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Journal articles on the topic 'Hierarchical Bayesian Priors'

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Published: 6 September 2023

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1

Song, Chengyuan, Dongchu Sun, Kun Fan, and Rongji Mu. "Posterior Propriety of an Objective Prior in a 4-Level Normal Hierarchical Model." Mathematical Problems in Engineering 2020 (February 14, 2020): 1–10. http://dx.doi.org/10.1155/2020/8236934.

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The use of hierarchical Bayesian models in statistical practice is extensive, yet it is dangerous to implement the Gibbs sampler without checking that the posterior is proper. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule approach or reference prior approach, are only implementable in simple hierarchical settings. In this paper, we consider a 4-level multivariate normal hierarchical model. We demonstrate the posterior using our recommended prior which is proper in the 4-level normal hierarchical models. A primary advantage of the recommended prior over other proposed objective priors is that it can be used at any level of a hierarchical model.
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Jiao, Yan, Christopher Hayes, and Enric Cortés. "Hierarchical Bayesian approach for population dynamics modelling of fish complexes without species-specific data." ICES Journal of Marine Science 66, no. 2 (September 26, 2008): 367–77. http://dx.doi.org/10.1093/icesjms/fsn162.

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Abstract Jiao, Y., Hayes, C., and Cortés, E. 2009. Hierarchical Bayesian approach for population dynamics modelling of fish complexes without species-specific data. – ICES Journal of Marine Science, 66: 367–377. Modelling the population dynamics of fish complexes is challenging, and many species have been assessed and managed as a complex that was treated as a single species. Two Bayesian state-space surplus production models with multilevel priors (hierarchical models) were developed to simulate variability in population growth rates of species in a complex, using the hammerhead shark complex (Sphyrna spp.) of the Atlantic and Gulf of Mexico coasts of the US as an example. The complex consists of three species: scalloped (Sphyrna lewini), great (Sphyrna mokarran), and smooth hammerhead (Sphyrna zygaena). Bayesian state-space surplus production models with multilevel priors fitted the hammerhead data better than a model based on single-level priors. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that do not include variability among species, and highly parameterized models that assign an estimate of parameters to each species. By ignoring the variability among species, confidence intervals of the estimates of stock status indicators can be unrealistically narrow, possibly leading to high-risk management strategies being adopted. Use of multilevel priors in a hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modelling fish complexes lacking species-specific data.
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Zhang, Hai, Puyu Wang, Qing Dong, and Pu Wang. "Sparse Bayesian linear regression using generalized normal priors." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 03 (February 16, 2017): 1750021. http://dx.doi.org/10.1142/s0219691317500217.

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A sparse Bayesian linear regression model is proposed that generalizes the Bayesian Lasso to a class of Bayesian models with scale mixtures of normal distributions as priors for the regression coefficients. We assume a hierarchical Bayesian model with a binary indicator for whether a predictor variable is included in the model, a generalized normal prior distribution for the coefficients of the included variables, and a Student-t error model for robustness to heavy tailed noise. Our model out-performs other popular sparse regression estimators on synthetic and real data.
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Chan, Joshua C. C. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs." International Journal of Forecasting 37, no. 3 (July 2021): 1212–26. http://dx.doi.org/10.1016/j.ijforecast.2021.01.002.

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Scarpa, Bruno, and David B. Dunson. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors." Biometrics 65, no. 3 (January 23, 2009): 772–80. http://dx.doi.org/10.1111/j.1541-0420.2008.01163.x.

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6

Gu, Xiaojing, Henry Leung, and Xingsheng Gu. "Bayesian Sparse Estimation Using Double Lomax Priors." Mathematical Problems in Engineering 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/176249.

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Sparsity-promoting prior along with Bayesian inference is an effective approach in solving sparse linear models (SLMs). In this paper, we first introduce a new sparsity-promoting prior coined as Double Lomax prior, which corresponds to a three-level hierarchical model, and then we derive a full variational Bayesian (VB) inference procedure. When noninformative hyperprior is assumed, we further show that the proposed method has one more latent variable than the canonical automatic relevance determination (ARD). This variable has a smoothing effect on the solution trajectories, thus providing improved convergence performance. The effectiveness of the proposed method is demonstrated by numerical simulations including autoregressive (AR) model identification and compressive sensing (CS) problems.
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Liang, Xinya, Akihito Kamata, and Ji Li. "Hierarchical Bayes Approach to Estimate the Treatment Effect for Randomized Controlled Trials." Educational and Psychological Measurement 80, no. 6 (March 16, 2020): 1090–114. http://dx.doi.org/10.1177/0013164420909885.

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One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance hyperparameters for estimating the treatment effect in a two-group randomized controlled trial. Assuming a random sample of treatment effect sizes is obtained from past studies, the hyper priors can be constructed based on the sampling distributions of the effect size mean and precision. The performance of the hierarchical Bayes approach was compared with the empirical Bayes approach (hyperparameters are fixed values or point estimates) and the ordinary least squares (OLS) method via simulation. The design factors for data generation included the sample treatment effect size, treatment/control group size ratio, and sample size. Each generated data set was analyzed using the hierarchical Bayes approach with three hyper priors, the empirical Bayes approach with twelve priors (including correct and inaccurate priors), and the OLS method. Results indicated that the proposed hierarchical Bayes approach generally outperformed the empirical Bayes approach and the OLS method, especially with small samples. When more sample effect sizes were available, the treatment effect was estimated more accurately regardless of the sample sizes. Practical implications and future research directions are discussed.
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Nam, Hyun Woo. "Modeling hyper-priors for Bayesian IRT equating: Fixed hyper-parameters or Hierarchical hyper-priors." Korean Society for Educational Evaluation 32, no. 4 (December 30, 2019): 777–95. http://dx.doi.org/10.31158/jeev.2019.32.4.777.

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Wang, Mengxi, Qingwang Liu, Liyong Fu, Guangxing Wang, and Xiongqing Zhang. "Airborne LIDAR-Derived Aboveground Biomass Estimates Using a Hierarchical Bayesian Approach." Remote Sensing 11, no. 9 (May 3, 2019): 1050. http://dx.doi.org/10.3390/rs11091050.

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Conventional ground survey data are very accurate, but expensive. Airborne lidar data can reduce the costs and effort required to conduct large-scale forest surveys. It is critical to improve biomass estimation and evaluate carbon stock when we use lidar data. Bayesian methods integrate prior information about unknown parameters, reduce the parameter estimation uncertainty, and improve model performance. This study focused on predicting the independent tree aboveground biomass (AGB) with a hierarchical Bayesian model using airborne LIDAR data and comparing the hierarchical Bayesian model with classical methods (nonlinear mixed effect model, NLME). Firstly, we chose the best diameter at breast height (DBH) model from several widely used models through a hierarchical Bayesian method. Secondly, we used the DBH predictions together with the tree height (LH) and canopy projection area (CPA) derived by airborne lidar as independent variables to develop the AGB model through a hierarchical Bayesian method with parameter priors from the NLME method. We then compared the hierarchical Bayesian method with the NLME method. The results showed that the two methods performed similarly when pooling the data, while for small sample sizes, the Bayesian method was much better than the classical method. The results of this study imply that the Bayesian method has the potential to improve the estimations of both DBH and AGB using LIDAR data, which reduces costs compared with conventional measurements.
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Krishnan, Ranganath, Mahesh Subedar, and Omesh Tickoo. "Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4477–84. http://dx.doi.org/10.1609/aaai.v34i04.5875.

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Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dimensional weight space. We propose MOdel Priors with Empirical Bayes using DNN (MOPED) method to choose informed weight priors in Bayesian neural networks. We formulate a two-stage hierarchical modeling, first find the maximum likelihood estimates of weights with DNN, and then set the weight priors using empirical Bayes approach to infer the posterior with variational inference. We empirically evaluate the proposed approach on real-world tasks including image classification, video activity recognition and audio classification with varying complex neural network architectures. We also evaluate our proposed approach on diabetic retinopathy diagnosis task and benchmark with the state-of-the-art Bayesian deep learning techniques. We demonstrate MOPED method enables scalable variational inference and provides reliable uncertainty quantification.
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11

Cucchi, Karina, Falk Heße, Nura Kawa, Changhong Wang, and Yoram Rubin. "Ex-situ priors: A Bayesian hierarchical framework for defining informative prior distributions in hydrogeology." Advances in Water Resources 126 (April 2019): 65–78. http://dx.doi.org/10.1016/j.advwatres.2019.02.003.

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12

Shan, Bowei. "Estimation of Response Functions Based on Variational Bayes Algorithm in Dynamic Images Sequences." BioMed Research International 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/4851401.

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We proposed a nonparametric Bayesian model based on variational Bayes algorithm to estimate the response functions in dynamic medical imaging. In dynamic renal scintigraphy, the impulse response or retention functions are rather complicated and finding a suitable parametric form is problematic. In this paper, we estimated the response functions using nonparametric Bayesian priors. These priors were designed to favor desirable properties of the functions, such as sparsity or smoothness. These assumptions were used within hierarchical priors of the variational Bayes algorithm. We performed our algorithm on the real online dataset of dynamic renal scintigraphy. The results demonstrated that this algorithm improved the estimation of response functions with nonparametric priors.
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Negrín-Hernández, Miguel-Angel, María Martel-Escobar, and Francisco-José Vázquez-Polo. "Bayesian Meta-Analysis for Binary Data and Prior Distribution on Models." International Journal of Environmental Research and Public Health 18, no. 2 (January 19, 2021): 809. http://dx.doi.org/10.3390/ijerph18020809.

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In meta-analysis, the structure of the between-sample heterogeneity plays a crucial role in estimating the meta-parameter. A Bayesian meta-analysis for binary data has recently been proposed that measures this heterogeneity by clustering the samples and then determining the posterior probability of the cluster models through model selection. The meta-parameter is then estimated using Bayesian model averaging techniques. Although an objective Bayesian meta-analysis is proposed for each type of heterogeneity, we concentrate the attention of this paper on priors over the models. We consider four alternative priors which are motivated by reasonable but different assumptions. A frequentist validation with simulated data has been carried out to analyze the properties of each prior distribution for a set of different number of studies and sample sizes. The results show the importance of choosing an adequate model prior as the posterior probabilities for the models are very sensitive to it. The hierarchical Poisson prior and the hierarchical uniform prior show a good performance when the real model is the homogeneity, or when the sample sizes are high enough. However, the uniform prior can detect the true model when it is an intermediate model (neither homogeneity nor heterogeneity) even for small sample sizes and few studies. An illustrative example with real data is also given, showing the sensitivity of the estimation of the meta-parameter to the model prior.
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14

Ghoreishi, S. K. "Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors." Journal of Statistical Theory and Applications 16, no. 1 (2017): 53. http://dx.doi.org/10.2991/jsta.2017.16.1.5.

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15

Bhattacharya, Samir K., and Ram C. Tiwari. "Hierarchical Bayesian reliability analysis using Erlang families of priors and hyperpriors." Microelectronics Reliability 32, no. 1-2 (January 1992): 241–47. http://dx.doi.org/10.1016/0026-2714(92)90102-q.

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16

Peters, Megan A. K., Ling-Qi Zhang, and Ladan Shams. "The material-weight illusion is a Bayes-optimal percept under competing density priors." PeerJ 6 (October 11, 2018): e5760. http://dx.doi.org/10.7717/peerj.5760.

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The material-weight illusion (MWI) is one example in a class of weight perception illusions that seem to defy principled explanation. In this illusion, when an observer lifts two objects of the same size and mass, but that appear to be made of different materials, the denser-looking (e.g., metal-look) object is perceived as lighter than the less-dense-looking (e.g., polystyrene-look) object. Like the size-weight illusion (SWI), this perceptual illusion occurs in the opposite direction of predictions from an optimal Bayesian inference process, which predicts that the denser-looking object should be perceived as heavier, not lighter. The presence of this class of illusions challenges the often-tacit assumption that Bayesian inference holds universal explanatory power to describe human perception across (nearly) all domains: If an entire class of perceptual illusions cannot be captured by the Bayesian framework, how could it be argued that human perception truly follows optimal inference? However, we recently showed that the SWI can be explained by an optimal hierarchical Bayesian causal inference process (Peters, Ma & Shams, 2016) in which the observer uses haptic information to arbitrate among competing hypotheses about objects’ possible density relationship. Here we extend the model to demonstrate that it can readily explain the MWI as well. That hierarchical Bayesian inference can explain both illusions strongly suggests that even puzzling percepts arise from optimal inference processes.
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17

Mohite, Siddharth R., Priyadarshini Rajkumar, Shreya Anand, David L. Kaplan, Michael W. Coughlin, Ana Sagués-Carracedo, Muhammed Saleem, et al. "Inferring Kilonova Population Properties with a Hierarchical Bayesian Framework. I. Nondetection Methodology and Single-event Analyses." Astrophysical Journal 925, no. 1 (January 1, 2022): 58. http://dx.doi.org/10.3847/1538-4357/ac3981.

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Abstract We present nimbus: a hierarchical Bayesian framework to infer the intrinsic luminosity parameters of kilonovae (KNe) associated with gravitational-wave (GW) events, based purely on nondetections. This framework makes use of GW 3D distance information and electromagnetic upper limits from multiple surveys for multiple events and self-consistently accounts for the finite sky coverage and probability of astrophysical origin. The framework is agnostic to the brightness evolution assumed and can account for multiple electromagnetic passbands simultaneously. Our analyses highlight the importance of accounting for model selection effects, especially in the context of nondetections. We show our methodology using a simple, two-parameter linear brightness model, taking the follow-up of GW190425 with the Zwicky Transient Facility as a single-event test case for two different prior choices of model parameters: (i) uniform/uninformative priors and (ii) astrophysical priors based on surrogate models of Monte Carlo radiative-transfer simulations of KNe. We present results under the assumption that the KN is within the searched region to demonstrate functionality and the importance of prior choice. Our results show consistency with simsurvey—an astronomical survey simulation tool used previously in the literature to constrain the population of KNe. While our results based on uniform priors strongly constrain the parameter space, those based on astrophysical priors are largely uninformative, highlighting the need for deeper constraints. Future studies with multiple events having electromagnetic follow-up from multiple surveys should make it possible to constrain the KN population further.
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Nabi, Sareh, Houssam Nassif, Joseph Hong, Hamed Mamani, and Guido Imbens. "Bayesian Meta-Prior Learning Using Empirical Bayes." Management Science 68, no. 3 (March 2022): 1737–55. http://dx.doi.org/10.1287/mnsc.2021.4136.

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Adding domain knowledge to a learning system is known to improve results. In multiparameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, the various model parameters can have different learning rates in real-world problems, especially with skewed data. Two often-faced challenges in operation management and management science applications are the absence of informative priors and the inability to control parameter learning rates. In this study, we propose a hierarchical empirical Bayes approach that addresses both challenges and that can generalize to any Bayesian framework. Our method learns empirical meta-priors from the data itself and uses them to decouple the learning rates of first-order and second-order features (or any other given feature grouping) in a generalized linear model. Because the first-order features are likely to have a more pronounced effect on the outcome, focusing on learning first-order weights first is likely to improve performance and convergence time. Our empirical Bayes method clamps features in each group together and uses the deployed model’s observed data to empirically compute a hierarchical prior in hindsight. We report theoretical results for the unbiasedness, strong consistency, and optimal frequentist cumulative regret properties of our meta-prior variance estimator. We apply our method to a standard supervised learning optimization problem as well as an online combinatorial optimization problem in a contextual bandit setting implemented in an Amazon production system. During both simulations and live experiments, our method shows marked improvements, especially in cases of small traffic. Our findings are promising because optimizing over sparse data is often a challenge. This paper was accepted by Hamid Nazerzadeh, Management Science Special Section on Data-Driven Prescriptive Analytics.
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LIU, Shuai, Licheng JIAO, Shuyuan YANG, and Hongying LIU. "Hierarchical Sparse Bayesian Learning with Beta Process Priors for Hyperspectral Imagery Restoration." IEICE Transactions on Information and Systems E100.D, no. 2 (2017): 350–58. http://dx.doi.org/10.1587/transinf.2016edp7322.

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20

Keefe, Matthew J., Marco A. R. Ferreira, and Christopher T. Franck. "Objective Bayesian Analysis for Gaussian Hierarchical Models with Intrinsic Conditional Autoregressive Priors." Bayesian Analysis 14, no. 1 (March 2019): 181–209. http://dx.doi.org/10.1214/18-ba1107.

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21

Bell, Andrew, and Kelvyn Jones. "Bayesian informative priors with Yang and Land’s hierarchical age–period–cohort model." Quality & Quantity 49, no. 1 (December 25, 2013): 255–66. http://dx.doi.org/10.1007/s11135-013-9985-3.

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22

Donegan, Connor, Yongwan Chun, and Amy E. Hughes. "Bayesian estimation of spatial filters with Moran’s eigenvectors and hierarchical shrinkage priors." Spatial Statistics 38 (August 2020): 100450. http://dx.doi.org/10.1016/j.spasta.2020.100450.

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23

Zhou, Feng, and Xueru Bai. "High-Resolution Sparse Subband Imaging Based on Bayesian Learning With Hierarchical Priors." IEEE Transactions on Geoscience and Remote Sensing 56, no. 8 (August 2018): 4568–80. http://dx.doi.org/10.1109/tgrs.2018.2827072.

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24

Abdelnour, Farras, Christopher Genovese, and Theodore Huppert. "Hierarchical Bayesian regularization of reconstructions for diffuse optical tomography using multiple priors." Biomedical Optics Express 1, no. 4 (October 6, 2010): 1084. http://dx.doi.org/10.1364/boe.1.001084.

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25

McCandless, Lawrence C., Paul Gustafson, Adrian R. Levy, and Sylvia Richardson. "Hierarchical priors for bias parameters in Bayesian sensitivity analysis for unmeasured confounding." Statistics in Medicine 31, no. 4 (January 17, 2012): 383–96. http://dx.doi.org/10.1002/sim.4453.

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26

Odegaard, Brian, and Ladan Shams. "The Relationship Between Audiovisual Binding Tendencies and Prodromal Features of Schizophrenia in the General Population." Clinical Psychological Science 5, no. 4 (June 9, 2017): 733–41. http://dx.doi.org/10.1177/2167702617704014.

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Current theoretical accounts of schizophrenia have considered the disorder within the framework of hierarchical Bayesian inference, positing that symptoms arise from a deficit in the brain’s capacity to combine incoming sensory information with preexisting priors. Here, we present the first investigation to examine the relationship between priors governing multisensory perception and subclinical, prodromal features of schizophrenia in the general population. We tested participants in two complementary tasks (one spatial, one temporal) and employed a Bayesian model to estimate both the precision of unisensory encoding and the prior tendency to integrate audiovisual signals (i.e., the “binding tendency”). Results revealed that lower binding tendency scores in the spatial task were associated with higher numbers of self-reported prodromal features. These results indicate decreased binding of audiovisual spatial information may be moderately related to the frequency of prodromal characteristics in the general population.
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MacNab, Ying C. "On Gaussian Markov random fields and Bayesian disease mapping." Statistical Methods in Medical Research 20, no. 1 (June 14, 2010): 49–68. http://dx.doi.org/10.1177/0962280210371561.

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We discuss the nature of Gaussian Markov random fields (GMRFs) as they are typically formulated via full conditionals, also named conditional autoregressive or CAR formulations, to represent small area relative risks ensemble priors within a Bayesian hierarchical model framework for statistical inference in disease mapping and spatial regression. We present a partial review on GMRF/CAR and multivariate GMRF prior formulations in univariate and multivariate disease mapping models and communicate insights into various prior characteristics for representing disease risks variability and ‘spatial interaction.’ We also propose convolution prior modifications to the well known BYM model for attainment of identifiability and Bayesian robustness in univariate and multivariate disease mapping and spatial regression. Several illustrative examples of disease mapping and spatial regression are presented.
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GILL, JEFF, and JOHN R. FREEMAN. "Dynamic elicited priors for updating covert networks." Network Science 1, no. 1 (April 2013): 68–94. http://dx.doi.org/10.1017/nws.2012.6.

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AbstractThe study of covert networks is plagued by the fact that individuals conceal their attributes and associations. To address this problem, we develop a technology for eliciting this information from qualitative subject-matter experts to inform statistical social network analysis. We show how the information from the subjective probability distributions can be used as input to Bayesian hierarchical models for network data. In the spirit of “proof of concept,” the results of a test of the technology are reported. Our findings show that human subjects can use the elicitation tool effectively, supplying attribute and edge information to update a network indicative of a covert one.
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Yang, Bishan, Claire Cardie, and Peter Frazier. "A Hierarchical Distance-dependent Bayesian Model for Event Coreference Resolution." Transactions of the Association for Computational Linguistics 3 (December 2015): 517–28. http://dx.doi.org/10.1162/tacl_a_00155.

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We present a novel hierarchical distance-dependent Bayesian model for event coreference resolution. While existing generative models for event coreference resolution are completely unsupervised, our model allows for the incorporation of pairwise distances between event mentions — information that is widely used in supervised coreference models to guide the generative clustering processing for better event clustering both within and across documents. We model the distances between event mentions using a feature-rich learnable distance function and encode them as Bayesian priors for nonparametric clustering. Experiments on the ECB+ corpus show that our model outperforms state-of-the-art methods for both within- and cross-document event coreference resolution.
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Delgado, H. E., L. M. Sarro, G. Clementini, T. Muraveva, and A. Garofalo. "Hierarchical Bayesian model to inferPL(Z)relations usingGaiaparallaxes." Astronomy & Astrophysics 623 (March 2019): A156. http://dx.doi.org/10.1051/0004-6361/201832945.

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In a recent study we analysed period–luminosity–metallicity (PLZ) relations for RR Lyrae stars using theGaiaData Release 2 (DR2) parallaxes. It built on a previous work that was based on the firstGaiaData Release (DR1), and also included period–luminosity (PL) relations for Cepheids and RR Lyrae stars. The method used to infer the relations fromGaiaDR2 data and one of the methods used forGaiaDR1 data was based on a Bayesian model, the full description of which was deferred to a subsequent publication. This paper presents the Bayesian method for the inference of the parameters ofPL(Z) relations used in those studies, the main feature of which is to manage the uncertainties on observables in a rigorous and well-founded way. The method encodes the probability relationships between the variables of the problem in a hierarchical Bayesian model and infers the posterior probability distributions of thePL(Z) relationship coefficients using Markov chain Monte Carlo simulation techniques. We evaluate the method with several semi-synthetic data sets and apply it to a sample of 200 fundamental and first-overtone RR Lyrae stars for whichGaiaDR1 parallaxes and literatureKs-band mean magnitudes are available. We define and test several hyperprior probabilities to verify their adequacy and check the sensitivity of the solution with respect to the prior choice. The main conclusion of this work, based on the test with semi-syntheticGaiaDR1 parallaxes, is the absolute necessity of incorporating the existing correlations between the period, metallicity, and parallax measurements in the form of model priors in order to avoid systematically biased results, especially in the case of non-negligible uncertainties in the parallaxes. The relation coefficients obtained here have been superseded by those presented in our recent paper that incorporates the findings of this work and the more recentGaiaDR2 measurements.
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Liu, Qinghua, Yuanxin He, Kai Ding, and Quanmin Xie. "Complex Multisnapshot Sparse Bayesian Learning for Offgrid DOA Estimation." International Journal of Antennas and Propagation 2022 (February 28, 2022): 1–12. http://dx.doi.org/10.1155/2022/4500243.

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Direction of arrival (DOA) estimation has recently been developed based on sparse signal reconstruction (SSR). Sparse Bayesian learning (SBL) is a typical method of SSR. In SBL, the two-layer hierarchical model in Gaussian scale mixtures (GSMs) has been used to model sparsity-inducing priors. However, this model is mainly applied to real-valued signal models. In order to apply SBL to complex-valued signal models, a general class of sparsity-inducing priors is proposed for complex-valued signal models by complex Gaussian scale mixtures (CGSMs), and the special cases correspond to complex versions of several classical priors are provided, which is helpful to analyze the connections with different modeling methods. In addition, the expression of the SBL form of the real- and complex-valued model is unified by parameter values, which makes it possible to generalize and improve the properties of the SBL methods. Finally, the SBL complex-valued form is applied to the offgrid DOA estimation complex-valued model, and the performance between different sparsity-inducing priors is compared. Theoretical analysis and simulation results show that the proposed algorithm can effectively process complex-valued signal models and has lower algorithm complexity.
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32

Muller, Peter, and Gary L. Rosner. "A Bayesian Population Model With Hierarchical Mixture Priors Applied to Blood Count Data." Journal of the American Statistical Association 92, no. 440 (December 1997): 1279. http://dx.doi.org/10.2307/2965398.

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Yu, Rongjie, and Mohamed Abdel-Aty. "Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions." Accident Analysis & Prevention 56 (July 2013): 51–58. http://dx.doi.org/10.1016/j.aap.2013.03.023.

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Yang, Jie, and Yixin Yang. "Sparse Bayesian DOA Estimation Using Hierarchical Synthesis Lasso Priors for Off-Grid Signals." IEEE Transactions on Signal Processing 68 (2020): 872–84. http://dx.doi.org/10.1109/tsp.2020.2967665.

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Müller, Peter, and Gary L. Rosner. "A Bayesian Population Model with Hierarchical Mixture Priors Applied to Blood Count Data." Journal of the American Statistical Association 92, no. 440 (December 1997): 1279–92. http://dx.doi.org/10.1080/01621459.1997.10473649.

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36

Leoni, Leonardo, Farshad BahooToroody, Saeed Khalaj, Filippo De Carlo, Ahmad BahooToroody, and Mohammad Mahdi Abaei. "Bayesian Estimation for Reliability Engineering: Addressing the Influence of Prior Choice." International Journal of Environmental Research and Public Health 18, no. 7 (March 24, 2021): 3349. http://dx.doi.org/10.3390/ijerph18073349.

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Over the last few decades, reliability analysis has attracted significant interest due to its importance in risk and asset integrity management. Meanwhile, Bayesian inference has proven its advantages over other statistical tools, such as maximum likelihood estimation (MLE) and least square estimation (LSE), in estimating the parameters characterizing failure modelling. Indeed, Bayesian inference can incorporate prior beliefs and information into the analysis, which could partially overcome the lack of data. Accordingly, this paper aims to provide a closed-mathematical representation of Bayesian analysis for reliability assessment of industrial components while investigating the effect of the prior choice on future failures predictions. To this end, hierarchical Bayesian modelling (HBM) was tested on three samples with distinct sizes, while five different prior distributions were considered. Moreover, a beta-binomial distribution was adopted to represent the failure behavior of the considered device. The results show that choosing strong informative priors leads to distinct predictions, even if a larger sample size is considered. The outcome of this research could help maintenance engineers and asset managers in integrating their prior beliefs into the reliability estimation process.
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37

Millar, Russell B., and Wayne S. Stewart. "Automatic calculation of the sensitivity of Bayesian fisheries models to informative priors." Canadian Journal of Fisheries and Aquatic Sciences 62, no. 5 (May 1, 2005): 1028–36. http://dx.doi.org/10.1139/f04-240.

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The derivatives of Bayes estimators, with respect to changes in hyper-parameters of the prior density, are posterior covariances. Hence, these derivatives can be readily estimated from a posterior sample and the calculation is shown to be especially straightforward for parameters having a marginal prior that is of exponential family form. Three examples are given. The first fits a Ricker curve to stock–recruit data and, for several important management parameters, examines the sensitivity of the Bayes estimates to the informative log-normal priors placed on the maximum annual reproductive rate and density-dependent compensation parameters. Using the WinBUGS software, it is demonstrated that these derivatives can easily be estimated by a minor addition to the program code. The utility of the estimated sensitivities is examined by refitting the Ricker model using a range of different priors. The second example revisits a hierarchical model that was used to perform a meta-stock assessment on several US West Coast rockfish (Sebastes spp.) stocks, and examines the sensitivity of the Bayes estimate of bulk catchability to the hyper-prior. The final example looks at an example from the literature and uses summary statistics provided therein to determine the sensitivity of model parameters to their prior means.
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38

Zhang, Li, and Ying-Ying Zhang. "The Bayesian Posterior and Marginal Densities of the Hierarchical Gamma–Gamma, Gamma–Inverse Gamma, Inverse Gamma–Gamma, and Inverse Gamma–Inverse Gamma Models with Conjugate Priors." Mathematics 10, no. 21 (October 28, 2022): 4005. http://dx.doi.org/10.3390/math10214005.

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Positive, continuous, and right-skewed data are fit by a mixture of gamma and inverse gamma distributions. For 16 hierarchical models of gamma and inverse gamma distributions, there are only 8 of them that have conjugate priors. We first discuss some common typical problems for the eight hierarchical models that do not have conjugate priors. Then, we calculate the Bayesian posterior densities and marginal densities of the eight hierarchical models that have conjugate priors. After that, we discuss the relations among the eight analytical marginal densities. Furthermore, we find some relations among the random variables of the marginal densities and the beta densities. Moreover, we discuss random variable generations for the gamma and inverse gamma distributions by using the R software. In addition, some numerical simulations are performed to illustrate four aspects: the plots of marginal densities, the generations of random variables from the marginal density, the transformations of the moment estimators of the hyperparameters of a hierarchical model, and the conclusions about the properties of the eight marginal densities that do not have a closed form. Finally, we illustrate our method by a real data example, in which the original and transformed data are fit by the marginal density with different hyperparameters.
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Pibouleau, Leslie, and Sylvie Chevret. "BAYESIAN HIERARCHICAL META-ANALYSIS MODEL FOR MEDICAL DEVICE EVALUATION: APPLICATION TO INTRACRANIAL STENTS." International Journal of Technology Assessment in Health Care 29, no. 2 (April 2013): 123–30. http://dx.doi.org/10.1017/s0266462313000093.

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Objectives: The aim of this study was to propose a statistical model that takes into account clinical data on earlier versions when evaluating the latest version of an implantable medical device (IMD).Methods: We compared the performances of a Bayesian three-level hierarchical meta-analysis model with those of a Bayesian random-effects model through a simulation study. Posterior mean estimates of the success rate for each IMD version were computed as well as the probability that the latest version improved in effectiveness. Models were compared using the Deviance Information Criterion (DIC), the estimated bias and the standard deviation of the mean success rates. Sensitivity analyses to the choice of the priors were performed. These methods were applied to the evaluation of an intracranial stent used to treat wide-necked aneurysms.Results: When IMD versions did not differ in effectiveness, the best-fitting model was the random-effects model. By contrast, when there was a version effect, the hierarchical model was selected in more than 95 percent of the cases. It provided precise estimations of success rates of each IMD version and allowed detecting an improvement in effectiveness of the latest version, with a low influence of the choice of the priors. No evidence of benefit from the latest version of the intracranial stent was found.Conclusions: In the setting of IMD assessment, comparison of DIC between the two proposed models appeared useful for detecting version effects. In that case, Bayesian hierarchical meta-analysis model may help the decision maker by providing useful information on the latest version of IMD compared with the previous versions.
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Thorson, James T., and Jim Berkson. "Multispecies estimation of Bayesian priors for catchability trends and density dependence in the US Gulf of Mexico." Canadian Journal of Fisheries and Aquatic Sciences 67, no. 6 (June 2010): 936–54. http://dx.doi.org/10.1139/f10-040.

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Fishery-dependent catch-per-unit-effort (CPUE) derived indices of stock abundance are commonly used in fishery stock assessment models and may be significantly biased due to changes in catchability over time. Factors causing time-varying catchability include density-dependent habitat selection and technology improvements such as global positioning systems. In this study, we develop a novel multispecies method to estimate Bayesian priors for catchability functional parameters. This method uses the deviance information criterion to select a parsimonious functional model for catchability among 10 hierarchical and measurement error models. The parsimonious model is then applied to multispecies data, while excluding one species at a time, to develop Bayesian priors that can be used for each excluded species. We use this method to estimate catchability trends and density dependence for seven stocks and four gears in the Gulf of Mexico by comparing CPUE-derived index data with abundance estimates from virtual population analysis calibrated with fishery-independent indices. Catchability density dependence estimates mean that CPUE indices are hyperstable, implying that stock rebuilding in the Gulf may be progressing faster than previously estimated. This method for estimating Bayesian priors can provide a parsimonious method to compensate for time-varying catchability and uses multispecies fishery data in a novel manner.
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Montano, Diego. "Multivariate hierarchical Bayesian models and choice of priors in the analysis of survey data." Journal of Applied Statistics 44, no. 16 (December 20, 2016): 3011–32. http://dx.doi.org/10.1080/02664763.2016.1267120.

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42

Dunson, David B., and Kenneth R. Tindall. "Bayesian Analysis of Mutational Spectra." Genetics 156, no. 3 (November 1, 2000): 1411–18. http://dx.doi.org/10.1093/genetics/156.3.1411.

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Abstract Studies that examine both the frequency of gene mutation and the pattern or spectrum of mutational changes can be used to identify chemical mutagens and to explore the molecular mechanisms of mutagenesis. In this article, we propose a Bayesian hierarchical modeling approach for the analysis of mutational spectra. We assume that the total number of independent mutations and the numbers of mutations falling into different response categories, defined by location within a gene and/or type of alteration, follow binomial and multinomial sampling distributions, respectively. We use prior distributions to summarize past information about the overall mutation frequency and the probabilities corresponding to the different mutational categories. These priors can be chosen on the basis of data from previous studies using an approach that accounts for heterogeneity among studies. Inferences about the overall mutation frequency, the proportions of mutations in each response category, and the category-specific mutation frequencies can be based on posterior distributions, which incorporate past and current data on the mutant frequency and on DNA sequence alterations. Methods are described for comparing groups and for assessing doserelated trends. We illustrate our approach using data from the literature.
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43

Pacifico, Antonio. "Structural Compressed Panel VAR with Stochastic Volatility: A Robust Bayesian Model Averaging Procedure." Econometrics 10, no. 3 (July 12, 2022): 28. http://dx.doi.org/10.3390/econometrics10030028.

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This paper improves the existing literature on the shrinkage of high dimensional model and parameter spaces through Bayesian priors and Markov Chains algorithms. A hierarchical semiparametric Bayes approach is developed to overtake limits and misspecificity involved in compressed regression models. Methodologically, a multicountry large structural Panel Vector Autoregression is compressed through a robust model averaging to select the best subset across all possible combinations of predictors, where robust stands for the use of mixtures of proper conjugate priors. Concerning dynamic analysis, volatility changes and conditional density forecasts are addressed ensuring accurate predictive performance and capability. An empirical and simulated experiment are developed to highlight and discuss the functioning of the estimating procedure and forecasting accuracy.
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Cunanan, Kristen M., Alexia Iasonos, Ronglai Shen, and Mithat Gönen. "Variance prior specification for a basket trial design using Bayesian hierarchical modeling." Clinical Trials 16, no. 2 (December 7, 2018): 142–53. http://dx.doi.org/10.1177/1740774518812779.

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Background: In the era of targeted therapies, clinical trials in oncology are rapidly evolving, wherein patients from multiple diseases are now enrolled and treated according to their genomic mutation(s). In such trials, known as basket trials, the different disease cohorts form the different baskets for inference. Several approaches have been proposed in the literature to efficiently use information from all baskets while simultaneously screening to find individual baskets where the drug works. Most proposed methods are developed in a Bayesian paradigm that requires specifying a prior distribution for a variance parameter, which controls the degree to which information is shared across baskets. Methods: A common approach used to capture the correlated binary endpoints across baskets is Bayesian hierarchical modeling. We evaluate a Bayesian adaptive design in the context of a non-randomized basket trial and investigate three popular prior specifications: an inverse-gamma prior on the basket-level variance, a uniform prior and half-t prior on the basket-level standard deviation. Results: From our simulation study, we can see that the inverse-gamma prior is highly sensitive to the input hyperparameters. When the prior mean value of the variance parameter is set to be near zero [Formula: see text], this can lead to unacceptably high false-positive rates [Formula: see text] in some scenarios. Thus, use of this prior requires a fully comprehensive sensitivity analysis before implementation. Alternatively, we see that a prior that places sufficient mass in the tail, such as the uniform or half-t prior, displays desirable and robust operating characteristics over a wide range of prior specifications, with the caveat that the upper bound of the uniform prior and the scale parameter of the half-t prior must be larger than 1. Conclusion: Based on the simulation results, we recommend that those involved in designing basket trials that implement hierarchical modeling avoid using a prior distribution that places a majority of the density mass near zero for the variance parameter. Priors with this property force the model to share information regardless of the true efficacy configuration of the baskets. Many commonly used inverse-gamma prior specifications have this undesirable property. We recommend to instead consider the more robust uniform prior or half-t prior on the standard deviation.
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45

Mangipudi, Abhi, Eric Thrane, and Csaba Balazs. "Bayesian WIMP detection with the Cherenkov Telescope Array." Journal of Cosmology and Astroparticle Physics 2022, no. 11 (November 1, 2022): 010. http://dx.doi.org/10.1088/1475-7516/2022/11/010.

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Abstract Over the past decades Bayesian methods have become increasingly popular in astronomy and physics as stochastic samplers have enabled efficient investigation of high-dimensional likelihood surfaces. In this work we develop a hierarchical Bayesian inference framework to detect the presence of dark matter annihilation events in data from the Cherenkov Telescope Array (CTA). Gamma-ray events are weighted based on their measured sky position Ω̂ m and energy Em in order to derive a posterior distribution for the dark matter's velocity averaged cross section 〈σv〉. The dark matter signal model and the astrophysical background model are cast as prior distributions for (Ω̂ m , Em ). The shape of these prior distributions can be fixed based on first-principle models; or one may adopt flexible priors to include theoretical uncertainty, for example, in the dark matter annihilation spectrum or the astrophysical distribution of sky location. We demonstrate the utility of this formalism using simulated data with a Galactic Centre signal from scalar singlet dark-matter model. The sensitivity according to our method is comparable to previous estimates of the CTA sensitivity.
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Asmarian, Naeimehossadat, Seyyed Mohammad Taghi Ayatollahi, Zahra Sharafi, and Najaf Zare. "Bayesian Spatial Joint Model for Disease Mapping of Zero-Inflated Data with R-INLA: A Simulation Study and an Application to Male Breast Cancer in Iran." International Journal of Environmental Research and Public Health 16, no. 22 (November 13, 2019): 4460. http://dx.doi.org/10.3390/ijerph16224460.

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Hierarchical Bayesian log-linear models for Poisson-distributed response data, especially Besag, York and Mollié (BYM) model, are widely used for disease mapping. In some cases, due to the high proportion of zero, Bayesian zero-inflated Poisson models are applied for disease mapping. This study proposes a Bayesian spatial joint model of Bernoulli distribution and Poisson distribution to map disease count data with excessive zeros. Here, the spatial random effect is simultaneously considered into both logistic and log-linear models in a Bayesian hierarchical framework. In addition, we focus on the BYM2 model, a re-parameterization of the common BYM model, with penalized complexity priors for the latent level modeling in the joint model and zero-inflated Poisson models with different type of zeros. To avoid model fitting and convergence issues, Bayesian inferences are implemented using the integrated nested Laplace approximation (INLA) method. The models are compared according to the deviance information criterion and the logarithmic scoring. A simulation study with different proportions of zero exhibits INLA ability in running the models and also shows slight differences between the popular BYM and BYM2 models in terms of model choice criteria. In an application, we apply the fitting models on male breast cancer data in Iran at county level in 2014.
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Yang, Haoyuan, Xiuqin Su, Jing Wu, and Songmao Chen. "Non-blind image blur removal method based on a Bayesian hierarchical model with hyperparameter priors." Optik 204 (February 2020): 164178. http://dx.doi.org/10.1016/j.ijleo.2020.164178.

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48

van Erp, Bart, Wouter W. L. Nuijten, Thijs van de Laar, and Bert de Vries. "Automating Model Comparison in Factor Graphs." Entropy 25, no. 8 (July 29, 2023): 1138. http://dx.doi.org/10.3390/e25081138.

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Bayesian state and parameter estimation are automated effectively in a variety of probabilistic programming languages. The process of model comparison on the other hand, which still requires error-prone and time-consuming manual derivations, is often overlooked despite its importance. This paper efficiently automates Bayesian model averaging, selection, and combination by message passing on a Forney-style factor graph with a custom mixture node. Parameter and state inference, and model comparison can then be executed simultaneously using message passing with scale factors. This approach shortens the model design cycle and allows for the straightforward extension to hierarchical and temporal model priors to accommodate for modeling complicated time-varying processes.
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Silva, Fabyano Fonseca e., Thelma Sáfadi, Joel Augusto Muniz, Guilherme Jordão Magalhães Rosa, Luiz Henrique de Aquino, Gerson Barreto Mourão, and Carlos Henrique Osório Silva. "Bayesian analysis of autoregressive panel data model: application in genetic evaluation of beef cattle." Scientia Agricola 68, no. 2 (April 2011): 237–45. http://dx.doi.org/10.1590/s0103-90162011000200015.

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The animal breeding values forecasting at futures times is a relevant technological innovation in the field of Animal Science, since its enables a previous indication of animals that will be either kept by the producer for breeding purposes or discarded. This study discusses an MCMC Bayesian methodology applied to panel data in a time series context. We consider Bayesian analysis of an autoregressive, AR(p), panel data model of order p, using an exact likelihood function, comparative analysis of prior distributions and predictive distributions of future observations. The methodology was tested by a simulation study using three priors: hierarchical Multivariate Normal-Inverse Gamma (model 1), independent Multivariate Student's t Inverse Gamma (model 2) and Jeffrey's (model 3). Comparisons by Pseudo-Bayes Factor favored model 2. The proposed methodology was applied to longitudinal data relative to Expected Progeny Difference (EPD) of beef cattle sires. The forecast efficiency was around 80%. Regarding the mean width of the EPD interval estimation (95%) in a future time, a great advantage was observed for the proposed Bayesian methodology over usual asymptotic frequentist method.
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Hassan, Masoud M. "A Fully Bayesian Logistic Regression Model for Classification of ZADA Diabetes Dataset." Science Journal of University of Zakho 8, no. 3 (September 30, 2020): 105–11. http://dx.doi.org/10.25271/sjuoz.2020.8.3.707.

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Classification of diabetes data with existing data mining and machine learning algorithms is challenging and the predictions are not always accurate. We aim to build a model that effectively addresses these challenges (misclassification) and can accurately diagnose and classify diabetes. In this study, we investigated the use of Bayesian Logistic Regression (BLR) for mining such data to diagnose and classify various diabetes conditions. This approach is fully Bayesian suited for automating Markov Chain Monte Carlo (MCMC) simulation. Using Bayesian methods in analysing medical data is useful because of the rich hierarchical models, uncertainty quantification, and prior information they provide. The analysis was done on a real medical dataset created for 909 patients in Zakho city with a binary class label and seven independent variables. Three different prior distributions (Gaussian, Laplace and Cauchy) were investigated for our proposed model implemented by MCMC. The performance and behaviour of the Bayesian approach were illustrated and compared with the traditional classification algorithms on this dataset using 10-fold cross-validation. Experimental results show overall that classification under BLR with informative Gaussian priors performed better in terms of various accuracy metrics. It provides an accuracy of 92.53%, a recall of 94.85%, a precision of 91.42% and an F1 score of 93.11%. Experimental results suggest that it is worthwhile to explore the application of BLR to predictive modelling tasks in medical studies using informative prior distributions.
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