture the over-dispersion due to the effect of varying population sizes across the districts (regions), and the spatial auto-correlation inherent in the childhood mortality at districts (state) level in Nigeria.Methods:This cross-sectional study was based on 31842 children data extracted from the 2013 Nigeria Demographic and Health Survey (DHS). Of these children, 2886 died before reaching the age of five years. A Standardized Mortality Ratio (SMR) was estimated for each district (state) and mapped to highlight the risk patterns and detect an unusual low (high) clusters relative risk of childhood mortality. Generalized Poisson regression models were formulated with random effects to estimate the mortality risk and then explored to investigate the relationship of under-five child mortality and the regional risk factors. The random effects are formulated to reflect the potential tendency of “neighbouring” regions to have similar risk patterns and the spatial heterogeneity effect was used to capture geographical inequalities in the mortality outcomes. The models were implemented using a full Bayesian framework. All model parameters were estimated in WinBUGSviaMarkov Chain Monte Carlos (MCMC) simulation techniques.Results:The results showed that of the economically deprived households, 2.088: 95% CI (1.088, 3.165) were significantly associated with childhood mortality, while unhygienic sanitation and lack of access to improved water sources were positively associated with child mortality, but not statistically significant at 5% probability level. The geographical variation of the under-five mortality prevalence was found to be attributed to 69% clustering and 31% was due to spatial heterogeneity factors. The predicted probability maps identified clusters of high risk mortality in the northern regions and low prevalence of concentrated mortality in the south-west regions of Nigeria.Conclusion:The results demonstrated the flexibility of the approach that explored the geographical variation in the potential risk factors of child mortality and that it provides a better understanding of the regional variations of mortality risks. Nonetheless, both representations can help to provide information for the initiation of public health interventions.

Breeding site fidelity of blue‐winged teal in South Dakota

ABSTRACTAssumptions about breeding site fidelity (i.e., fidelity) in blue‐winged teal (Spatula discors) are based on limited recapture data and analytic techniques. We banded female blue‐winged teal (n = 12,543) from 2003 to 2014 in a 3,800‐ha sample area in north‐central South Dakota, USA, and used a Bayesian hierarchical modeling approach combining live recapture and dead recovery data to predict probabilities of fidelity, survival, recapture, and reporting. We explored sources of variation including time, annual wet area on the landscape, age, and nest survival, and compared our results to other dabbling ducks that nest in the Prairie Pothole Region, a critically important breeding area for waterfowl in central North America. We found annual estimates of fidelity ranging from 0.20 to 0.91, with mean values of 0.62 and 0.67 for hatch year birds and after hatch year birds, respectively. Our findings indicate that environmental factors may cause blue‐winged teal to return to breeding sites more frequently than previously assumed. © The Wildlife Society, 2019

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Characterisation of the skeletal muscle’s passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors’ knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. Statement of SignificanceThis article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres’ load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle’s functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.

Parallel Markov chain Monte Carlo for Bayesian hierarchical models with big data, in two stages

ABSTRACTDue to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common for the full data set, with most parameters being group specific. Thus, parallel Bayesian MCMC methods that take into account the structure of the model and split the full data set by groups rather than by observations are a more natural approach for analysis. Here, we adapt and extend a recently introduced two-stage Bayesian hierarchical modeling approach, and we partition complete data sets by groups. In stage 1, the group-specific parameters are estimated independently in parallel. The stage 1 posteriors are used as proposal distributions in stage 2, where the target distribution is the full model. Using three-level and four-level models, we show in both simulation and real data studies that results of our method agree closely with the full data analysis, with greatly increased MCMC efficiency and greatly reduced computation times. The advantages of our method versus existing parallel MCMC computing methods are also described.

Borrowing From Historical Control Data in Cancer Drug Development: A Cautionary Tale and Practical Guidelines

Some clinical trialists, especially those working in rare or pediatric disease, have suggested borrowing information from similar but already-completed clinical trials. This article begins with a case study in which relying solely on historical control information would have erroneously resulted in concluding a significant treatment effect. We then attempt to catalog situations where borrowing historical information may or may not be advisable using a series of carefully designed simulation studies. We use an MCMC-driven Bayesian hierarchical parametric survival modeling approach to analyze data from a sponsor’s colorectal cancer study. We also apply these same models to simulated data comparing the effective historical sample size, bias, 95% credible interval widths, and empirical coverage probabilities across the simulated cases. We find that even after accounting for variations in study design, baseline characteristics, and standard-of-care improvement, our approach consistently identifies Bayesianly significant differences between the historical and concurrent controls under a range of priors on the degree of historical data borrowing. Our simulation studies are far from exhaustive, but inform the design of future trials. When the historical and current controls are dissimilar, Bayesian methods can still moderate borrowing to a more appropriate level by adjusting for important covariates and adopting sensible priors.

Individual Differences in Cortical Processing Speed Predict Cognitive Abilities: a Model-Based Cognitive Neuroscience Account

Previous research has shown that individuals with greater cognitive abilities display a greater speed of higher-order cognitive processing. These results suggest that speeded neural information processing may facilitate evidence accumulation during decision making and memory updating and thus yield advantages in general cognitive abilities. We used a hierarchical Bayesian cognitive modeling approach to test the hypothesis that individual differences in the velocity of evidence accumulation mediate the relationship between neural processing speed and cognitive abilities. We found that a higher neural speed predicted both the velocity of evidence accumulation across behavioral tasks and cognitive ability test scores. However, only a negligible part of the association between neural processing speed and cognitive abilities was mediated by individual differences in the velocity of evidence accumulation. The model demonstrated impressive forecasting abilities by predicting 36% of individual variation in cognitive ability test scores in an entirely new sample solely based on their electrophysiological and behavioral data. Our results suggest that individual differences in neural processing speed might affect a plethora of higher-order cognitive processes, that only in concert explain the large association between neural processing speed and cognitive abilities, instead of the effect being entirely explained by differences in evidence accumulation speeds.

A Hierarchical Bayesian Modeling Approach for the Habitat Distribution of Smooth Dogfish by Sex and Season in Inshore Coastal Waters of the U.S. Northwest Atlantic

AbstractThe Smooth Dogfish Mustelus canis is an abundant, small coastal shark occurring along the U.S. Atlantic coast. Despite being targeted by a directed fishery and having recently undergone a stock assessment that found the population neither overfished nor experiencing overfishing, little is known about the spatial and temporal distribution of this species. Here, we used catch data from the spring and fall Northeast Area Monitoring and Assessment Program's fishery‐independent trawl surveys conducted between 2007 and 2016 and various environmental factors to perform hierarchical Bayesian modeling as a first attempt to spatially predict adult Smooth Dogfish CPUE in U.S. northwest Atlantic Ocean waters by sex and season. Relevant environmental variables differed between both sexes and seasons. Male and female CPUEs were similarly associated with lower salinity and shallower depth in the spring. During fall, male CPUE was associated with sea surface temperature and bottom rugosity, and female CPUE was associated with chlorophyll‐a concentration, bottom rugosity, and year. Habitat modeling results predicted that areas of high male and female CPUEs would overlap during spring but strongly diverge during fall, when greater predicted CPUEs for males were distributed considerably farther north. These results suggest sexual segregation among Smooth Dogfish during fall, with the springtime overlap in distribution coinciding with the pupping and mating season in this population. This difference in distribution during fall may allow for a male‐only directed fishery for Smooth Dogfish in the northern extent of the species’ range in waters near southern New England and Georges Bank.

Investigating varying effect of road-level factors on crash frequency across regions: A Bayesian hierarchical random parameter modeling approach

This study aims to quantitatively examine the variations in effect of road-level factors on crash frequency across different regions. Treating the hierarchical structure existing in the crash data that road entity nested within the geographic region, a hierarchical random parameter model, which allows the coefficients of road-level variables to vary with regions, is proposed. A Poisson lognormal model and a hierarchical random intercept model are also built for the purpose of comparison. A specific roadway facility type, urban two-lane two-way roadway segments in Florida, with crash and road level data including traffic volume, road length, surface condition, and access density for three-year period are used for a case study. The result shows that, in the hierarchical-random parameter model, the local regression coefficients and marginal effects of the road level factors vary over a wide range in the selected counties, which clearly illustrates the non-stationary in the relationships between road level factors and crash frequency across the counties. In regard to the model comparison, the hierarchical random parameter model outperforms the Poisson lognormal model and the hierarchical random intercept model in term of deviance information criterion (DIC). This further confirms the necessity of the use of hierarchical random parameter model in analyzing the crash frequency for road entities in different regions. This study provides a potential in guidance of model construction that considers regional variations (heterogeneities) in safety effects of road-level factors.

Topography and neighborhood crowding can interact to shape species growth and distribution in a diverse Amazonian forest.

Abiotic constraints and biotic interactions act simultaneously to shape communities. However, these community assembly mechanisms are often studied independently, which can limit understanding of how they interact to affect species dynamics and distributions. We develop a hierarchical Bayesian neighborhood modeling approach to quantify the simultaneous effects of topography and crowding by neighbors on the growth of 124,704 individual stems ≥1cm DBH for 1,047 tropical tree species in a 25-ha mapped rainforest plot in Amazonian Ecuador. We build multi-level regression models to evaluate how four key functional traits (specific leaf area, maximum tree size, wood specific gravity and seed mass) mediate tree growth response to topography and neighborhood crowding. Tree growth is faster in valleys than on ridges and is reduced by neighborhood crowding. Topography and crowding interact to influence tree growth in ~10% of the species. Specific leaf area, maximum tree size and seed mass are associated with growth responses to topography, but not with responses to neighborhood crowding or with the interaction between topography and crowding. In sum, our study reveals that topography and neighborhood crowding each influence tree growth in tropical forests, but act largely independently in shaping species distributions. While traits were associated with species response to topography, their role in species response to neighborhood crowding was less clear, which suggests that trait effects on neighborhood dynamics may depend on the direction (negative/positive) and degree of symmetry of biotic interactions. Our study emphasizes the importance of simultaneously assessing the individual and interactive role of multiple mechanisms in shaping species dynamics in high diversity tropical systems.

Integrative Bayesian analysis of brain functional networks incorporating anatomical knowledge

Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization by integrating information on both brain structure and function. In particular, incorporating anatomical knowledge leads to desirable outcomes such as increased accuracy in brain network estimates and greater reproducibility of topological features across scanning sessions. Despite the clear advantages, major challenges persist in integrative analyses including an incomplete understanding of the structure-function relationship and inaccuracies in mapping anatomical structures due to inherent deficiencies in existing imaging technology. This calls for the development of advanced network modeling tools that appropriately incorporate anatomical structure in constructing brain functional networks. We propose a hierarchical Bayesian Gaussian graphical modeling approach which models the brain functional networks via sparse precision matrices whose degree of edge specific shrinkage is a random variable that is modeled using both anatomical structure and an independent baseline component. The proposed approach adaptively shrinks functional connections and flexibly identifies functional connections supported by structural connectivity knowledge. This enables robust brain network estimation even in the presence of misspecified anatomical knowledge, while accommodating heterogeneity in the structure-function relationship. We implement the approach via an efficient optimization algorithm which yields maximum a posteriori estimates. Extensive numerical studies involving multiple functional network structures reveal the clear advantages of the proposed approach over competing methods in accurately estimating brain functional connectivity, even when the anatomical knowledge is misspecified up to a certain degree. An application of the approach to data from the Philadelphia Neurodevelopmental Cohort (PNC) study reveals gender based connectivity differences across multiple age groups, and higher reproducibility in the estimation of network metrics compared to alternative methods.