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Academic literature on the topic 'Hierarchical Bayesian Priors'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Hierarchical Bayesian Priors"

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 propo

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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 (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

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3

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 (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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4

Chan, Joshua C. C. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs." International Journal of Forecasting 37, no. 3 (2021): 1212–26. http://dx.doi.org/10.1016/j.ijforecast.2021.01.002.

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5

Scarpa, Bruno, and David B. Dunson. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors." Biometrics 65, no. 3 (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 im

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7

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 (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

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8

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 (2019): 777–95. http://dx.doi.org/10.31158/jeev.2019.32.4.777.

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9

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 (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

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10

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 (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

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