Relevant bibliographies by topics / Empirical Bayes methods

Academic literature on the topic 'Empirical Bayes methods'

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Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Empirical Bayes methods"

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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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Stephenson, W. Robert. "Empirical Bayes Methods." Journal of Quality Technology 22, no. 3 (July 1990): 249–50. http://dx.doi.org/10.1080/00224065.1990.11979250.

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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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Denham, Mike, J. S. Maritz, and T. Lwin. "Empirical Bayes Methods." Statistician 39, no. 1 (1990): 97. http://dx.doi.org/10.2307/2348214.

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Laird, Nan M., and Thomas A. Louis. "Empirical Bayes Ranking Methods." Journal of Educational Statistics 14, no. 1 (March 1989): 29–46. http://dx.doi.org/10.3102/10769986014001029.

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Ranking problems arise in setting priorities for investigations, in providing a simple summary of performance, in comparing objects in a manner robust to measurement scale, and in a wide variety of other applications. Commonly, rankings are computed from measurements that depend on the true attribute. Using the Gaussian model, we propose and compare methods for using these measurements to estimate the ranks of the underlying attributes and show that those based on an empirical Bayes model produce estimates that differ from ranking observed data. These differences result both from the effect of shrinking posterior means towards a common value by an amount that depends on the precision of individual measurements and from the Bayes processing of the posterior distribution to produce estimates that account for the uncertainty in the distribution of the ranks. We illustrate different ranking methods using data on school achievement reported by Aitkin and Longford (1986) . Mathematical and empirical results highlight the importance of using appropriate ranking methods and identify issues requiring further research.
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Laird, Nan M., and Thomas A. Louis. "Empirical Bayes Ranking Methods." Journal of Educational Statistics 14, no. 1 (1989): 29. http://dx.doi.org/10.2307/1164724.

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Casella, George. "Illustrating empirical Bayes methods." Chemometrics and Intelligent Laboratory Systems 16, no. 2 (October 1992): 107–25. http://dx.doi.org/10.1016/0169-7439(92)80050-e.

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Maritz, J. S., and T. Lwin. "Empirical Bayes Methods, 2nd Edition." Biometrics 46, no. 3 (September 1990): 886. http://dx.doi.org/10.2307/2532124.

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Dissertations / Theses on the topic "Empirical Bayes methods"

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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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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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Jakimauskas, Gintautas. "Analysis and application of empirical Bayes methods in data mining." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140423_090853-72998.

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The research object is data mining empirical Bayes methods and algorithms applied in the analysis of large populations of large dimensions. The aim and objectives of the research are to create methods and algorithms for testing nonparametric hypotheses for large populations and for estimating the parameters of data models. The following problems are solved to reach these objectives: 1. To create an efficient data partitioning algorithm of large dimensional data. 2. To apply the data partitioning algorithm of large dimensional data in testing nonparametric hypotheses. 3. To apply the empirical Bayes method in testing the independence of components of large dimensional data vectors. 4. To develop an algorithm for estimating probabilities of rare events in large populations, using the empirical Bayes method and comparing Poisson-gamma and Poisson-Gaussian mathematical models, by selecting an optimal model and a respective empirical Bayes estimator. 5. To create an algorithm for logistic regression of rare events using the empirical Bayes method. The results obtained enables us to perform very fast and efficient partitioning of large dimensional data; testing the independence of selected components of large dimensional data; selecting the optimal model in the estimation of probabilities of rare events, using the Poisson-gamma and Poisson-Gaussian mathematical models and empirical Bayes estimators. The nonsingularity condition in the case of the Poisson-gamma model is presented.
Darbo tyrimų objektas yra duomenų tyrybos empiriniai Bajeso metodai ir algoritmai, taikomi didelio matavimų skaičiaus didelių populiacijų duomenų analizei. Darbo tyrimų tikslas yra sudaryti metodus ir algoritmus didelių populiacijų neparametrinių hipotezių tikrinimui ir duomenų modelių parametrų vertinimui. Šiam tikslui pasiekti yra sprendžiami tokie uždaviniai: 1. Sudaryti didelio matavimo duomenų skaidymo algoritmą. 2. Pritaikyti didelio matavimo duomenų skaidymo algoritmą neparametrinėms hipotezėms tikrinti. 3. Pritaikyti empirinį Bajeso metodą daugiamačių duomenų komponenčių nepriklausomumo hipotezei tikrinti su skirtingais matematiniais modeliais, nustatant optimalų modelį ir atitinkamą empirinį Bajeso įvertinį. 4. Sudaryti didelių populiacijų retų įvykių dažnių vertinimo algoritmą panaudojant empirinį Bajeso metodą palyginant Puasono-gama ir Puasono-Gauso matematinius modelius. 5. Sudaryti retų įvykių logistinės regresijos algoritmą panaudojant empirinį Bajeso metodą. Darbo metu gauti nauji rezultatai įgalina atlikti didelio matavimo duomenų skaidymą; atlikti didelio matavimo nekoreliuotų duomenų pasirinktų komponenčių nepriklausomumo tikrinimą; parinkti didelių populiacijų retų įvykių optimalų modelį ir atitinkamą empirinį Bajeso įvertinį. Pateikta nesinguliarumo sąlyga Puasono-gama modelio atveju.
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Everitt, Niklas. "Module identification in dynamic networks: parametric and empirical Bayes methods." Doctoral thesis, KTH, Reglerteknik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-208920.

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The purpose of system identification is to construct mathematical models of dynamical system from experimental data. With the current trend of dynamical systems encountered in engineering growing ever more complex, an important task is to efficiently build models of these systems. Modelling the complete dynamics of these systems is in general not possible or even desired. However, often, these systems can be modelled as simpler linear systems interconnected in a dynamic network. Then, the task of estimating the whole network or a subset of the network can be broken down into subproblems of estimating one simple system, called module, embedded within the dynamic network. The prediction error method (PEM) is a benchmark in parametric system identification. The main advantage with PEM is that for Gaussian noise, it corresponds to the so called maximum likelihood (ML) estimator and is asymptotically efficient. One drawback is that the cost function is in general nonconvex and a gradient based search over the parameters has to be carried out, rendering a good starting point crucial. Therefore, other methods such as subspace or instrumental variable methods are required to initialize the search. In this thesis, an alternative method, called model order reduction Steiglitz-McBride (MORSM) is proposed. As MORSM is also motivated by ML arguments, it may also be used on its own and will in some cases provide asymptotically efficient estimates. The method is computationally attractive since it is composed of a sequence of least squares steps. It also treats the part of the network of no direct interest nonparametrically, simplifying model order selection for the user. A different approach is taken in the second proposed method to identify a module embedded in a dynamic network. Here, the impulse response of the part of the network of no direct interest is modelled as a realization of a Gaussian process. The mean and covariance of the Gaussian process is parameterized by a set of parameters called hyperparameters that needs to be estimated together with the parameters of the module of interest. Using an empirical Bayes approach, all parameters are estimated by maximizing the marginal likelihood of the data. The maximization is carried out by using an iterative expectation/conditional-maximization scheme, which alternates so called expectation steps with a series of conditional-maximization steps. When only the module input and output sensors are used, the expectation step admits an analytical expression. The conditional-maximization steps reduces to solving smaller optimization problems, which either admit a closed form solution, or can be efficiently solved by using gradient descent strategies. Therefore, the overall optimization turns out computationally efficient. Using markov chain monte carlo techniques, the method is extended to incorporate additional sensors. Apart from the choice of identification method, the set of chosen signals to use in the identification will determine the covariance of the estimated modules. To chose these signals, well known expressions for the covariance matrix could, together with signal constraints, be formulated as an optimization problem and solved. However, this approach does neither tell us why a certain choice of signals is optimal nor what will happen if some properties change. The expressions developed in this part of the thesis have a different flavor in that they aim to reformulate the covariance expressions into a form amenable for interpretation. These expressions illustrate how different properties of the identification problem affects the achievable accuracy. In particular, how the power of the input and noise signals, as well as model structure, affect the covariance.
Systemidentifiering används för att skatta en modell av ett dynamiskt system genom att anpassa modellens parametrar utifrån experimentell mätdata inhämtad från systemet som ska modelleras. Systemen som modelleras tenderar att växa sig så omfattande i skala och så komplexa att direkt modellering varken är genomförbar eller önskad. I många fall går det komplexa systemet att beskriva som en komposition av enklare linära system (moduler) sammakopplade i något vi kallar dynamiska nätverk. Uppgiften att modellera hela eller delar av nätverket kan därmed brytas ner till deluppgiften att modellera en modul i det dynamiska nätverket. Det vanligaste sättet att skatta parametrarna hos en model är genom att minimera det så kallade prediktionsfelet. Den här typen av metod har nyligen anpassats för att identifiera moduler i dynamiska nätverk. Metoden åtnjuter goda egenskaper vad det gäller det modelfel som härrör från stokastisk störningar under experimentet och i de fall där störningarna är normalfördelade sammanfaller metoden med maximum likelihood-metoden. En nackdel med metoden är att functionen som minimeras vanligen är inte är konvex och därmed riskerar metoden att fastna i ett lokalt minimum. Det är därför essentiellt med en bra startpunkt. Andra metoder krävs därmed för att hitta en startpunkt, till exempel kan instrumentvariabelmetoder användas. I den här avhandlingen föreslås en alternativ metod kallad MORSM. MORSM är motiverad med argument hämtade från maximum likelihood och är också asymptotiskt effektiv i vissa fall. MORSM består av steg som kan lösas med minstakvadratmetoden och är därmed beräkningsmässigt attraktiv. Den del av nätverket som är utan intresse skattas enbart ickeparametriskt vilket underlättar valet av modellordning för användaren. En annan utgångspunkt tas i den andra metoden som föreslås för att skatta en modul inbäddad i ett dynamiskt nätverk. Impulssvaret från den del av nätverket som är utan intresse modelleras som realisation av en Gaussisk process. Medelvärdet och kovariansen hos den Gaussiska processen parametriseras av en mängd parametrar kallade hyperparametrar vilka skattas tillsammans med parametrarna för modulen. Parametrarna skattas genom att maximera den marginella likelihood funktionen. Optimeringen utförs iterativt med ECM, en variant av förväntan och maximering algoritmen (EM). Algoritmen har två steg. E-steget har en analytisk lösning medan CM-steget reduceras till delproblem som antingen har analytisk lösning eller har låg dimensionalitet och därmed kan lösas med gradientbaserade metoder. Den övergripande optimeringen är därmed beräkningsmässigt attraktiv. Med hjälp av MCMC tekniker generaliseras metoden till att inkludera ytterligare sensorer vars impulssvar också modelleras som Gaussiska processer. Förutom valet av metod så påverkar valet av signaler vilken nogrannhet eller kovarians den skattade modulen har. Klassiska uttryck för kovariansmatrisen kan användas för att optimera valet av signaler. Dock så ger dessa uttryck ingen insikt i varför valet av vissa signaler är optimalt eller vad som skulle hända om förutsättningarna vore annorlunda. Uttrycken som framställs i den här delen av avhandlingen har ett annat syfte. De försöker i stället uttrycka kovariansen i termer som kan ge insikt i vad som påverkar den nogrannhet som kan uppnås. Mer specifikt uttrycks kovariansen med bland annat avseende på insignalernas spektra, brussignalernas spektra samt modellstruktur.

QC 20170614

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Duan, Xiuwen. "Revisiting Empirical Bayes Methods and Applications to Special Types of Data." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42340.

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Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of the empirical Bayesian methods and develops new applications. We first look at a linear empirical Bayes estimator and apply it on ranking and symbolic data. Next, we consider Tweedie’s formula and show how it can be applied to analyze a microarray dataset. The application of the formula is simplified with the Pearson system of distributions. Saddlepoint approximations enable us to generalize several results in this direction. The results show that the proposed methods perform well in applications to real data sets.
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Hort, Molly. "A comparison of hypothesis testing procedures for two population proportions." Manhattan, Kan. : Kansas State University, 2008. http://hdl.handle.net/2097/725.

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Kisamore, Jennifer L. "Validity Generalization and Transportability: An Investigation of Distributional Assumptions of Random-Effects Meta-Analytic Methods." [Tampa, Fla.] : University of South Florida, 2003. http://purl.fcla.edu/fcla/etd/SFE0000060.

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Jakimauskas, Gintautas. "Duomenų tyrybos empirinių Bajeso metodų tyrimas ir taikymas." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140423_090834-67696.

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Darbo tyrimų objektas yra duomenų tyrybos empiriniai Bajeso metodai ir algoritmai, taikomi didelio matavimų skaičiaus didelių populiacijų duomenų analizei. Darbo tyrimų tikslas yra sudaryti metodus ir algoritmus didelių populiacijų neparametrinių hipotezių tikrinimui ir duomenų modelių parametrų vertinimui. Šiam tikslui pasiekti yra sprendžiami tokie uždaviniai: 1. Sudaryti didelio matavimo duomenų skaidymo algoritmą. 2. Pritaikyti didelio matavimo duomenų skaidymo algoritmą neparametrinėms hipotezėms tikrinti. 3. Pritaikyti empirinį Bajeso metodą daugiamačių duomenų komponenčių nepriklausomumo hipotezei tikrinti su skirtingais matematiniais modeliais, nustatant optimalų modelį ir atitinkamą empirinį Bajeso įvertinį. 4. Sudaryti didelių populiacijų retų įvykių dažnių vertinimo algoritmą panaudojant empirinį Bajeso metodą palyginant Puasono-gama ir Puasono-Gauso matematinius modelius. 5. Sudaryti retų įvykių logistinės regresijos algoritmą panaudojant empirinį Bajeso metodą. Darbo metu gauti nauji rezultatai įgalina atlikti didelio matavimo duomenų skaidymą; atlikti didelio matavimo nekoreliuotų duomenų pasirinktų komponenčių nepriklausomumo tikrinimą; parinkti didelių populiacijų retų įvykių optimalų modelį ir atitinkamą empirinį Bajeso įvertinį. Pateikta nesinguliarumo sąlyga Puasono-gama modelio atveju.
The research object is data mining empirical Bayes methods and algorithms applied in the analysis of large populations of large dimensions. The aim and objectives of the research are to create methods and algorithms for testing nonparametric hypotheses for large populations and for estimating the parameters of data models. The following problems are solved to reach these objectives: 1. To create an efficient data partitioning algorithm of large dimensional data. 2. To apply the data partitioning algorithm of large dimensional data in testing nonparametric hypotheses. 3. To apply the empirical Bayes method in testing the independence of components of large dimensional data vectors. 4. To develop an algorithm for estimating probabilities of rare events in large populations, using the empirical Bayes method and comparing Poisson-gamma and Poisson-Gaussian mathematical models, by selecting an optimal model and a respective empirical Bayes estimator. 5. To create an algorithm for logistic regression of rare events using the empirical Bayes method. The results obtained enables us to perform very fast and efficient partitioning of large dimensional data; testing the independence of selected components of large dimensional data; selecting the optimal model in the estimation of probabilities of rare events, using the Poisson-gamma and Poisson-Gaussian mathematical models and empirical Bayes estimators. The nonsingularity condition in the case of the Poisson-gamma model is presented.
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Books on the topic "Empirical Bayes methods"

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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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Large-scale inference: Empirical Bayes methods for estimation, testing, and prediction. Cambridge: Cambridge University Press, 2010.

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Phillips, Peter C. B. Bayes methods for trending multiple time eries with an empirical application to the U. S. economy. New Haven, CN: Yale University, Cowles Foundation, 1992.

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Maritz, J. S., and T. Lwin. Empirical Bayes Methods. Routledge, 2018. http://dx.doi.org/10.4324/9781351140645.

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Maritz, J. S. Empirical Bayes Methods with Applications. Taylor & Francis Group, 2018.

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Maritz, J. S. Empirical Bayes Methods with Applications. Taylor & Francis Group, 2018.

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Maritz, J. S. Empirical Bayes Methods with Applications. Taylor & Francis Group, 2018.

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Book chapters on the topic "Empirical Bayes methods"

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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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Ghosh, M., and G. Meeden. "Empirical Bayes estimation." In Bayesian Methods for Finite Population Sampling, 161–220. Boca Raton: Routledge, 2021. http://dx.doi.org/10.1201/9781315138169-4.

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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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Newton, Michael A., and Christina Kendziorski. "Parametric Empirical Bayes Methods for Microarrays." In Statistics for Biology and Health, 254–71. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/0-387-21679-0_11.

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Chaudhuri, Arijit, and Sanghamitra Pal. "Prediction Approach: Robustness, Bayesian Methods, Empirical Bayes." In Indian Statistical Institute Series, 169–82. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1418-8_8.

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Mukhopadhyay, Nitai, and Jayanta Ghosh. "Parametric empirical Bayes model selection---some theory, methods and simulation." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 229–45. Beachwood, OH: Institute of Mathematical Statistics, 2003. http://dx.doi.org/10.1214/lnms/1215091667.

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Singh, Radhey S. "Empirical Bayes Procedures For Testing The Quality and Reliability With Respect To Mean Life." In Quality Improvement Through Statistical Methods, 371–79. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-1776-3_30.

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Tang, Weihua, and Cun-Hui Zhang. "Empirical Bayes methods for controlling the false discovery rate with dependent data." In Complex Datasets and Inverse Problems, 151–60. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007. http://dx.doi.org/10.1214/074921707000000111.

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Yasuda, Muneki. "Empirical Bayes Method for Boltzmann Machines." In Sublinear Computation Paradigm, 277–93. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4095-7_11.

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AbstractThe framework of the empirical Bayes method allows the estimation of the values of the hyperparameters in the Boltzmann machine by maximizing a specific likelihood function referred to as the empirical Bayes likelihood function. However, the maximization is computationally difficult because the empirical Bayes likelihood function involves intractable integrations of the partition function. The method presented in this chapter avoids this computational problem by using the replica method and the Plefka expansion, which is quite simple and fast because it does not require any iterative procedures and gives reasonable estimates under certain conditions.
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Pillonetto, Gianluigi, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, and Lennart Ljung. "Bayesian Interpretation of Regularization." In Regularized System Identification, 95–134. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95860-2_4.

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AbstractIn the previous chapter, it has been shown that the regularization approach is particularly useful when information contained in the data is not sufficient to obtain a precise estimate of the unknown parameter vector and standard methods, such as least squares, yield poor solutions. The fact itself that an estimate is regarded as poor suggests the existence of some form of prior knowledge on the degree of acceptability of candidate solutions. It is this knowledge that guides the choice of the regularization penalty that is added as a corrective term to the usual sum of squared residuals. In the previous chapters, this design process has been described in a deterministic setting where only the measurement noises are random. In this chapter, we will see that an alternative formalization of prior information is obtained if a subjective/Bayesian estimation paradigm is adopted. The major difference is that the parameters, rather than being regarded as deterministic, are now treated as a random vector. This stochastic setting permits the definition of new powerful tools for both priors selection, e.g., through the maximum entropy principle, and for regularization parameters tuning, e.g., through the empirical Bayes approach and its connection with the concept of equivalent degrees of freedom.
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Conference papers on the topic "Empirical Bayes methods"

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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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Han, Rujun, Michael Gill, Arthur Spirling, and Kyunghyun Cho. "Conditional Word Embedding and Hypothesis Testing via Bayes-by-Backprop." In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2018. http://dx.doi.org/10.18653/v1/d18-1527.

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Aminghafari, Mina, and Adel Mohammadpour. "An Alternative Approach to the Parametric Empirical Bayes Selection of Wavelet Thresholding." In Bayesian Inference and Maximum Entropy Methods In Science and Engineering. AIP, 2006. http://dx.doi.org/10.1063/1.2423304.

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"Empirical Study of Domain Adaptation with Naïve Bayes on the Task of Splice Site Prediction." In International Conference on Bioinformatics Models, Methods and Algorithms. SCITEPRESS - Science and and Technology Publications, 2014. http://dx.doi.org/10.5220/0004806800570067.

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Shin, Sungtae, Reza Langari, and Reza Tafreshi. "A Performance Comparison of EMG Classification Methods for Hand and Finger Motion." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-5993.

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For recognizing human motion intent, electromyogram (EMG) based pattern recognition approaches have been studied for many years. A number of methods for classifying EMG patterns have been introduced in the literature. On the purpose of selecting the best performing method for the practical application, this paper compares EMG pattern recognition methods in terms of motion type, feature extraction, dimension reduction, and classification algorithm. Also, for more usability of this research, hand and finger EMG motion data set which had been published online was used. Time-domain, empirical mode decomposition, discrete wavelet transform, and wavelet packet transform were adopted as the feature extraction. Three cases, such as no dimension reduction, principal component analysis (PCA), and linear discriminant analysis (LDA), were compared. Six classification algorithms were also compared: naïve Bayes, k-nearest neighbor, quadratic discriminant analysis, support vector machine, multi-layer perceptron, and extreme machine learning. The performance of each case was estimated by three perspectives: classification accuracy, train time, and test (prediction) time. From the experimental results, the time-domain feature set and LDA were required for the highest classification accuracy. Fast train time and test time are dependent on the classification methods.
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Sung, Mujeen, Jinhyuk Lee, Sean Yi, Minji Jeon, Sungdong Kim, and Jaewoo Kang. "Can Language Models be Biomedical Knowledge Bases?" In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2021. http://dx.doi.org/10.18653/v1/2021.emnlp-main.388.

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Yensy, Nurul Astuty. "The Small Area Estimation by Using Empirical Bayes Method." In International Conference on Educational Sciences and Teacher Profession (ICETeP 2020). Paris, France: Atlantis Press, 2021. http://dx.doi.org/10.2991/assehr.k.210227.058.

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Lin, Yankai, Zhiyuan Liu, Huanbo Luan, Maosong Sun, Siwei Rao, and Song Liu. "Modeling Relation Paths for Representation Learning of Knowledge Bases." In Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2015. http://dx.doi.org/10.18653/v1/d15-1082.

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Safavi, Tara, Jing Zhu, and Danai Koutra. "NegatER: Unsupervised Discovery of Negatives in Commonsense Knowledge Bases." In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2021. http://dx.doi.org/10.18653/v1/2021.emnlp-main.456.

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Abujabal, Abdalghani, Rishiraj Saha Roy, Mohamed Yahya, and Gerhard Weikum. "QUINT: Interpretable Question Answering over Knowledge Bases." In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing: System Demonstrations. Stroudsburg, PA, USA: Association for Computational Linguistics, 2017. http://dx.doi.org/10.18653/v1/d17-2011.

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Reports on the topic "Empirical Bayes methods"

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Gu, Jiaying, and Roger Koenker. Rebayes: an R package for empirical bayes mixture methods. The IFS, August 2017. http://dx.doi.org/10.1920/wp.cem.2017.3717.

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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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Carlin, Bradley P., and Alan E. Gelfand. A Sample Reuse Method for Accurate Parametric Empirical Bayes Confidence Intervals. Fort Belvoir, VA: Defense Technical Information Center, November 1989. http://dx.doi.org/10.21236/ada216198.

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Mykhayliv, Natalya. THE SUBJECT OF OF “VOGUE” AND “HARPER’S BAZAAR” MAGAZINES. Ivan Franko National University of Lviv, February 2021. http://dx.doi.org/10.30970/vjo.2021.49.11066.

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In the article according to the theory of the subject, patterns of the existence and genesis of the subject of “Vogue” and “Harper’s Bazaar” (USA) magazines was analysed, perspective of the emergence of new subjects was established, classification of the current subjects into universal and synthetic was suggested and some regularities of authorial creation of new subjects was examined. The main objective of the study is to identify patterns of existence of actual and formation of new topics in the Means of Mass Communication on the example of “Vogue” and “Harper’s Bazaar” magazines. In studying of the empiric basis of the research the method of observation is applied; in finding common themes for both publications – a comparative method was used. The method of analysis was used in the decomposition of topics into separate topics; in isolation from the features of the topic, uncharacteristic of a journalistic work – abstraction was applied. The elucidation that the subject appears as a formal verbal expression of a set of homogeneous topics was done by applying the method of formalization. The main results of the research are: obtaining the new classification of topics of “Vogue” and “Harper’s Bazaar” magazines; identification of a significant manifestation of universal themes on the pages of publications; establishment of the basic subjective (deontological) bases of formation of new subjects. A theoretical level of their knowledge will enrich science, equip practice, promote individual and world harmony.
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