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Journal articles on the topic 'Hierarchal Bayesian statistics'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Yada, Shinjo, and Chikuma Hamada. "A Bayesian hierarchal modeling approach to shortening phase I/II trials of anticancer drug combinations." Pharmaceutical Statistics 17, no. 6 (August 15, 2018): 750–60. http://dx.doi.org/10.1002/pst.1895.

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2

Zhuang, Lili, and Noel Cressie. "Bayesian hierarchical statistical SIRS models." Statistical Methods & Applications 23, no. 4 (November 2014): 601–46. http://dx.doi.org/10.1007/s10260-014-0280-9.

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3

Price, M. A., J. D. McEwen, X. Cai, and T. D. Kitching (for the LSST Dark Energy Science Collaboration). "Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations." Monthly Notices of the Royal Astronomical Society 489, no. 3 (August 26, 2019): 3236–50. http://dx.doi.org/10.1093/mnras/stz2373.

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ABSTRACT Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.

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4

Ghosh, Malay, Tapabrata Maiti, Dalho Kim, Sounak Chakraborty, and Ashutosh Tewari. "Hierarchical Bayesian Neural Networks." Journal of the American Statistical Association 99, no. 467 (September 2004): 601–8. http://dx.doi.org/10.1198/016214504000000665.

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5

Telesca, Donatello, and Lurdes Y. T. Inoue. "Bayesian Hierarchical Curve Registration." Journal of the American Statistical Association 103, no. 481 (March 1, 2008): 328–39. http://dx.doi.org/10.1198/016214507000001139.

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6

Dunson, David B. "Bayesian nonparametric hierarchical modeling." Biometrical Journal 51, no. 2 (April 2009): 273–84. http://dx.doi.org/10.1002/bimj.200800183.

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7

Zhuang, Haoxin, Liqun Diao, and Grace Y. Yi. "A Bayesian hierarchical copula model." Electronic Journal of Statistics 14, no. 2 (2020): 4457–88. http://dx.doi.org/10.1214/20-ejs1784.

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8

Han, Ming. "E-Bayesian Estimation and Hierarchical Bayesian Estimation of Failure Probability." Communications in Statistics - Theory and Methods 40, no. 18 (September 15, 2011): 3303–14. http://dx.doi.org/10.1080/03610926.2010.498643.

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9

AlKheder, Sharaf, and Moudhi Al-Rashidi. "Bayesian hierarchical statistics for traffic safety modelling and forecasting." International Journal of Injury Control and Safety Promotion 27, no. 2 (September 18, 2019): 99–111. http://dx.doi.org/10.1080/17457300.2019.1665550.

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10

Angers, Jean-François, and Mohan Delampady. "Hierarchical bayesian curve fitting and smoothing." Canadian Journal of Statistics 20, no. 1 (March 1992): 35–49. http://dx.doi.org/10.2307/3315573.

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11

Cohen, Jacqueline, Daniel Nagin, Garrick Wallstrom, and Larry Wasserman. "Hierarchical Bayesian Analysis of Arrest Rates." Journal of the American Statistical Association 93, no. 444 (December 1998): 1260–70. http://dx.doi.org/10.1080/01621459.1998.10473787.

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12

Mitra, Riten, Ryan Gill, Sinjini Sikdar, and Susmita Datta. "Bayesian hierarchical model for protein identifications." Journal of Applied Statistics 46, no. 1 (March 25, 2018): 30–46. http://dx.doi.org/10.1080/02664763.2018.1454893.

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13

Park, Goeun, Heesun Jung, Seok-Jae Heo, and Inkyung Jung. "Comparison of Data Mining Methods for the Signal Detection of Adverse Drug Events with a Hierarchical Structure in Postmarketing Surveillance." Life 10, no. 8 (August 5, 2020): 138. http://dx.doi.org/10.3390/life10080138.

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There are several different proposed data mining methods for the postmarketing surveillance of drug safety. Adverse events are often classified into a hierarchical structure. Our objective was to compare the performance of several of these different data mining methods for adverse drug events data with a hierarchical structure. We generated datasets based on the World Health Organization’s Adverse Reaction Terminology (WHO-ART) hierarchical structure. We evaluated different data mining methods for signal detection, including several frequentist methods such as reporting odds ratio (ROR), proportional reporting ratio (PRR), information component (IC), the likelihood ratio test-based method (LRT), and Bayesian methods such as gamma Poisson shrinker (GPS), Bayesian confidence propagating neural network (BCPNN), the new IC method, and the simplified Bayesian method (sB), as well as the tree-based scan statistic through an extensive simulation study. We also applied the methods to real data on two diabetes drugs, voglibose and acarbose, from the Korea Adverse event reporting system. Only the tree-based scan statistic method maintained the type I error rate at the desired level. Likelihood ratio test-based methods and Bayesian methods tended to be more conservative than other methods in the simulation study and detected fewer signals in the real data example. No method was superior to the others in terms of the statistical power and sensitivity of detecting true signals. It is recommended that those conducting drug‒adverse event surveillance use not just one method, but make a decision based on several methods.

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14

Dunlop, Matthew M., Marco A. Iglesias, and Andrew M. Stuart. "Hierarchical Bayesian level set inversion." Statistics and Computing 27, no. 6 (September 21, 2016): 1555–84. http://dx.doi.org/10.1007/s11222-016-9704-8.

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15

Jeffrey, Niall, and Filipe B. Abdalla. "Parameter inference and model comparison using theoretical predictions from noisy simulations." Monthly Notices of the Royal Astronomical Society 490, no. 4 (October 18, 2019): 5749–56. http://dx.doi.org/10.1093/mnras/stz2930.

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ABSTRACT When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order to generate theoretical predictions. For realistic simulations of noisy data, this is identical to drawing realizations of the data from a likelihood distribution. Though the estimated summary statistic from simulated data vectors may be unbiased, the estimator has variance that should be accounted for. We show how to correct the likelihood in the presence of an estimated summary statistic by marginalizing over the true summary statistic in the framework of a Bayesian hierarchical model. For Gaussian likelihoods where the covariance must also be estimated from simulations, we present an alteration to the Sellentin–Heavens corrected likelihood. We show that excluding the proposed correction leads to an incorrect estimate of the Bayesian evidence with Joint Light-Curve Analysis data. The correction is highly relevant for cosmological inference that relies on simulated data for theory (e.g. weak lensing peak statistics and simulated power spectra) and can reduce the number of simulations required.

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16

DiMaggio, Charles, Sandro Galea, and David Abramson. "Analyzing Postdisaster Surveillance Data: The Effect of the Statistical Method." Disaster Medicine and Public Health Preparedness 2, no. 2 (June 2008): 119–26. http://dx.doi.org/10.1097/dmp.0b013e31816c7475.

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ABSTRACTData from existing administrative databases and ongoing surveys or surveillance methods may prove indispensable after mass traumas as a way of providing information that may be useful to emergency planners and practitioners. The analytic approach, however, may affect exposure prevalence estimates and measures of association. We compare Bayesian hierarchical modeling methods to standard survey analytic techniques for survey data collected in the aftermath of a terrorist attack. Estimates for the prevalence of exposure to the terrorist attacks of September 11, 2001, varied by the method chosen. Bayesian hierarchical modeling returned the lowest estimate for exposure prevalence with a credible interval spanning nearly 3 times the range of the confidence intervals (CIs) associated with both unadjusted and survey procedures. Bayesian hierarchical modeling also returned a smaller point estimate for measures of association, although in this instance the credible interval was tighter than that obtained through survey procedures. Bayesian approaches allow a consideration of preexisting assumptions about survey data, and may offer potential advantages, particularly in the uncertain environment of postterrorism and disaster settings. Additional comparative analyses of existing data are necessary to guide our ability to use these techniques in future incidents. (Disaster Med Public Health Preparedness. 2008;2:119–126)

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17

Landes, Reid D., Peter G. Loutzenhiser, and Stephen B. Vardeman. "Hierarchical Bayesian Statistical Analysis for a Calibration Experiment." IEEE Transactions on Instrumentation and Measurement 55, no. 6 (December 2006): 2165–71. http://dx.doi.org/10.1109/tim.2006.884128.

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18

Corani, Giorgio, Alessio Benavoli, Janez Demšar, Francesca Mangili, and Marco Zaffalon. "Statistical comparison of classifiers through Bayesian hierarchical modelling." Machine Learning 106, no. 11 (May 18, 2017): 1817–37. http://dx.doi.org/10.1007/s10994-017-5641-9.

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19

STEINBAKK, GUNNHILDUR HÖGNADÓTTIR, and GEIR OLVE STORVIK. "Posterior Predictivep-values in Bayesian Hierarchical Models." Scandinavian Journal of Statistics 36, no. 2 (June 2009): 320–36. http://dx.doi.org/10.1111/j.1467-9469.2008.00630.x.

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20

Song, Hae-Ryoung, Andrew B. Lawson, and Daniela Nitcheva. "Bayesian hierarchical models for food frequency assessment." Canadian Journal of Statistics 38, no. 3 (March 10, 2010): 506–16. http://dx.doi.org/10.1002/cjs.10052.

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21

Mashford, John, Yong Song, Q. J. Wang, and David Robertson. "A Bayesian hierarchical spatio-temporal rainfall model." Journal of Applied Statistics 46, no. 2 (May 15, 2018): 217–29. http://dx.doi.org/10.1080/02664763.2018.1473347.

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22

Ogle, Kiona. "Hierarchical Bayesian statistics: merging experimental and modeling approaches in ecology." Ecological Applications 19, no. 3 (April 2009): 577–81. http://dx.doi.org/10.1890/08-0560.1.

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23

Han, Ming. "The E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter." Communications in Statistics - Theory and Methods 46, no. 4 (March 8, 2016): 1606–20. http://dx.doi.org/10.1080/03610926.2015.1024861.

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24

Steffey, Duane. "Hierarchical bayesian modeling with elicited prior information." Communications in Statistics - Theory and Methods 21, no. 3 (January 1992): 799–821. http://dx.doi.org/10.1080/03610929208830816.

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25

Berliner, Mark. "Hierarchical Bayesian modeling in the environmental sciences." Allgemeines Statistisches Archiv 84, no. 2 (July 6, 2000): 141–53. http://dx.doi.org/10.1007/s101820050013.

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26

Arjas, Elja, Liping Liu, and Niko Maglaperidze. "Prediction of Growth: A Hierarchical Bayesian Approach." Biometrical Journal 39, no. 6 (1997): 741–59. http://dx.doi.org/10.1002/bimj.4710390612.

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27

Landes, Reid D. "Hierarchical Bayesian Calibration of Untested Devices." Communications in Statistics - Simulation and Computation 39, no. 7 (July 15, 2010): 1351–64. http://dx.doi.org/10.1080/03610918.2010.493274.

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28

Yang, Hongxia, and Jun Wang. "Bayesian Hierarchical Kernelized Probabilistic Matrix Factorization." Communications in Statistics - Simulation and Computation 45, no. 7 (June 23, 2014): 2528–40. http://dx.doi.org/10.1080/03610918.2014.906612.

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29

Karklin, Yan, and Michael S. Lewicki. "A Hierarchical Bayesian Model for Learning Nonlinear Statistical Regularities in Nonstationary Natural Signals." Neural Computation 17, no. 2 (February 1, 2005): 397–423. http://dx.doi.org/10.1162/0899766053011474.

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Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of density components. Each density component describes a common pattern of deviation from the marginal density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal.

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30

Chen, Jie, Jinglin Zhong, and Lei Nie. "Bayesian hierarchical modeling of drug stability data." Statistics in Medicine 27, no. 13 (2008): 2361–80. http://dx.doi.org/10.1002/sim.3220.

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31

Zhang, Min, Robert L. Strawderman, Mark E. Cowen, and Martin T. Wells. "Bayesian Inference for a Two-Part Hierarchical Model." Journal of the American Statistical Association 101, no. 475 (September 2006): 934–45. http://dx.doi.org/10.1198/016214505000001429.

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32

Micheas, Athanasios C., and Christopher K. Wikle. "A Bayesian Hierarchical Nonoverlapping Random Disc Growth Model." Journal of the American Statistical Association 104, no. 485 (March 2009): 274–83. http://dx.doi.org/10.1198/jasa.2009.0124.

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33

Song, Joon Jin, and Bani Mallick. "Hierarchical Bayesian models for predicting spatially correlated curves." Statistics 53, no. 1 (November 21, 2018): 196–209. http://dx.doi.org/10.1080/02331888.2018.1547905.

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34

Hurn, Merrilee, Peter J. Green, and Fahimah Al-Awadhi. "A Bayesian hierarchical model for photometric red shifts." Journal of the Royal Statistical Society: Series C (Applied Statistics) 57, no. 4 (September 2008): 487–504. http://dx.doi.org/10.1111/j.1467-9876.2008.00621.x.

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35

Di Narzo, A. F., and D. Cocchi. "A Bayesian hierarchical approach to ensemble weather forecasting." Journal of the Royal Statistical Society: Series C (Applied Statistics) 59, no. 3 (May 2010): 405–22. http://dx.doi.org/10.1111/j.1467-9876.2009.00700.x.

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36

Rouder, Jeffrey N., Dongchu Sun, Paul L. Speckman, Jun Lu, and Duo Zhou. "A hierarchical bayesian statistical framework for response time distributions." Psychometrika 68, no. 4 (December 2003): 589–606. http://dx.doi.org/10.1007/bf02295614.

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37

Bunnin, F. O., and J. Q. Smith. "A Bayesian Hierarchical Model for Criminal Investigations." Bayesian Analysis 16, no. 1 (2021): 1–30. http://dx.doi.org/10.1214/19-ba1192.

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38

Everson, Philip J. "Exact bayesian inference for normal hierarchical models." Journal of Statistical Computation and Simulation 68, no. 3 (February 2001): 223–41. http://dx.doi.org/10.1080/00949650108812068.

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39

Armero, Carmen, and David Conesa. "Bayesian hierarchical models in manufacturing bulk service queues." Journal of Statistical Planning and Inference 136, no. 2 (February 2006): 335–54. http://dx.doi.org/10.1016/j.jspi.2004.07.007.

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40

Rodrigues, Josemar, Luis A. Milan, and José G. Leite. "Hierarchical Bayesian Estimation for the Number of Species." Biometrical Journal 43, no. 6 (October 2001): 737. http://dx.doi.org/10.1002/1521-4036(200110)43:6<737::aid-bimj737>3.0.co;2-w.

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41

Roussos, Evangelos. "Variational Bayesian Learning of SMoGs: Modelling and Their Application to Synthetic Aperture Radar." Mathematical and Computational Applications 26, no. 2 (June 7, 2021): 45. http://dx.doi.org/10.3390/mca26020045.

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We show how modern Bayesian Machine Learning tools can be effectively used in order to develop efficient methods for filtering Earth Observation signals. Bayesian statistical methods can be thought of as a generalization of the classical least-squares adjustment methods where both the unknown signals and the parameters are endowed with probability distributions, the priors. Statistical inference under this scheme is the derivation of posterior distributions, that is, distributions of the unknowns after the model has seen the data. Least squares can then be thought of as a special case that uses Gaussian likelihoods, or error statistics. In principle, for most non-trivial models, this framework requires performing integration in high-dimensional spaces. Variational methods are effective tools for approximate inference in Statistical Machine Learning and Computational Statistics. In this paper, after introducing the general variational Bayesian learning method, we apply it to the modelling and implementation of sparse mixtures of Gaussians (SMoG) models, intended to be used as adaptive priors for the efficient representation of sparse signals in applications such as wavelet-type analysis. Wavelet decomposition methods have been very successful in denoising real-world, non-stationary signals that may also contain discontinuities. For this purpose we construct a constrained hierarchical Bayesian model capturing the salient characteristics of such sets of decomposition coefficients. We express our model as a Dirichlet mixture model. We then show how variational ideas can be used to derive efficient methods for bypassing the need for integration: the task of integration becomes one of optimization. We apply our SMoG implementation to the problem of denoising of Synthetic Aperture Radar images, inherently affected by speckle noise, and show that it achieves improved performance compared to established methods, both in terms of speckle reduction and image feature preservation.

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42

Su, Zhenming, Milo D. Adkison, and Benjamin W. Van Alen. "A hierarchical Bayesian model for estimating historical salmon escapement and escapement timing." Canadian Journal of Fisheries and Aquatic Sciences 58, no. 8 (August 1, 2001): 1648–62. http://dx.doi.org/10.1139/f01-099.

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In this paper, we present an improved methodology for estimating salmon escapements from stream count data. The new method uses a hierarchical Bayesian model that improves estimates in years when data are sparse by "borrowing strength" from counts in other years. We present a model of escapement and of count data, a hierarchical Bayesian statistical framework, a Gibbs sampling approach for evaluation of the posterior distributions of the quantities of interest, and criteria for determining when the model and inference are adequate. We then apply the hierarchical Bayesian model to estimating historical escapement and escapement timing for pink salmon (Oncorhynchus gorbuscha) returns to Kadashan Creek in Southeast Alaska.

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43

Chen, Younan, and Keying Ye. "A Bayesian hierarchical approach to dual response surface modelling." Journal of Applied Statistics 38, no. 9 (September 2011): 1963–75. http://dx.doi.org/10.1080/02664763.2010.545106.

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44

Gabrio, Andrea. "Bayesian hierarchical models for the prediction of volleyball results." Journal of Applied Statistics 48, no. 2 (February 6, 2020): 301–21. http://dx.doi.org/10.1080/02664763.2020.1723506.

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45

Stangl, Dalene K. "Prediction and decision making using Bayesian hierarchical models." Statistics in Medicine 14, no. 20 (October 30, 1995): 2173–90. http://dx.doi.org/10.1002/sim.4780142002.

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46

O'Malley, A. James, and Kelly H. Zou. "Bayesian multivariate hierarchical transformation models for ROC analysis." Statistics in Medicine 25, no. 3 (2005): 459–79. http://dx.doi.org/10.1002/sim.2187.

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47

Chu, Yiyi, and Ying Yuan. "A Bayesian basket trial design using a calibrated Bayesian hierarchical model." Clinical Trials 15, no. 2 (March 2, 2018): 149–58. http://dx.doi.org/10.1177/1740774518755122.

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Background: The basket trial evaluates the treatment effect of a targeted therapy in patients with the same genetic or molecular aberration, regardless of their cancer types. Bayesian hierarchical modeling has been proposed to adaptively borrow information across cancer types to improve the statistical power of basket trials. Although conceptually attractive, research has shown that Bayesian hierarchical models cannot appropriately determine the degree of information borrowing and may lead to substantially inflated type I error rates. Methods: We propose a novel calibrated Bayesian hierarchical model approach to evaluate the treatment effect in basket trials. In our approach, the shrinkage parameter that controls information borrowing is not regarded as an unknown parameter. Instead, it is defined as a function of a similarity measure of the treatment effect across tumor subgroups. The key is that the function is calibrated using simulation such that information is strongly borrowed across subgroups if their treatment effects are similar and barely borrowed if the treatment effects are heterogeneous. Results: The simulation study shows that our method has substantially better controlled type I error rates than the Bayesian hierarchical model. In some scenarios, for example, when the true response rate is between the null and alternative, the type I error rate of the proposed method can be inflated from 10% up to 20%, but is still better than that of the Bayesian hierarchical model. Limitation: The proposed design assumes a binary endpoint. Extension of the proposed design to ordinal and time-to-event endpoints is worthy of further investigation. Conclusion: The calibrated Bayesian hierarchical model provides a practical approach to design basket trials with more flexibility and better controlled type I error rates than the Bayesian hierarchical model. The software for implementing the proposed design is available at http://odin.mdacc.tmc.edu/~yyuan/index_code.html

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48

Silverman, Noah. "A HIERARCHICAL BAYESIAN ANALYSIS OF HORSE RACING." Journal of Prediction Markets 6, no. 3 (January 22, 2013): 1–13. http://dx.doi.org/10.5750/jpm.v6i3.590.

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Horse racing is the most popular sport in Hong Kong. Nowhere else in the world is such attention paid to the races and such large sums of money bet. It is literally a “national sport”. Popular literature has many stories about computerized “betting teams” winning fortunes by using statistical analysis.[1] Additionally, numerous academic papers have been published on the subject, implementing a variety of statistical methods. The academic justiﬁcation for these papers is that a parimutuel game represents a study in decisions under uncertainty, eﬃciency of markets, and even investor psychology. A review of the available published literature has failed to ﬁnd any Bayesian approach to this modeling challenge.This study will attempt to predict the running speed of a horse in a given race. To that eﬀect, the coeﬃcients of a linear model are estimated using the Bayesian method of Markov Chain Monte Carlo. Two methods of computing the sampled posterior are used and their results compared. The Gibbs method assumes that all the coeﬃcients are normally distributed, while the Metropolis method allows for their distribution to have an unknown shape. I will calculate and compare the predictive results of several models using these Bayesian Methods.

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49

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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50

Sun, Dongchu, and Paul L. Speckman. "Bayesian hierarchical linear mixed models for additive smoothing splines." Annals of the Institute of Statistical Mathematics 60, no. 3 (April 19, 2007): 499–517. http://dx.doi.org/10.1007/s10463-007-0127-3.

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