Hierarchical Modeling Framework Research Articles

Hierarchical Bayesian Modeling Framework for Model Updating and Robust Predictions in Structural Dynamics using Modal Features

Hierarchical Bayesian Modeling Framework for Model Updating and Robust Predictions in Structural Dynamics using Modal Features

A new item response theory model for rater centrality using a hierarchical rater model approach.

Rater centrality, in which raters overuse middle scores for rating, is a common rater error which can affect test scores and subsequent decisions. Past studies on rater errors have focused on rater severity and inconsistency, neglecting rater centrality. This study proposes a new model within the hierarchical rater model framework to explicitly specify and directly estimate rater centrality in addition to rater severity and inconsistency. Simulations were conducted using the freeware JAGS to evaluate the parameter recovery of the new model and the consequences of ignoring rater centrality. The results revealed that the model had good parameter recovery with small bias, low root mean square errors, and high test score reliability, especially when a fully crossed linking design was used. Ignoring centrality yielded poor item difficulty estimates, person ability estimates, rater errors estimates, and underestimated reliability. We also showcase how the new model can be used, using an empirical example involving English essays in the Advanced Placement exam.

Hierarchical framework for maintenance and production scheduling of continuous ball mills in tile industries under TOU electricity pricing

In this paper, the interaction among Time-of-Use (TOU) electricity prices, production scheduling, and preventive maintenance of continuous slurry ball mills is addressed via a hierarchical mathematical modelling framework. Slurry ball mills are considered as the main consumer of electrical energy so that they impose high energy costs on tile factories. However, rarely energy expenses have been taken into consideration in the scheduling. In this study, a mixed-integer energy-cost-aware hierarchical formulation (ECA-H) is proposed and its superiority in terms of various indicators compared to its four possible counterparts is shown. The main contribution of the proposed model in reducing energy costs is obtained by reducing the peak load, and a small share is related to the energy saving. Based on the average of the numerical results, the proposed model compared to its classic counterpart leads to 26% reduction in energy costs, 73% reduction in the peak load, and 3% reduction in the energy consumption. Finally, several easy-yet-effective managerial insights are extracted for mangers to benefit from the findings of our study when they face practical limitations to implement the proposed mathematical model.

Fault detection and diagnosis for variable-air-volume systems using combined residual, qualitative and quantitative techniques

Due to its complex structure and frequent operation, the variable-air-volume (VAV) system are prone to failure. Since faults in VAV systems can reduce its efficiency and increase its energy consumption dramatically, various fault detection and diagnosis (FDD) strategies have been developed. However, due to the diversity of buildings and system structural complexity, most of these efforts are limited to local scale and fault detection at system level has rarely been considered. In this study, the complexity of VAV system modeling is dispersed with a hierarchical modeling framework, and a system level to component scale FDD strategy for VAV systems using combined residual, qualitative and quantitative techniques is developed. The three layers of the modelling framework, namely system layer, unit layer and component layer, adopt different modeling and fault diagnosis methods to improve the accuracy and reliability of FDD. On the other hand, detecting progressive faults is not easy for VAV systems because their symptoms are non-obvious. This study proposes a control quantity based residual statistics in the unit layer, which detects progressive failures with the residual between fault-free-model-predicted and measured control quantities of the zone thermal system. The proposed method is easy to implement and integrate within existing VAV control systems. The results of experiments and a simulation based on the Skyspark platform data from an office building verify the effectiveness of the approach.

Assessing the Role of Sampling Uncertainty When Predicting Behavioral Responses of Tagged Cetaceans Exposed to Naval Sonar

Concerns over cetacean mortality events coincident with maritime warfare exercises have motivated efforts to characterize the effects of anthropogenic noise on free-ranging whales and dolphins. By monitoring the movement, diving, and acoustic behaviors of individual whales before, during, and after sound exposure, behavioral response studies (BRSs) have supported significant progress in our understanding of the sensitivity of various cetacean species to high-powered naval sonar signals. However, differences in the designs and sampling capabilities of animal-borne tags typically used in BRS experiments prompt questions about the influence of data resolution in quantitative assessments of noise impacts. We conducted simulations to examine how uncertainty in the acoustic dose either measured on high-resolution multi-sensor biologging tags or modeled from position-transmitting satellite telemetry tags may affect predictions of behavioral responses in Cuvier’s beaked whales (Ziphius cavirostris) exposed to low- and mid-frequency active sonar. We considered an array of scenarios representative of real-world BRSs and used posterior estimates of dose-response functions obtained under an established Bayesian hierarchical modeling framework to explore the consequences of different tag choices for management decision-making. Our results indicate that (1) the zone of impact from a sonar source is under-estimated in most test conditions, (2) substantial reductions in the uncertainty surrounding dose-response relationships are possible at higher sample sizes, and (3) this largely holds true irrespective of tag choice under the scenarios considered, unless positional fixes from satellite tags are consistently poor. Strategic monitoring approaches that combine both archival biologging and satellite biotelemetry are essential for characterizing complex patterns of behavioral change in cetaceans exposed to increasing levels of acoustic disturbance. We suggest ways in which BRS protocols can be optimized to curtail the effects of uncertainty.

Nonlinear Model Updating through a Hierarchical Bayesian Modeling Framework

Nonlinear Model Updating through a Hierarchical Bayesian Modeling Framework

A two-layer modelling framework for predicting passenger flow on trains: A case study of London underground trains

A model that anticipates the passenger flow on trains will help passengers to avoid overcrowded trains in their journey planning. Such a model will also help rail industry to understand the current use of train capacity and plan the distribution of rolling stock, personnel and facilities. However, the existing studies only developed the models for forecasting the passenger flow in stations, which cannot reflect the true passenger number on trains. In this paper, a hierarchical modelling framework for passenger flow prediction is proposed. It includes two layers of fuzzy models, where a global model is used to predict for ordinary circumstances and a number of local models are used to predict the variations in passenger number due to specific factors, such as events and weather. A new data sifting method is proposed to obtain the most informative and representative data for model training, which greatly improves the modelling efficiency. The proposed method is then validated using a case study of forecasting the passenger flow of London Underground trains.

Hierarchical Bayesian Model for Assessing Extreme Daily Rainfall Through Combining Climatic and Topographic Information

Frequency analysis of the annual maximum rainfall time series is essential for designing infrastructures to provide protection against local floods and related events. However, the results of the frequency analysis obtained are ambiguous. In this study, we aimed to develop a spatial hierarchical Bayesian model framework through combining the climatic and topographic information. To confirm the applicability of the proposed method, the results of at-site frequency analysis and regional frequency analysis using the index flood method were compared in the Busan-Ulsan-Gyeongnam region. Furthermore, a hierarchical Bayesian model was developed, in which the parameters of the generalized logistic distribution comprised relatively simple covariate relationships upon considering the possibility of expansion into various probability distributions and more complex covariate structures. The uncertainty of this model was analyzed using the coefficient of variation of rainfall quantile ensemble. The results confirmed that the regional frequency analysis using the hierarchical Bayesian model combined with the climatic and topographic information could provide an accurate estimate of extreme daily rainfall with relatively good agreement with the estimate at a specific site, but is a more reliable approach.

A Framework for Estimating Human-Wildlife Conflict Probabilities Conditional on Species Occupancy

Managing human-wildlife conflicts (HWCs) is an important conservation objective for the many terrestrial landscapes dominated by humans. Forecasting where future conflicts are likely to occur and assessing risks to lives and livelihoods posed by wildlife are central to informing HWC management strategies. Existing assessments of the spatial occurrence patterns of HWC are based on either understanding spatial patterns of past conflicts or patterns of species distribution. In the former case, the absence of conflicts at a site cannot be attributed to the absence of the species. In the latter case, the presence of a species may not be an accurate measure of the probability of conflict occurrence. We present a Bayesian hierarchical modeling framework that integrates conflict reporting data and species distribution data, thus allowing the estimation of the probability that conflicts with a species are reported from a site, conditional on the species being present. In doing so, our model corrects for both false-positive and false-negative conflict reporting errors. We provide study design recommendations using simulations that explore the performance of the model under a range of conflict reporting probabilities. We applied the model to data on wild boar (Sus scrofa) space use and conflicts collected from the Central Terai Landscape (CTL), an important tiger conservation landscape in India. We found that tolerance for wildlife was a predictor of the probability with which farmers report conflict with wild boars from sites not used by the species. We also discuss useful extensions of the model when conflict data are verified for potential false-positive errors and when landscapes are monitored over multiple seasons.

Chlorophyll a as an indicator of microcystin: Short-term forecasting and risk assessment in Lake Erie

We developed a Bayesian hierarchical modeling framework to establish a short-term forecasting model of particulate cyanobacterial toxin concentrations in Western Lake Erie using chlorophyll a concentration as the predictor. The model evolves over time with additional data to reflect the changing dynamics of cyanobacterial toxin production. Specifically, parameters of the empirical relationship between the cyanobacterial toxin microcystin and chlorophyll a concentrations are allowed to vary annually and seasonally under a hierarchical framework. As such, the model updated using the most recent sampling data is suited to provide short-term forecasts. The reduced model predictive uncertainty makes the model a viable tool for risk assessment. Using data from the long-term Western Lake Erie harmful algal bloom monitoring program (2008–2018), we illustrate the model-building and model-updating process and the application of the model for short-term risk assessment. The modeling process demonstrates the use of the Bayesian hierarchical modeling framework for developing informative priors in Bayesian modeling.

OCRbayes: A Bayesian hierarchical modeling framework for Seahorse extracellular flux oxygen consumption rate data analysis.

Mitochondrial dysfunction is involved in many complex diseases. Efficient and accurate evaluation of mitochondrial functionality is crucial for understanding pathology as well as facilitating novel therapeutic developments. As a popular platform, Seahorse extracellular flux (XF) analyzer is widely used for measuring mitochondrial oxygen consumption rate (OCR) in living cells. A hidden feature of Seahorse XF OCR data is that it has a complex data structure, caused by nesting and crossing between measurement cycles, wells and plates. Surprisingly, statistical analysis of Seahorse XF data has not received sufficient attention, and current methods completely ignore the complex data structure, impairing the robustness of statistical inference. To rigorously incorporate the complex structure into data analysis, here we developed a Bayesian hierarchical modeling framework, OCRbayes, and demonstrated its applicability based on analysis of published data sets. We showed that OCRbayes can analyze Seahorse XF OCR experimental data derived from either single or multiple plates. Moreover, OCRbayes has potential to be used for diagnosing patients with mitochondrial diseases.

Hierarchical Bayesian Modeling Framework for Model Updating and Robust Predictions in Structural Dynamics using Modal Features

Hierarchical Bayesian Modeling Framework for Model Updating and Robust Predictions in Structural Dynamics using Modal Features

Outcome after acute ischemic stroke is linked to sex-specific lesion patterns

Acute ischemic stroke affects men and women differently. In particular, women are often reported to experience higher acute stroke severity than men. We derived a low-dimensional representation of anatomical stroke lesions and designed a Bayesian hierarchical modeling framework tailored to estimate possible sex differences in lesion patterns linked to acute stroke severity (National Institute of Health Stroke Scale). This framework was developed in 555 patients (38% female). Findings were validated in an independent cohort (n = 503, 41% female). Here, we show brain lesions in regions subserving motor and language functions help explain stroke severity in both men and women, however more widespread lesion patterns are relevant in female patients. Higher stroke severity in women, but not men, is associated with left hemisphere lesions in the vicinity of the posterior circulation. Our results suggest there are sex-specific functional cerebral asymmetries that may be important for future investigations of sex-stratified approaches to management of acute ischemic stroke.

Time Matters: How Default Resolution Times Impact Final Loss Rates

Abstract Using access to a unique bank loss database, we find positive dependencies of default resolution times (DRTs) of defaulted bank loan contracts and final loan loss rates (losses given default, LGDs). Due to this interconnection, LGD predictions made at the time of default and during resolution are subject to censoring. Pure (standard) LGD models are not able to capture effects of censoring. Accordingly, their LGD predictions may be biased and underestimate loss rates of defaulted loans. In this paper, we develop a Bayesian hierarchical modelling framework for DRTs and LGDs. In comparison to previous approaches, we derive final DRT estimates for loans in default which enables consistent LGD predictions conditional on the time in default. Furthermore, adequate unconditional LGD predictions can be derived. The proposed method is applicable to duration processes in general where the final outcomes depend on the duration of the process and are affected by censoring. By this means, we avoid bias of parameter estimates to ensure adequate predictions.

Spatial-temporal multivariate semi-Bayesian hierarchical framework for extreme precipitation frequency analysis

We present a semi-Bayesian hierarchical modeling framework for conducting space–time frequency analysis of precipitation extremes over a large domain. In this framework, the data layer, the precipitation extreme – i.e., seasonal maximum precipitation, at each station in each year is modeled using a generalized extreme value (GEV) distribution with temporally varying parameters, which are decomposed as linear functions of covariates. The coefficients of the covariates are estimated via maximum likelihood (ML). In the process layer, the estimated ML coefficients of each of the covariates across the stations are spatially modeled with a Gaussian multivariate process which enables capturing the spatial structure and correlation between the spatial model parameters. Suitable priors are used for the spatial model hyperparameters to complete the Bayesian formulation. Since the Bayesian formulation is only at the second level, our model is semi-Bayesian and thus, the posteriors are conditional posterior distributions. With the conditional posterior distribution of spatial fields of the GEV parameters for each time, conditional posterior distribution of the nonstationary space–time return levels of the precipitation extremes are obtained. We demonstrate this framework by application to summer precipitation extreme at 73 stations covering a large domain of Southwest US consisting of Arizona, New Mexico, Colorado, and Utah. The results from fitting and cross-validation indicate that our model captures the historical variability at the stations very well. Conditional posterior distributions of return levels are simulated on a grid over the domain, which will be of immense utility in management of natural resources and infrastructure.

Landscape epidemiology of Batrachochytrium salamandrivorans: reconciling data limitations and conservation urgency.

Starting in 2010, rapid fire salamander (Salamandra salamandra) population declines in northwestern Europe heralded the emergence of Batrachochytrium salamandrivorans (Bsal), a salamander-pathogenic chytrid fungus. Bsal poses an imminent threat to global salamander diversity owing to its wide host range, high pathogenicity, and long-term persistence in ecosystems. While there is a pressing need to develop further research and conservation actions, data limitations inherent to recent pathogen emergence obscure necessary insights into Bsal disease ecology. Here, we use a hierarchical modeling framework to describe Bsal landscape epidemiology of outbreak sites in light of these methodological challenges. Using model selection and machine learning, we find that Bsal presence is associated with humid and relatively cool, stable climates. Outbreaks are generally located in areas characterized by low landscape heterogeneity and low steepness of slope. We further find an association between Bsal presence and high trail density, suggesting that human-mediated spread may increase risk for spillover between populations. We then use distribution modeling to show that favorable conditions occur in lowlands influenced by the North Sea, where increased survey effort is needed to determine how Bsal impacts local newt populations, but also in hill- and mountain ranges in northeastern France and the lower half of Germany. Finally, connectivity analyses suggest that these hill- and mountain ranges may act as stepping stones for further spread southward. Our results provide initial insight into regional environmental conditions underlying Bsal epizootics, present updated invasibility predictions for northwestern Europe, and lead us to discuss a wide variety of potential survey and research actions needed to advance future conservation and mitigation efforts.

Semi-Supervised Learning Using Hierarchical Mixture Models: Gene Essentiality Case Study

Integrating gene-level data is useful for predicting the role of genes in biological processes. This problem has typically focused on supervised classification, which requires large training sets of positive and negative examples. However, training data sets that are too small for supervised approaches can still provide valuable information. We describe a hierarchical mixture model that uses limited positively labeled gene training data for semi-supervised learning. We focus on the problem of predicting essential genes, where a gene is required for the survival of an organism under particular conditions. We applied cross-validation and found that the inclusion of positively labeled samples in a semi-supervised learning framework with the hierarchical mixture model improves the detection of essential genes compared to unsupervised, supervised, and other semi-supervised approaches. There was also improved prediction performance when genes are incorrectly assumed to be non-essential. Our comparisons indicate that the incorporation of even small amounts of existing knowledge improves the accuracy of prediction and decreases variability in predictions. Although we focused on gene essentiality, the hierarchical mixture model and semi-supervised framework is standard for problems focused on prediction of genes or other features, with multiple data types characterizing the feature, and a small set of positive labels.

Using a hierarchical model framework to investigate the relationships between fish spawning and abiotic factors for environmental flow management

The construction of dams worldwide has substantially altered natural flow and thermal regimes, leading to profound influences on fish spawning. Environmental flow (EFlow) assessments provide information on the links between river flow and river health and are a useful technique for specifically restoring species' life-history requirements. A full understanding of the abiotic–biotic relationships coupled with information on hydrological events and ecological processes is a vital step for acquiring explicit water management options. However, the incorporation of concurrent and antecedent flow, thermal parameters, and other water quality information, particularly their complex interaction effects, into the prediction of the relationships between fish spawning and abiotic factors is poorly studied. The present study proposes a hierarchical modeling framework that accounts for the different concurrent and antecedent habitat factors and the interaction effects between factors to predict the spawning intensities of three important endemic fish species (which spawn drifting eggs) collected from the upper Yangtze River, China. Our results show that 1) the abiotic factors significantly affecting fish spawning vary with species, and these factors are intricately linked to species-specific ecology; 2) the water transparency during spawning and the accumulated temperature before spawning are important predictors of the spawning intensity of some fish species, while the effective duration of rising flow discharge before spawning plays a consistently important role in affecting the spawning intensity of all three fish species; and 3) there are explicit interaction effects, mainly between the hydrological and thermal variables, on fish spawning intensity. The present study suggests that investigation of the relationships between fish spawning and abiotic factors should not only analyze individual species but should also fully consider the accumulated temperature and effective duration of flow discharge rising before spawning, as well as the interaction effects between habitat factors.

A hierarchical Bayesian model of storm surge and total water levels across the Great Lakes shoreline – Lake Ontario

This study presents a novel approach to determine the distribution of compound flood events composed of storm surge and static water levels along the Great Lakes shoreline. A mixture distribution of the bulk (Student-t) and tail (GPD-negative binomial) components of storm surge is estimated in a hierarchical Bayesian modeling framework. Parameters are modeled across the entire shoreline using Gaussian processes and hourly gauged data, with priors for spatial autocorrelation informed by numerical output from a lake hydrodynamic model. The distribution of total water levels is obtained through Monte Carlo sampling that combines the estimated distribution of surge with stochastic traces of static lake levels that account for water level management, seasonality, and plausible variability in water supplies. The approach can therefore support coastal flood risk assessments in cases when the distribution of static water levels changes are due to altered water level management or climate change. The model is applied in a case study on Lake Ontario. Results suggest that spatial variability in parameter estimates varies significantly by month and mixture distribution component. Evaluations of performance indicate the model is able to capture adequately storm surge behavior at gauges across the lakeshore, even under cross-validation. A frequency analysis of total water levels at two ungauged sites is presented, with specific attention given to the implications of model assumptions on uncertainty in design events. The paper concludes with a discussion of model limitations and avenues for future work.

Piecewise Growth Modeling Using SAS PROC MIXED

ABSTRACT Typical longitudinal growth models assume constant functional growth over time. However, there are often conditions where trajectories may not be constant over time. For example, trajectories of psychological behaviors may vary based on a participant’s age, or conversely, participants may experience an intervention that causes trajectories to change. Specifically, this article outlines how to build and estimate piecewise growth models (PGM) using SAS PROC MIXED in order to estimate discontinuous growth models over time in a hierarchical linear model (HLM) framework. Details of data coding schemes, model parameterization, analysis using SAS PROC MIXED, and interpretation of parameter estimates will be discussed using a simulated education intervention data set.