Relevant bibliographies by topics / Empirical Bayes

Academic literature on the topic 'Empirical Bayes'

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Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Empirical Bayes"

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Efron, Bradley. "Bayes, Oracle Bayes and Empirical Bayes." Statistical Science 34, no. 2 (May 2019): 177–201. http://dx.doi.org/10.1214/18-sts674.

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Efron, Bradley. "Rejoinder: Bayes, Oracle Bayes, and Empirical Bayes." Statistical Science 34, no. 2 (May 2019): 234–35. http://dx.doi.org/10.1214/19-sts674rej.

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Louis, Thomas A. "Comment: Bayes, Oracle Bayes, and Empirical Bayes." Statistical Science 34, no. 2 (May 2019): 202–5. http://dx.doi.org/10.1214/19-sts704.

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Laird, Nan. "Comment: Bayes, Oracle Bayes, and Empirical Bayes." Statistical Science 34, no. 2 (May 2019): 206–8. http://dx.doi.org/10.1214/19-sts705.

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van der Vaart, Aad. "Comment: Bayes, Oracle Bayes and Empirical Bayes." Statistical Science 34, no. 2 (May 2019): 214–18. http://dx.doi.org/10.1214/19-sts707.

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Karunamuni, R. J., and N. G. N. Prasad. "An improved Bayes empirical Bayes estimator." International Journal of Mathematics and Mathematical Sciences 2003, no. 2 (2003): 97–107. http://dx.doi.org/10.1155/s0161171203110046.

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Lindley, D. V., J. S. Maritz, and T. Lwin. "Empirical Bayes Methods." Mathematical Gazette 74, no. 467 (March 1990): 91. http://dx.doi.org/10.2307/3618894.

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Bagghi, Parthasarathy, J. S. Maritz, and T. Lwin. "Empirical Bayes Methods." Journal of the American Statistical Association 86, no. 413 (March 1991): 244. http://dx.doi.org/10.2307/2289739.

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Angus, John E. "Empirical Bayes Methods." Technometrics 33, no. 2 (May 1991): 243–45. http://dx.doi.org/10.1080/00401706.1991.10484821.

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Young, Karen, J. Maritz, and T. Lwin. "Empirical Bayes Methods." Applied Statistics 41, no. 3 (1992): 604. http://dx.doi.org/10.2307/2348097.

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Dissertations / Theses on the topic "Empirical Bayes"

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Benhaddou, Rida. "Nonparametric and Empirical Bayes Estimation Methods." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5765.

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In the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet series based empirical Bayes estimator constructed in Pensky and Alotaibi (2005). We propose an adaptive version of this estimator using Lepski's method and show that the estimator attains optimal convergence rates. The theory is supplemented by numerous examples. Our study of the functional deconvolution model expands results of Pensky and Sapatinas (2009, 2010, 2011) to the case of estimating an (r+1)-dimensional function or dependent errors. In both cases, we derive minimax lower bounds for the integrated square risk over a wide set of Besov balls and construct adaptive wavelet estimators that attain those optimal convergence rates. In particular, in the case of estimating a periodic (r+1)-dimensional function, we show that by choosing Besov balls of mixed smoothness, we can avoid the ''curse of dimensionality'' and, hence, obtain higher than usual convergence rates when r is large. The study of deconvolution of a multivariate function is motivated by seismic inversion which can be reduced to solution of noisy two-dimensional convolution equations that allow to draw inference on underground layer structures along the chosen profiles. The common practice in seismology is to recover layer structures separately for each profile and then to combine the derived estimates into a two-dimensional function. By studying the two-dimensional version of the model, we demonstrate that this strategy usually leads to estimators which are less accurate than the ones obtained as two-dimensional functional deconvolutions. Finally, we consider a multichannel deconvolution model with long-range dependent Gaussian errors. We do not limit our consideration to a specific type of long-range dependence, rather we assume that the eigenvalues of the covariance matrix of the errors are bounded above and below. We show that convergence rates of the estimators depend on a balance between the smoothness parameters of the response function, the smoothness of the blurring function, the long memory parameters of the errors, and how the total number of observations is distributed among the channels.
Ph.D.
Doctorate
Mathematics
Sciences
Mathematics
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Brandel, John. "Empirical Bayes methods for missing data analysis." Thesis, Uppsala University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121408.

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Lönnstedt, Ingrid. "Empirical Bayes Methods for DNA Microarray Data." Doctoral thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5865.

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cDNA microarrays is one of the first high-throughput gene expression technologies that has emerged within molecular biology for the purpose of functional genomics. cDNA microarrays compare the gene expression levels between cell samples, for thousands of genes simultaneously.

The microarray technology offers new challenges when it comes to data analysis, since the thousands of genes are examined in parallel, but with very few replicates, yielding noisy estimation of gene effects and variances. Although careful image analyses and normalisation of the data is applied, traditional methods for inference like the Student t or Fisher’s F-statistic fail to work.

In this thesis, four papers on the topics of empirical Bayes and full Bayesian methods for two-channel microarray data (as e.g. cDNA) are presented. These contribute to proving that empirical Bayes methods are useful to overcome the specific data problems. The sample distributions of all the genes involved in a microarray experiment are summarized into prior distributions and improves the inference of each single gene.

The first part of the thesis includes biological and statistical background of cDNA microarrays, with an overview of the different steps of two-channel microarray analysis, including experimental design, image analysis, normalisation, cluster analysis, discrimination and hypothesis testing. The second part of the thesis consists of the four papers. Paper I presents the empirical Bayes statistic B, which corresponds to a t-statistic. Paper II is based on a version of B that is extended for linear model effects. Paper III assesses the performance of empirical Bayes models by comparisons with full Bayes methods. Paper IV provides extensions of B to what corresponds to F-statistics.

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Farrell, Patrick John. "Empirical Bayes estimation of small area proportions." Thesis, McGill University, 1991. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=70301.

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Due to the nature of survey design, the estimation of parameters associated with small areas is extremely problematic. In this study, techniques for the estimation of small area proportions are proposed and implemented. More specifically, empirical Bayes estimation methodologies, where random effects which reflect the complex structure of a multi-stage sample design are incorporated into logistic regression models, are derived and studied.
The proposed techniques are applied to data from the 1950 United States Census to predict local labor force participation rates of females. Results are compared with those obtained using unbiased and synthetic estimation approaches.
Using the proposed methodologies, a sensitivity analysis concerning the prior distribution assumption, conducted with a view toward outlier detection, is performed. The use of bootstrap techniques to correct measures of uncertainty is also studied.
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Lönnstedt, Ingrid. "Empirical Bayes methods for DNA microarray data /." Uppsala : Matematiska institutionen, Univ. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5865.

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Wang, Xue. "Empirical Bayes block shrinkage for wavelet regression." Thesis, University of Nottingham, 2006. http://eprints.nottingham.ac.uk/13516/.

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There has been great interest in recent years in the development of wavelet methods for estimating an unknown function observed in the presence of noise, following the pioneering work of Donoho and Johnstone (1994, 1995) and Donoho et al. (1995). In this thesis, a novel empirical Bayes block (EBB) shrinkage procedure is proposed and the performance of this approach with both independent identically distributed (IID) noise and correlated noise is thoroughly explored. The first part of this thesis develops a Bayesian methodology involving the non-central X[superscript]2 distribution to simultaneously shrink wavelet coefficients in a block, based on the block sum of squares. A useful (and to the best of our knowledge, new) identity satisfied by the non-central X[superscript]2 density is exploited. This identity leads to tractable posterior calculations for suitable families of prior distributions. Also, the families of prior distribution we work with are sufficiently flexible to represent various forms of prior knowledge. Furthermore, an efficient method for finding the hyperparameters is implemented and simulations show that this method has a high degree of computational advantage. The second part relaxes the assumption of IID noise considered in the first part of this thesis. A semi-parametric model including a parametric component and a nonparametric component is presented to deal with correlated noise situations. In the parametric component, attention is paid to the covariance structure of the noise. Two distinct parametric methods (maximum likelihood estimation and time series model identification techniques) for estimating the parameters in the covariance matrix are investigated. Both methods have been successfully implemented and are believed to be new additions to smoothing methods.
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Fletcher, Douglas. "Generalized Empirical Bayes: Theory, Methodology, and Applications." Diss., Temple University Libraries, 2019. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/546485.

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Statistics
Ph.D.
The two key issues of modern Bayesian statistics are: (i) establishing a principled approach for \textit{distilling} a statistical prior distribution that is \textit{consistent} with the given data from an initial believable scientific prior; and (ii) development of a \textit{consolidated} Bayes-frequentist data analysis workflow that is more effective than either of the two separately. In this thesis, we propose generalized empirical Bayes as a new framework for exploring these fundamental questions along with a wide range of applications spanning fields as diverse as clinical trials, metrology, insurance, medicine, and ecology. Our research marks a significant step towards bridging the ``gap'' between Bayesian and frequentist schools of thought that has plagued statisticians for over 250 years. Chapters 1 and 2---based on \cite{mukhopadhyay2018generalized}---introduces the core theory and methods of our proposed generalized empirical Bayes (gEB) framework that solves a long-standing puzzle of modern Bayes, originally posed by Herbert Robbins (1980). One of the main contributions of this research is to introduce and study a new class of nonparametric priors ${\rm DS}(G, m)$ that allows exploratory Bayesian modeling. However, at a practical level, major practical advantages of our proposal are: (i) computational ease (it does not require Markov chain Monte Carlo (MCMC), variational methods, or any other sophisticated computational techniques); (ii) simplicity and interpretability of the underlying theoretical framework which is general enough to include almost all commonly encountered models; and (iii) easy integration with mainframe Bayesian analysis that makes it readily applicable to a wide range of problems. Connections with other Bayesian cultures are also presented in the chapter. Chapter 3 deals with the topic of measurement uncertainty from a new angle by introducing the foundation of nonparametric meta-analysis. We have applied the proposed methodology to real data examples from astronomy, physics, and medical disciplines. Chapter 4 discusses some further extensions and application of our theory to distributed big data modeling and the missing species problem. The dissertation concludes by highlighting two important areas of future work: a full Bayesian implementation workflow and potential applications in cybersecurity.
Temple University--Theses
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Mariotto, Angela Bacellar. "Empirical Bayes inference and the linear model." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47557.

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KWON, YEIL. "NONPARAMETRIC EMPIRICAL BAYES SIMULTANEOUS ESTIMATION FOR MULTIPLE VARIANCES." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/495491.

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Statistics
Ph.D.
The shrinkage estimation has proven to be very useful when dealing with a large number of mean parameters. In this dissertation, we consider the problem of simultaneous estimation of multiple variances and construct a shrinkage type, non-parametric estimator. We take the non-parametric empirical Bayes approach by starting with an arbitrary prior on the variances. Under an invariant loss function, the resultant Bayes estimator relies on the marginal cumulative distribution function of the sample variances. Replacing the marginal cdf by the empirical distribution function, we obtain a Non-parametric Empirical Bayes estimator for multiple Variances (NEBV). The proposed estimator converges to the corresponding Bayes version uniformly over a large set. Consequently, the NEBV works well in a post-selection setting. We then apply the NEBV to construct condence intervals for mean parameters in a post-selection setting. It is shown that the intervals based on the NEBV are shortest among all the intervals which guarantee a desired coverage probability. Through real data analysis, we have further shown that the NEBV based intervals lead to the smallest number of discordances, a desirable property when we are faced with the current "replication crisis".
Temple University--Theses
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Stein, Nathan Mathes. "Advances in Empirical Bayes Modeling and Bayesian Computation." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:11051.

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Chapter 1 of this thesis focuses on accelerating perfect sampling algorithms for a Bayesian hierarchical model. A discrete data augmentation scheme together with two different parameterizations yields two Gibbs samplers for sampling from the posterior distribution of the hyperparameters of the Dirichlet-multinomial hierarchical model under a default prior distribution. The finite-state space nature of this data augmentation permits us to construct two perfect samplers using bounding chains that take advantage of monotonicity and anti-monotonicity in the target posterior distribution, but both are impractically slow. We demonstrate however that a composite algorithm that strategically alternates between the two samplers' updates can be substantially faster than either individually. We theoretically bound the expected time until coalescence for the composite algorithm, and show via simulation that the theoretical bounds can be close to actual performance. Chapters 2 and 3 introduce a strategy for constructing scientifically sensible priors in complex models. We call these priors catalytic priors to suggest that adding such prior information catalyzes our ability to use richer, more realistic models. Because they depend on observed data, catalytic priors are a tool for empirical Bayes modeling. The overall perspective is data-driven: catalytic priors have a pseudo-data interpretation, and the building blocks are alternative plausible models for observations, yielding behavior similar to hierarchical models but with a conceptual shift away from distributional assumptions on parameters. The posterior under a catalytic prior can be viewed as an optimal approximation to a target measure, subject to a constraint on the posterior distribution's predictive implications. In Chapter 3, we apply catalytic priors to several familiar models and investigate the performance of the resulting posterior distributions. We also illustrate the application of catalytic priors in a preliminary analysis of the effectiveness of a job training program, which is complicated by the need to account for noncompliance, partially defined outcomes, and missing outcome data.
Statistics
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Books on the topic "Empirical Bayes"

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Maritz, J. S. Empirical Bayes methods. 2nd ed. London: Chapman and Hall, 1989.

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Carlin, Bradley P. Bayes and empirical Bayes methods for data analysis. Boca Raton: Chapman & Hall/CRC, 1998.

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Carlin, Bradley P. Bayes and Empirical Bayes methods for data analysis. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2000.

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1944-, Louis Thomas A., ed. Bayes and empirical Bayes methods for data analysis. London: Chapman & Hall, 1996.

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Ahmed, S. E., and N. Reid, eds. Empirical Bayes and Likelihood Inference. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0141-7.

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Norberg, Ragnar. Empirical bayes in the unbalanced case. Copenhagen: University of Copenhagen, 1989.

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Mohamed Adel Mohamed Ali Mousa. Empirical bayes estimates of a probability. Birmingham: University of Birmingham, 1987.

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Gaver, Donald Paul. Random parameter Markov population process models and their likelihood, Bayes, and empirical Bayes analysis. Monterey, Calif: Naval Postgraduate School, 1985.

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Kuo, Lynn. Empirical Bayes risk evaluation with type II censored data. Monterey, Calif: Naval Postgraduate School, 1991.

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Houston, Walter M. Empirical Bayes estimates of parameters from the logistic regression model. Iowa City, Iowa: ACT, Inc., 1997.

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Book chapters on the topic "Empirical Bayes"

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Ghosh, M., and G. Meeden. "Empirical Bayes estimation." In Bayesian Methods for Finite Population Sampling, 161–220. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4899-3416-1_4.

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Morris, Carl N. "Empirical Bayes: a frequency-Bayes compromise." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 195–203. Hayward, CA: Institute of Mathematical Statistics, 1986. http://dx.doi.org/10.1214/lnms/1215540299.

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Khatri, C. G., and C. Radhakrishna Rao. "Empirical Hierarchical Bayes Estimation." In Bayesian Analysis in Statistics and Econometrics, 147–61. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2944-5_8.

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Gupta, Shanti S., and TaChen Liang. "On Some Bayes and Empirical Bayes Selection Procedures." In Probability and Bayesian Statistics, 233–46. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4613-1885-9_24.

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Ghosh, Malay, and Parthasarathi Lahiri. "Bayes and Empirical Bayes Analysis in Multistage Sampling." In Statistical Decision Theory and Related Topics IV, 195–212. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4613-8768-8_22.

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Cover, Thomas M., and David H. Gluss. "Empirical Bayes stock market portfolios." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 235–36. Hayward, CA: Institute of Mathematical Statistics, 1986. http://dx.doi.org/10.1214/lnms/1215540302.

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Savchuk, Vladimir, and Chris P. Tsokos. "Empirical Bayes Estimates of Reliability." In Bayesian Theory and Methods with Applications, 193–218. Paris: Atlantis Press, 2011. http://dx.doi.org/10.2991/978-94-91216-14-5_7.

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Keener, Robert W. "Empirical Bayes and Shrinkage Estimators." In Theoretical Statistics, 205–18. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-93839-4_11.

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Barberousse, Anouk. "Empirical Bayes as a Tool." In Boston Studies in the Philosophy and History of Science, 157–73. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-54469-4_9.

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Robbins, Herbert. "An empirical Bayes estimation problem." In Herbert Robbins Selected Papers, 72–73. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5110-1_6.

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Conference papers on the topic "Empirical Bayes"

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Srinath, K. Pavan, and Ramji Venkataramanan. "Empirical Bayes Estimators for Sparse Sequences." In 2018 IEEE International Symposium on Information Theory (ISIT). IEEE, 2018. http://dx.doi.org/10.1109/isit.2018.8437812.

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DuMouchel, William, and Daryl Pregibon. "Empirical bayes screening for multi-item associations." In the seventh ACM SIGKDD international conference. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/502512.502526.

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Basawa, Ishwar V. "Empirical Bayes classification rules for minefield detection." In SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, edited by Abinash C. Dubey, Ivan Cindrich, James M. Ralston, and Kelly A. Rigano. SPIE, 1995. http://dx.doi.org/10.1117/12.211351.

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Barraza, Nestor R., Marcelo de Souza Lauretto, Carlos Alberto de Bragança Pereira, and Julio Michael Stern. "The Empirical Bayes Estimator and Mixed Distributions." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2008. http://dx.doi.org/10.1063/1.3038987.

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Gangopadhyay, Anirban. "An Empirical Bayes Approach to Topic Modeling." In 2020 25th International Conference on Pattern Recognition (ICPR). IEEE, 2021. http://dx.doi.org/10.1109/icpr48806.2021.9412837.

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Selen, Yngve, and Erik G. Larsson. "Empirical Bayes Linear Regression with Unknown Model Order." In 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07. IEEE, 2007. http://dx.doi.org/10.1109/icassp.2007.366794.

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Teng, Mingxiang, Yadong Wang, Yunlong Liu, Seongho Kim, Curt Balch, Kenneth P. Nephew, and Lang Li. "Empirical bayes model comparisons for differential methylation analysis." In 2011 IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS). IEEE, 2011. http://dx.doi.org/10.1109/gensips.2011.6169428.

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Lazebnik, Svetlana, and Maxim Raginsky. "An empirical Bayes approach to contextual region classification." In 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops). IEEE, 2009. http://dx.doi.org/10.1109/cvpr.2009.5206690.

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Lazebnik, S., and M. Raginsky. "An empirical Bayes approach to contextual region classification." In 2009 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2009. http://dx.doi.org/10.1109/cvprw.2009.5206690.

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Orellana, Rafael, Rodrigo Carvajal, and Juan C. Aguero. "Empirical Bayes estimation utilizing finite Gaussian Mixture Models." In 2019 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON). IEEE, 2019. http://dx.doi.org/10.1109/chilecon47746.2019.8987584.

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Reports on the topic "Empirical Bayes"

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Gupta, Shanti S., and TaChen Liang. On Bayes and Empirical Bayes Procedures for Selection Problems. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada174159.

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Carlin, Bradley P., and Alan E. Gelfand. Approaches for Empirical Bayes Confidence Intervals. Fort Belvoir, VA: Defense Technical Information Center, March 1989. http://dx.doi.org/10.21236/ada205775.

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Gupta, Shanti S. Simultaneous Inference, and Ranking Selection Procedure: Bayes and Empirical Bayes Approach. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada391935.

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Kuo, Lynn. A Note on Bayes Empirical Bayes Estimation by Means of Dirichlet Processes. Fort Belvoir, VA: Defense Technical Information Center, September 1985. http://dx.doi.org/10.21236/ada170039.

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Gupta, Shanti S., and Jinjun Lu. Empirical Bayes Estimation With Kernel Sequence Method. Fort Belvoir, VA: Defense Technical Information Center, September 2001. http://dx.doi.org/10.21236/ada396449.

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Yu, Kai F. On the Bounded Regret of Empirical Bayes Estimators. Fort Belvoir, VA: Defense Technical Information Center, May 1985. http://dx.doi.org/10.21236/ada169108.

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Gupta, Shanti S., and Jianjun Li. Empirical Bayes Tests For Some Non-Exponential Distribution Family. Fort Belvoir, VA: Defense Technical Information Center, August 1999. http://dx.doi.org/10.21236/ada370172.

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Gupta, Shanti S., and TaChen Liang. On Empirical Bayes Selection Rules for Negative Binomial Populations. Fort Belvoir, VA: Defense Technical Information Center, May 1988. http://dx.doi.org/10.21236/ada196994.

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Gupa, Shanti S., and Jianjun Li. Monotone Empirical Bayes Tests Based on Kernel Sequence Estimation. Fort Belvoir, VA: Defense Technical Information Center, February 2001. http://dx.doi.org/10.21236/ada393014.

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Kuo, Lynn, and Constantin Yiannoutsos. Empirical Bayes Risk Evaluation with Type 2 Censored Data. Fort Belvoir, VA: Defense Technical Information Center, July 1991. http://dx.doi.org/10.21236/ada242291.

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