Статті в журналах: "Hierarchical spatial modeling"

1

Lawson, Andrew B. "Hierarchical modeling in spatial epidemiology." Wiley Interdisciplinary Reviews: Computational Statistics 6, no. 6 (July 22, 2014): 405–17. http://dx.doi.org/10.1002/wics.1315.

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2

Gelfand, Alan E. "Hierarchical modeling for spatial data problems." Spatial Statistics 1 (May 2012): 30–39. http://dx.doi.org/10.1016/j.spasta.2012.02.005.

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3

Timiryanova, Venera, Kasim Yusupov, and Ruzel Salimyanov. "Relationship Between Consumption and Personal Income Within a Hierarchically Structured Spatial System." Spatial Economics 16, no. 4 (2020): 91–112. http://dx.doi.org/10.14530/se.2020.4.091-112.

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Differentiation in the level of socio-economic development of territories is largely manifested in both inter-regional and intra-regional differences in personal income and consumption of goods. In this regard the methods of hierarchical analysis (HLM, Hierarchical Linear Modeling) that make it possible to study variation at several levels taking into account both municipal and regional factors are acquiring special relevance. Along with hierarchical effects, neighborhood effects can be distinguished. This is possible due to the imposition of a spatial adjacency matrix on the data observing spatial interactions within the spatial-hierarchical models (HSAM, Hierarchical Spatial Autoregressive Modeling). The aim of the study is to better understand the relationship between consumption and personal income within a hierarchically structured and spatially oriented economic system. The analysis uses the data from 2319 municipalities (i.e. municipal districts or rayons) and urban districts (okrugs) in 84 constituent entities of the Russian Federation for 2018. It showed that 38.4% of the variation among municipalities in terms of sold foods volume is explained by regional factors. The developed hierarchical (two-level) model revealed the positive impact of the volume of social benefits and taxable personal income in the municipality, and the volume of per capita retail trade at the level of the Russian Federation constituent entities, on the volume of foods sold within municipalities, and substantiate the negative impact of the Gini index increase, as well as highlight the positive spatial effect

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4

Coburn, Timothy C. "Hierarchical Modeling and Analysis for Spatial Data." Mathematical Geology 39, no. 2 (April 14, 2007): 261–62. http://dx.doi.org/10.1007/s11004-006-9076-2.

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5

Alexander, Neal. "Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology." Journal of the Royal Statistical Society: Series A (Statistics in Society) 174, no. 2 (March 14, 2011): 512–13. http://dx.doi.org/10.1111/j.1467-985x.2010.00681_11.x.

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6

Yasenovskiy, Vladimir, and John Hodgson. "Hierarchical Location-Allocation with Spatial Choice Interaction Modeling." Annals of the Association of American Geographers 97, no. 3 (September 2007): 496–511. http://dx.doi.org/10.1111/j.1467-8306.2007.00560.x.

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7

Barber, Jarrett J., and Alan E. Gelfand. "Hierarchical spatial modeling for estimation of population size." Environmental and Ecological Statistics 14, no. 3 (July 10, 2007): 193–205. http://dx.doi.org/10.1007/s10651-007-0021-4.

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8

Alghamdi, Taghreed, Khalid Elgazzar, and Taysseer Sharaf. "Spatiotemporal Traffic Prediction Using Hierarchical Bayesian Modeling." Future Internet 13, no. 9 (August 30, 2021): 225. http://dx.doi.org/10.3390/fi13090225.

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Hierarchical Bayesian models (HBM) are powerful tools that can be used for spatiotemporal analysis. The hierarchy feature associated with Bayesian modeling enhances the accuracy and precision of spatiotemporal predictions. This paper leverages the hierarchy of the Bayesian approach using the three models; the Gaussian process (GP), autoregressive (AR), and Gaussian predictive processes (GPP) to predict long-term traffic status in urban settings. These models are applied on two different datasets with missing observation. In terms of modeling sparse datasets, the GPP model outperforms the other models. However, the GPP model is not applicable for modeling data with spatial points close to each other. The AR model outperforms the GP models in terms of temporal forecasting. The GP model is used with different covariance matrices: exponential, Gaussian, spherical, and Matérn to capture the spatial correlation. The exponential covariance yields the best precision in spatial analysis with the Gaussian process, while the Gaussian covariance outperforms the others in temporal forecasting.

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9

Huang, Ling, Xing-Xing Liu, Shu-Qiang Huang, Chang-Dong Wang, Wei Tu, Jia-Meng Xie, Shuai Tang, and Wendi Xie. "Temporal Hierarchical Graph Attention Network for Traffic Prediction." ACM Transactions on Intelligent Systems and Technology 12, no. 6 (December 31, 2021): 1–21. http://dx.doi.org/10.1145/3446430.

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As a critical task in intelligent traffic systems, traffic prediction has received a large amount of attention in the past few decades. The early efforts mainly model traffic prediction as the time-series mining problem, in which the spatial dependence has been largely ignored. As the rapid development of deep learning, some attempts have been made in modeling traffic prediction as the spatio-temporal data mining problem in a road network, in which deep learning techniques can be adopted for modeling the spatial and temporal dependencies simultaneously. Despite the success, the spatial and temporal dependencies are only modeled in a regionless network without considering the underlying hierarchical regional structure of the spatial nodes, which is an important structure naturally existing in the real-world road network. Apart from the challenge of modeling the spatial and temporal dependencies like the existing studies, the extra challenge caused by considering the hierarchical regional structure of the road network lies in simultaneously modeling the spatial and temporal dependencies between nodes and regions and the spatial and temporal dependencies between regions. To this end, this article proposes a new Temporal Hierarchical Graph Attention Network (TH-GAT). The main idea lies in augmenting the original road network into a region-augmented network, in which the hierarchical regional structure can be modeled. Based on the region-augmented network, the region-aware spatial dependence model and the region-aware temporal dependence model can be constructed, which are two main components of the proposed TH-GAT model. In addition, in the region-aware spatial dependence model, the graph attention network is adopted, in which the importance of a node to another node, of a node to a region, of a region to a node, and of a region to another region, can be captured automatically by means of the attention coefficients. Extensive experiments are conducted on two real-world traffic datasets, and the results have confirmed the superiority of the proposed TH-GAT model.

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10

Royle, J. Andrew, and L. Mark Berliner. "A Hierarchical Approach to Multivariate Spatial Modeling and Prediction." Journal of Agricultural, Biological, and Environmental Statistics 4, no. 1 (March 1999): 29. http://dx.doi.org/10.2307/1400420.

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11

Reza Najafi, Mohammad, and Hamid Moradkhani. "Analysis of runoff extremes using spatial hierarchical Bayesian modeling." Water Resources Research 49, no. 10 (October 2013): 6656–70. http://dx.doi.org/10.1002/wrcr.20381.

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12

Bai, Yue, Dipu Manandhar, Zhaowen Wang, John Collomosse, and Yun Fu. "Layout Representation Learning with Spatial and Structural Hierarchies." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 1 (June 26, 2023): 206–14. http://dx.doi.org/10.1609/aaai.v37i1.25092.

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We present a novel hierarchical modeling method for layout representation learning, the core of design documents (e.g., user interface, poster, template). Existing works on layout representation often ignore element hierarchies, which is an important facet of layouts, and mainly rely on the spatial bounding boxes for feature extraction. This paper proposes a Spatial-Structural Hierarchical Auto-Encoder (SSH-AE) that learns hierarchical representation by treating a hierarchically annotated layout as a tree format. On the one side, we model SSH-AE from both spatial (semantic views) and structural (organization and relationships) perspectives, which are two complementary aspects to represent a layout. On the other side, the semantic/geometric properties are associated at multiple resolutions/granularities, naturally handling complex layouts. Our learned representations are used for effective layout search from both spatial and structural similarity perspectives. We also newly involve the tree-edit distance (TED) as an evaluation metric to construct a comprehensive evaluation protocol for layout similarity assessment, which benefits a systematic and customized layout search. We further present a new dataset of POSTER layouts which we believe will be useful for future layout research. We show that our proposed SSH-AE outperforms the existing methods achieving state-of-the-art performance on two benchmark datasets. Code is available at github.com/yueb17/SSH-AE.

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13

Cai, Qingyuan, Xuecai Hu, Saihui Hou, Li Yao, and Yongzhen Huang. "Disentangled Diffusion-Based 3D Human Pose Estimation with Hierarchical Spatial and Temporal Denoiser." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 2 (March 24, 2024): 882–90. http://dx.doi.org/10.1609/aaai.v38i2.27847.

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Recently, diffusion-based methods for monocular 3D human pose estimation have achieved state-of-the-art (SOTA) performance by directly regressing the 3D joint coordinates from the 2D pose sequence. Although some methods decompose the task into bone length and bone direction prediction based on the human anatomical skeleton to explicitly incorporate more human body prior constraints, the performance of these methods is significantly lower than that of the SOTA diffusion-based methods. This can be attributed to the tree structure of the human skeleton. Direct application of the disentangled method could amplify the accumulation of hierarchical errors, propagating through each hierarchy. Meanwhile, the hierarchical information has not been fully explored by the previous methods. To address these problems, a Disentangled Diffusion-based 3D human Pose Estimation method with Hierarchical Spatial and Temporal Denoiser is proposed, termed DDHPose. In our approach: (1) We disentangle the 3d pose and diffuse the bone length and bone direction during the forward process of the diffusion model to effectively model the human pose prior. A disentanglement loss is proposed to supervise diffusion model learning. (2) For the reverse process, we propose Hierarchical Spatial and Temporal Denoiser (HSTDenoiser) to improve the hierarchical modelling of each joint. Our HSTDenoiser comprises two components: the Hierarchical-Related Spatial Transformer (HRST) and the Hierarchical-Related Temporal Transformer (HRTT). HRST exploits joint spatial information and the influence of the parent joint on each joint for spatial modeling, while HRTT utilizes information from both the joint and its hierarchical adjacent joints to explore the hierarchical temporal correlations among joints. Extensive experiments on the Human3.6M and MPI-INF-3DHP datasets show that our method outperforms the SOTA disentangled-based, non-disentangled based, and probabilistic approaches by 10.0%, 2.0%, and 1.3%, respectively.

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14

Iddrisu, Abdul-Karim, and Yaw Ampem Amoako. "Spatial Modeling and Mapping of Tuberculosis Using Bayesian Hierarchical Approaches." Open Journal of Statistics 06, no. 03 (2016): 482–513. http://dx.doi.org/10.4236/ojs.2016.63043.

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15

Bowman, F. DuBois, Brian Caffo, Susan Spear Bassett, and Clinton Kilts. "A Bayesian hierarchical framework for spatial modeling of fMRI data." NeuroImage 39, no. 1 (January 2008): 146–56. http://dx.doi.org/10.1016/j.neuroimage.2007.08.012.

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16

Conti, David V., and John S. Witte. "Hierarchical Modeling of Linkage Disequilibrum: Genetic Structure and Spatial Relations." American Journal of Human Genetics 72, no. 2 (February 2003): 351–63. http://dx.doi.org/10.1086/346117.

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17

Rahill-Marier, Bianca, Naresh Devineni, and Upmanu Lall. "Technical note: Modeling spatial fields of extreme precipitation – a hierarchical Bayesian approach." Hydrology and Earth System Sciences 26, no. 21 (November 11, 2022): 5685–95. http://dx.doi.org/10.5194/hess-26-5685-2022.

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Abstract. We introduce a hierarchical Bayesian model for the spatial distribution of rainfall corresponding to an extreme event of a specified duration that could be used with regional hydrologic models to perform a regional hydrologic risk analysis. An extreme event is defined if any gaging site in the watershed experiences an annual maximum rainfall event and the spatial field of rainfall at all sites corresponding to that occurrence is modeled. Applications to data from New York City demonstrate the effectiveness of the model for providing spatial scenarios that could be used for simulating loadings into the urban drainage system. Insights as to the homogeneity in spatial rainfall and its implications for modeling are provided by considering partial pooling in the hierarchical Bayesian framework.

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18

Jankoski, Radoslav, Ulrich Römer, and Sebastian Schöps. "Modeling of spatial uncertainties in the magnetic reluctivity." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 4 (July 3, 2017): 1151–67. http://dx.doi.org/10.1108/compel-10-2016-0438.

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Purpose The purpose of this paper is to present a computationally efficient approach for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines such as a single-phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen–Loève expansion (KLE). The stochastic model is further used to study the statistics of the self-inductance of the primary coil as a quantity of interest (QoI). Design/methodology/approach The computation of the KLE requires solving a generalized eigenvalue problem with dense matrices. The eigenvalues and the eigenfunction are computed by using the Lanczos method that needs only matrix vector multiplications. The complexity of performing matrix vector multiplications with dense matrices is reduced by using hierarchical matrices. Findings The suggested approach is used to study the impact of the spatial variability in the magnetic reluctivity on the QoI. The statistics of this parameter are influenced by the correlation lengths of the random reluctivity. Both, the mean value and the standard deviation increase as the correlation length of the random reluctivity increases. Originality/value The KLE, computed by using hierarchical matrices, is used for uncertainty quantification of low frequency electrical machines as a computationally efficient approach in terms of memory requirement, as well as computation time.

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19

Choi, Jungsoon, and Andrew B. Lawson. "Bayesian spatially dependent variable selection for small area health modeling." Statistical Methods in Medical Research 27, no. 1 (June 16, 2016): 234–49. http://dx.doi.org/10.1177/0962280215627184.

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Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.

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20

Maes, Marc A., and Markus Dann. "Hierarchical Bayes methods for systems with spatially varying condition states." Canadian Journal of Civil Engineering 34, no. 10 (October 1, 2007): 1289–98. http://dx.doi.org/10.1139/l07-049.

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In engineering decision making, we often face problems where the conditions governing certain response models vary spatially. In such cases, the use of hierarchical Bayesian models is often beneficial. Such models are based on a “condition state” vector that is assumed to be conditionally independent given a set of “hyper-parameters.” All other process parameters are then conditional on this state variable vector. Such models can be applied to a large variety of problems where data from various systems or sources need to be spatially “mixed,” such as in deteriorating infrastructure, spatial aspects of corrosion, preference and consequence modeling, and system failure models for large industrial plants. The models are especially useful for performing statistical inference and for updating in the context of life-cycle optimization, optimal inspection, and maintenance planning. A detailed extension is explored that allows for the spatial correlation of the individual “states” given the hyper-parameters. This allows an efficient posterior assessment of high-level upcrossing rates for the purpose of risk analysis.Key words: spatially distributed processes, hierarchical Bayes models, statistical inference for large systems, spatial correlation.

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21

Finley, Andrew O., Sudipto Banerjee, Patrik Waldmann, and Tore Ericsson. "Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets." Biometrics 65, no. 2 (August 27, 2008): 441–51. http://dx.doi.org/10.1111/j.1541-0420.2008.01115.x.

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22

Timiryanova, Venera, Alexandr Zimin, and Kasim Yusupov. "Economic Activity of Territories: Comparative Analysis of the Spatial Effects Assessing Methods." Spatial Economics 17, no. 4 (2021): 41–68. http://dx.doi.org/10.14530/se.2021.4.041-068.

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The article discusses a hierarchical and spatial approach to assessing the spatial dependence of data. The advantages and disadvantages of each approach and the potential for their combination are determined on the basis of a literature review.The results of the OLS, SAR, SEM, HLM, HSAR models are compared. Despite an interesting set of data (2285 municipalities in the context of 85 constituent entities of the Russian Federation), the emphasis in the work is not on identifying the relationship between the dependent variable and factors, but on comparing spatial effects that can be identified within each of the models under consideration. The calculations showed a significant influence on the dependent variable of the following factors: the share of the average number of employees in the resident population, the volume of investments in fixed assets per capita and the share of the urban population. This result was shown by all the constructed models. In the context of models, the identified spatial effects have their own characteristics. The inclusion of spatial matrices is possible at the upper (for example, the subject of the Russian Federation), lower (for example, the municipal level), or both levels simultaneously. In hierarchical models, spatial relationships are additionally taken into account by grouping the objects of observation on a territorial basis. Calculations have shown that the spatial lag is not significant in all models. Spatial error is significant at the municipal level in the SEM model and at the regional level in the HLM and HSAR models. Additionally, hierarchical models showed a significant influence of the region on the municipalities variation. In general, the results of modeling and evaluating modelsquality are ambiguous. Despite this, the potential for expanding spatial econometrics on the basis of a combination of spatial and hierarchical (multilevel) modeling approaches is noted, and the need to select a model for each case is substantiated, taking into account the significance of spatial and hierarchical effects

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23

Zimeras, Stelios, and Yiannis G. Matsinos. "Modeling Uncertainty Based on Spatial Models in Spreading Diseases." International Journal of Reliable and Quality E-Healthcare 8, no. 4 (October 2019): 55–66. http://dx.doi.org/10.4018/ijrqeh.2019100103.

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Lately, spatial models have become a powerful, necessary statistical tool to estimate parameters where data are represented by regions of interests using the window method . Estimation processes based on the high dimensionality of the data have become difficult to implement especially in cases where variability in the spatial models is the main task to investigate. Variability between spatial models considering hierarchical levels of scale, most of the time, involves errors leading to uncertainty in spatial regions. Solving the problem with uncertainty via the estimation of errors in spatial models, complex models could be simplified in easiest ones and important decisions for the quality of data could be taken.

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24

Yang, Xiaofei, Yuxiong Luo, Zhen Zhang, Dong Tang, Zheng Zhou, and Haojin Tang. "AMHFN: Aggregation Multi-Hierarchical Feature Network for Hyperspectral Image Classification." Remote Sensing 16, no. 18 (September 13, 2024): 3412. http://dx.doi.org/10.3390/rs16183412.

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Deep learning methods like convolution neural networks (CNNs) and transformers are successfully applied in hyperspectral image (HSI) classification due to their ability to extract local contextual features and explore global dependencies, respectively. However, CNNs struggle in modeling long-term dependencies, and transformers may miss subtle spatial-spectral features. To address these challenges, this paper proposes an innovative hybrid HSI classification method aggregating hierarchical spatial-spectral features from a CNN and long pixel dependencies from a transformer. The proposed aggregation multi-hierarchical feature network (AMHFN) is designed to capture various hierarchical features and long dependencies from HSI, improving classification accuracy and efficiency. The proposed AMHFN consists of three key modules: (a) a Local-Pixel Embedding module (LPEM) for capturing prominent spatial-spectral features; (b) a Multi-Scale Convolutional Extraction (MSCE) module to capture multi-scale local spatial-spectral features and aggregate hierarchical local features; (c) a Multi-Scale Global Extraction (MSGE) module to explore multi-scale global dependencies and integrate multi-scale hierarchical global dependencies. Rigorous experiments on three public hyperspectral image (HSI) datasets demonstrated the superior performance of the proposed AMHFN method.

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25

Choi, Jieun, and Man Sik Park. "On the Hierarchical Modeling of Spatial Measurements from Different Station Networks." Korean Journal of Applied Statistics 26, no. 1 (February 28, 2013): 93–109. http://dx.doi.org/10.5351/kjas.2013.26.1.093.

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26

Cooley, Daniel, and Stephan R. Sain. "Spatial Hierarchical Modeling of Precipitation Extremes From a Regional Climate Model." Journal of Agricultural, Biological, and Environmental Statistics 15, no. 3 (March 30, 2010): 381–402. http://dx.doi.org/10.1007/s13253-010-0023-9.

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27

Mather, Frances J., Vivien W. Chen, Leslie H. Morgan, Catherine N. Correa, Jeffrey G. Shaffer, Sudesh K. Srivastav, Janet C. Rice, et al. "Hierarchical Modeling and Other Spatial Analyses in Prostate Cancer Incidence Data." American Journal of Preventive Medicine 30, no. 2 (February 2006): S88—S100. http://dx.doi.org/10.1016/j.amepre.2005.09.012.

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28

Bracken, C., B. Rajagopalan, L. Cheng, W. Kleiber, and S. Gangopadhyay. "Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain." Water Resources Research 52, no. 8 (August 2016): 6643–55. http://dx.doi.org/10.1002/2016wr018768.

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Monogan, James E., and Jeff Gill. "Measuring State and District Ideology with Spatial Realignment." Political Science Research and Methods 4, no. 1 (April 15, 2015): 97–121. http://dx.doi.org/10.1017/psrm.2015.5.

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We develop a new approach for modeling public sentiment by micro-level geographic region based on Bayesian hierarchical spatial modeling. Recent production of detailed geospatial political data means that modeling and measurement lag behind available information. The output of the models gives not only nuanced regional differences and relationships between states, but more robust state-level aggregations that update past research on measuring constituency opinion. We rely here on the spatial relationships among observations and units of measurement in order to extract measurements of ideology as geographically narrow as measured covariates. We present an application in which we measure state and district ideology in the United States in 2008.

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30

Wang, Yan Fei. "Application of Spatial Adaptive Filter in the Tilting Mode of Digital Image Restoration." Advanced Materials Research 791-793 (September 2013): 1992–96. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.1992.

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With the development of computer technology and large scale integrated circuit technology, since 1960s, the development of spatial adaptive filter has become one important part of signal processing, its application field has been extended, especially it is used in the digital image processing, and it has become one of the hot research topics in current. This paper presents the recovery method of introducing spatial adaptive filter in the digital image restoration. Firstly, the spatial adaptive filter theory is described, on the basis of this, the hierarchical modeling equilibrium is proposed in the tilting mode digital image restoration, to carry on the analysis of random signal prediction. At the same time, the hierarchical modeling equilibrium will carry out adaptive weight control based on transverse spatial filtering, to reach image restoration for the right cross point. Finally, this paper carries out in-depth analysis for the realization principle of this method, to provide technology support and practical guidance for the research of this field to a certain extent.

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Mahdi, Esam, Sana Alshamari, Maryam Khashabi, and Alya Alkorbi. "Hierarchical Bayesian Spatio-Temporal Modeling for PM10 Prediction." Journal of Applied Mathematics 2021 (September 11, 2021): 1–11. http://dx.doi.org/10.1155/2021/8003952.

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Over the past few years, hierarchical Bayesian models have been extensively used for modeling the joint spatial and temporal dependence of big spatio-temporal data which commonly involves a large number of missing observations. This article represented, assessed, and compared some recently proposed Bayesian and non-Bayesian models for predicting the daily average particulate matter with a diameter of less than 10 (PM10) measured in Qatar during the years 2016–2019. The disaggregating technique with a Markov chain Monte Carlo method with Gibbs sampler are used to handle the missing data. Based on the obtained results, we conclude that the Gaussian predictive processes with autoregressive terms of the latent underlying space-time process model is the best, compared with the Bayesian Gaussian processes and non-Bayesian generalized additive models.

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32

Osei, Frank, Alfred Stein, and Anthony Ofosu. "Poisson-Gamma Mixture Spatially Varying Coefficient Modeling of Small-Area Intestinal Parasites Infection." International Journal of Environmental Research and Public Health 16, no. 3 (January 26, 2019): 339. http://dx.doi.org/10.3390/ijerph16030339.

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Understanding the spatially varying effects of demographic factors on the spatio-temporal variation of intestinal parasites infections is important for public health intervention and monitoring. This paper presents a hierarchical Bayesian spatially varying coefficient model to evaluate the effects demographic factors on intestinal parasites morbidities in Ghana. The modeling relied on morbidity data collected by the District Health Information Management Systems. We developed Poisson and Poisson-gamma spatially varying coefficient models. We used the demographic factors, unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal as model covariates. The models were fitted using the integrated nested Laplace approximations (INLA). The overall risk of intestinal parasites infection was estimated to be 10.9 per 100 people with a wide spatial variation in the district-specific posterior risk estimates. Substantial spatial variation of increasing multiplicative effects of unsafe drinking water, unsafe toilet, and unsafe liquid waste disposal occurs on the variation of intestinal parasites risk. The structured residual spatial variation widely dominates the unstructured component, suggesting that the unaccounted-for risk factors are spatially continuous in nature. The study concludes that both the spatial distribution of the posterior risk and the associated exceedance probability maps are essential for monitoring and control of intestinal parasites.

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33

Cheng, Vincent Y. S., George B. Arhonditsis, David M. L. Sills, William A. Gough, and Heather Auld. "Predicting the Climatology of Tornado Occurrences in North America with a Bayesian Hierarchical Modeling Framework*." Journal of Climate 29, no. 5 (March 1, 2016): 1899–917. http://dx.doi.org/10.1175/jcli-d-15-0404.1.

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Abstract Destruction and fatalities from recent tornado outbreaks in North America have raised considerable concerns regarding their climatic and geographic variability. However, regional characterization of tornado activity in relation to large-scale climatic processes remains highly uncertain. Here, a novel Bayesian hierarchical framework is developed for elucidating the spatiotemporal variability of the factors underlying tornado occurrence in North America. It is demonstrated that regional variability of tornado activity can be characterized using a hierarchical parameterization of convective available potential energy, storm relative helicity, and vertical wind shear quantities. It is shown that the spatial variability of tornado occurrence during the warm summer season can be explained by convective available potential energy and storm relative helicity alone, while vertical wind shear is clearly better at capturing the spatial variability of the cool season tornado activity. The results suggest that the Bayesian hierarchical modeling approach is effective for understanding the regional tornadic environment and in forming the basis for establishing tornado prognostic tools in North America.

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Liu, Haiyue, Chuanyun Fu, Chaozhe Jiang, Yue Zhou, Chengyuan Mao, and Jining Zhang. "Bayesian hierarchical spatial count modeling of taxi speeding events based on GPS trajectory data." PLOS ONE 15, no. 11 (November 13, 2020): e0241860. http://dx.doi.org/10.1371/journal.pone.0241860.

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Speeding behavior, especially serious speeding, is more common in taxi driver than other driving population due to their high exposure under traffic environment, which increases the risk of being involved in crashes. In order to prevent the taxi and other road users from speed-related crash, previous studies have revealed contributors of demographic and driving operation affecting taxi speeding frequency. However, researches regarding road factors, and spatial effect are typically rare. For this sake, the current study explores the contributions of 10 types of road characteristics and two kinds of spatial effects (spatial correlation and spatial heterogeneity) on taxi total speeding and serious speeding frequency. Taxi GPS trajectory data in a Chinese metropolis were used to identify speeding event. The study then established four kinds of Bayesian hierarchical count models base on Poisson and negative binominal distribution to estimate the contributor impacts, respectively. Results show that Bayesian hierarchical spatial Poisson log-linear model is optimum for fitting both total and serious speeding frequency. For the analysis, it is found that drivers are more likely to commit speeding on long multilane road with median strip, and road with non-motorized vehicle lane, bus-only lane and viaduct or road tunnel. Roads with low speed limit, and work zone are associated with increasing speeding as well. In terms of serious speeding, bus-only lane is not a contributor, while road speed camera number and one-way organization are significantly positive to the speeding frequency. Furthermore, it reveals that two spatial effects significantly increase the occurrence of speeding events; the impact of spatial heterogeneity is more critical.

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Zheng, Yanbing Z., Jun Zhu, and Dong Li. "Analyzing Spatial Panel Data of Cigarette Demand: A Bayesian Hierarchical Modeling Approach." Journal of Data Science 6, no. 4 (July 11, 2021): 467–89. http://dx.doi.org/10.6339/jds.2008.06(4).428.

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Law, J. "Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology by LAWSON, A. B." Biometrics 65, no. 2 (May 28, 2009): 661–62. http://dx.doi.org/10.1111/j.1541-0420.2009.01247_2.x.

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王, 行风. "Hierarchical Modeling of Indoor and Outdoor Road Network Based on Spatial Cognition." Geomatics Science and Technology 06, no. 02 (2018): 141–50. http://dx.doi.org/10.12677/gst.2018.62016.

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38

Majumdar, Anandamayee, Jason Kaye, Corinna Gries, Diane Hope, and Nancy Grimm. "Hierarchical Spatial Modeling and Prediction of Multiple Soil Nutrients and Carbon Concentrations." Communications in Statistics - Simulation and Computation 37, no. 2 (February 2008): 434–53. http://dx.doi.org/10.1080/03610910701792588.

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39

Ghosh, Jayanta K. "Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology by Andrew B. Lawson." International Statistical Review 77, no. 2 (August 2009): 325–26. http://dx.doi.org/10.1111/j.1751-5823.2009.00085_26.x.

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40

Persad, Ravi Ancil. "Hierarchical Bayesian modeling for the spatial analysis of robberies in Toronto, Canada." Spatial Information Research 28, no. 2 (June 20, 2019): 173–85. http://dx.doi.org/10.1007/s41324-019-00279-9.

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41

Khani, Navid, Ali Nadernezhad, Paulo Bartolo, and Bahattin Koc. "Hierarchical and spatial modeling and bio-additive manufacturing of multi-material constructs." CIRP Annals 66, no. 1 (2017): 229–32. http://dx.doi.org/10.1016/j.cirp.2017.04.132.

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42

Vergara, Pablo M., Santiago Saura, Christian G. Pérez-Hernández, and Gerardo E. Soto. "Hierarchical spatial decisions in fragmented landscapes: Modeling the foraging movements of woodpeckers." Ecological Modelling 300 (March 2015): 114–22. http://dx.doi.org/10.1016/j.ecolmodel.2015.01.006.

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43

Gray, Simone C., Alan E. Gelfand, and Marie Lynn Miranda. "Hierarchical spatial modeling of uncertainty in air pollution and birth weight study." Statistics in Medicine 30, no. 17 (May 17, 2011): 2187–98. http://dx.doi.org/10.1002/sim.4234.

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44

Jaya, I. Gede Nyoman Mindra, Anna Chadidjah, Yudhie Andriyana, Farah Kristiani, and Anggi Nur Fauziah. "Bayesian hierarchical spatiotemporal modeling for forecasting diarrhea risk among children under 5 in Bandung city, Indonesia." International Journal of Data and Network Science 7, no. 4 (2023): 1551–62. http://dx.doi.org/10.5267/j.ijdns.2023.8.008.

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The main objectives of this research are to identify significant spatial and temporal compo-nents associated with diarrhea and provide an accurate forecast. Using data from the Ban-dung city health surveillance system, the analysis reveals a decreasing trend in both the number of incidences and the estimated relative risks of diarrhea in most districts. Key fac-tors contributing to diarrhea variation include temporally structured, spatially structured, and unstructured effects of space-time interaction Type I. No clear seasonal pattern is observed in diarrhea incidence among children under five, emphasizing the need for consistent vigilance and preventive measures. Spatial clustering was observed in the eastern and western parts of Bandung city. The forecasting model predicts a continued decline in diarrhea incidence and relative risk throughout 2022.

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Jaya, I. Gede Nyoman Mindra, Farah Kristiani, Yudhie Andriyana, and Anna Chadidjah. "Sensitivity Analysis on Hyperprior Distribution of the Variance Components of Hierarchical Bayesian Spatiotemporal Disease Mapping." Mathematics 12, no. 3 (January 31, 2024): 451. http://dx.doi.org/10.3390/math12030451.

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Spatiotemporal disease mapping modeling with count data is gaining increasing prominence. This approach serves as a benchmark in developing early warning systems for diverse disease types. Spatiotemporal modeling, characterized by its inherent complexity, integrates spatial and temporal dependency structures, as well as interactions between space and time. A Bayesian approach employing a hierarchical structure serves as a solution for spatial model inference, addressing the identifiability problem often encountered when utilizing classical approaches like the maximum likelihood method. However, the hierarchical Bayesian approach faces a significant challenge in determining the hyperprior distribution for the variance components of hierarchical Bayesian spatiotemporal models. Commonly used distributions include logGamma for log inverse variance, Half-Cauchy, Penalized Complexity, and Uniform distribution for hyperparameter standard deviation. While the logGamma approach is relatively straightforward with faster computing times, it is highly sensitive to changes in hyperparameter values, specifically scale and shape. This research aims to identify the most optimal hyperprior distribution and its parameters under various conditions of spatial and temporal autocorrelation, as well as observation units, through a Monte Carlo study. Real data on dengue cases in West Java are utilized alongside simulation results. The findings indicate that, across different conditions, the Uniform hyperprior distribution proves to be the optimal choice.

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KOMAROVA, NATALIA L. "STOCHASTIC MODELING OF LOSS- AND GAIN-OF-FUNCTION MUTATIONS IN CANCER." Mathematical Models and Methods in Applied Sciences 17, supp01 (November 2007): 1647–73. http://dx.doi.org/10.1142/s021820250700242x.

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Here we review some spatial and non-spatial stochastic methods developed to study the dynamics of cancer progression. We illustrate the methodology with applications to the two most common patterns in cancer initiation and progression: loss-of-function and gain-of-function mutations. An example of a gain-of-function mutation is an activation of an oncogene; for such mutations we are interested in the process of mutant take-over. An example of a loss-of-function mutation is an inactivation of a tumor suppressor gene; for such processes we calculate the rate of production of double-hit mutants. We consider three stochastic models of cell populations with a constant size: a simple mass-action model, a spatial model and a hierarchical model which contains stem cells and daughter cells. Interestingly, the process of mutation accumulation and spread develops differently in different models. This suggests that simple mass-action models can be misleading when studying cancer dynamics. Moreover, our results also allow us to think about various types of tissue architecture and its protective role against cancer. In particular, we show that hierarchical tissue organization lowers the risk of cancerous transformations. Also, cellular motility and long-range signaling can decrease the risk of cancer in solid tissues.

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47

Dudek, Adrian, and Jerzy Baranowski. "Spatial Modeling of Air Pollution Using Data Fusion." Electronics 12, no. 15 (August 5, 2023): 3353. http://dx.doi.org/10.3390/electronics12153353.

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Air pollution is a widespread issue. One approach to predicting air pollution levels in specific locations is through the development of mathematical models. Spatial models are one such category, and they can be optimized using calculation methods like the INLA (integrated nested Laplace approximation) package. It streamlines the complex computational process by combining the Laplace approximation and numerical integration to approximate the model and provides a computationally efficient alternative to traditional MCMC (Markov chain Monte Carlo) methods for Bayesian inference in complex hierarchical models. Another crucial aspect is obtaining data for this type of problem. Relying only on official or professional monitoring stations can pose challenges, so it is advisable to employ data fusion techniques and integrate data from various sensors, including amateur ones. Moreover, when modeling spatial air pollution, careful consideration should be given to factors such as the range of impact and potential obstacles that may affect a pollutant’s dispersion. This study showcases the utilization of INLA spatial modeling and data fusion to address multiple problems, such as pollution in industrial facilities and urban areas. The results show promise for resolving such problems with the proposed algorithms.

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48

Wikle, Christopher K., and Andrew Zammit-Mangion. "Statistical Deep Learning for Spatial and Spatiotemporal Data." Annual Review of Statistics and Its Application 10, no. 1 (March 10, 2023): 247–70. http://dx.doi.org/10.1146/annurev-statistics-033021-112628.

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Deep neural network models have become ubiquitous in recent years and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatiotemporal data through, for example, the use of multilevel Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatiotemporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.

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49

Casanova, Joaquin, Garett Heineck, and David Huggins. "A Comparison of Yield Prediction Approaches Using Long-Term Multi-Crop Site-Specific Data." Journal of the ASABE 67, no. 3 (2024): 601–15. http://dx.doi.org/10.13031/ja.15216.

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Highlights Long-term site-specific multiple-crop yield data is used in two modeling approaches. Different sources of data, including soil properties, topography, weather, and multispectral data, are tested. Linear modeling and Bayesian hierarchical modeling (BHM) are evaluated by examining predictions of relative yield. BHM with spatio-temporal effects provides the best estimates, handles missing data, and provides uncertainty estimates in time and space. Abstract. Growers in the inland Pacific Northwest face numerous challenges in managing cropping systems. Climate variability, soil degradation, and topography all lead to significant spatial and temporal variability in yield. Often, yield modeling approaches such as deep learning can be “black boxes” or suffer from parameter uncertainty and instability, as with process-based crop models. To explore an alternative, we examined nearly two decades of crop rotation data from the R.J. Cook Agronomy Farm, along with soil properties, topography, weather, and multispectral data. We then tested two modeling approaches to estimate yield: linear modeling (LM) and Bayesian hierarchical modeling (BHM). We found BHM with spatial and temporal random effects performed best in predicting relative yield, both using soil variables as predictors or remotely sensed data. Since the BHM approach handles missing data, offers the possibility of farmer knowledge to be incorporated into prior probabilities, and gives uncertainty, this methodology lends itself well to decision support tools and on-farm study design. Keywords: Bayesian, Long-term, Modeling, Remote sensing, Yield.

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50

Ojiambo, P. S., and E. L. Kang. "Modeling Spatial Frailties in Survival Analysis of Cucurbit Downy Mildew Epidemics." Phytopathology® 103, no. 3 (March 2013): 216–27. http://dx.doi.org/10.1094/phyto-07-12-0152-r.

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Cucurbit downy mildew caused by Pseudoperonospora cubensis is economically the most important disease of cucurbits globally, and the pathogen is disseminated aerially over a large spatial scale. Spatio-temporal spread of the disease was characterized during phase I (low and sporadic disease outbreaks) and II (rapid increase in disease outbreaks) of the epidemic using records collected from sentinel plots from 2008 to 2009 in 23 states in the eastern United States as part of the United States Department of Agriculture Cucurbit Downy Mildew ipmPIPE network. A substantive goal of this study was to explain the pattern of time to disease outbreak using important covariates while accounting for spatially correlated differences in risk of disease outbreak among the states. Survival analyses that accounts for spatial dependence were performed on time to disease outbreak, and posterior median frailties (or random effects) were mapped to identify states with high or low risk for disease outbreak. From February to October, disease occurred in 195 and 172 out of 413 and 556 cases monitored in 2008 and 2009, respectively. Disease outbreaks were spatially aggregated, with a spatial dependence of up to ≈1,025 km where clustering of outbreaks in phase I and II of the epidemic were similar. However, unlike in phase I of the epidemic, space–time point pattern analysis was significant (P < 0.0001) for outbreaks in phase II, during which the highest risk window as estimated by the space–time function was within 1.5 months and 500 km of the initial outbreak. The risk of disease outbreak peaked around July and decreased thereafter until the end of the study period. Spatially correlated analysis of time to disease outbreak indicated the need to incorporate spatial frailties in standard survival analysis models. Evaluation of alternative formulations of the spatial models demonstrated that a Bayesian hierarchical spatially structured frailty model best described time to disease outbreak. This frailty model showed clustering of outbreaks at the state level and indicated that states in the mid-Atlantic region have high spatial frailties and a high risk of downy mildew outbreak.

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