Parametric Empirical Bayes Inference: Theory and Applications

Morris, Carl N.

doi:10.1080/01621459.1983.10477920

Cited by 1,105 publications

(563 citation statements)

References 24 publications

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“…Notice that the weights themselves must be estimated by finding an initial estimate for A. To avoid iteration without losing too much accuracy, A is estimated by the unweighted mean of the A;s. So xwj where k -I ~= ( k -1) b + F + ( k -1)3 +' The estimator Ap is not the maximum likelihood estimator for A, but is similar to the one given by Morris (1983b). Other related estimates appear in Carter andRolph (1974), Dempster et al (1977) and Fay and Herriot (1979).…”

Section: Hierarchical Bayes and Empirical Bayes Confidence Intervals-mentioning

confidence: 99%

“…The batting averages for these players during the remainder of the season, considered to be the true values 0j, are presented in the last column of Table 2. The estimator t)i as well as normal approximations of the confidence intervals was calculated by Morris (1977Morris ( , 1983b. Not only was the estimator_0' = (01,..., 018) about three times as efficient as the sample mean vector X'= (X1,..., X18) but the intervals were 37% shorter while containing the true values with greater frequency than nominally claimed.…”

Section: Baseball Datamentioning

confidence: 99%

“…In most hierarchical and empirical Bayes cases these posterior distributions are difficult to derive and cannot be obtained in closed form. Numerical integration, normal approximations (Morris (1977(Morris ( , 1983b and Berger (1985)) or other asymptotic approximations of the posterior distribution are then used to obtain *Financially supported by the CSIR and the University of the Orange Free State, Central Research Fund. confidence intervals of the unknown parameter values.…”

Section: Introductionmentioning

confidence: 99%

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Approximated Bayes and empirical Bayes confidence intervals—The known variance case

1988

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Section: Hierarchical Bayes and Empirical Bayes Confidence Intervals-mentioning

confidence: 99%

Section: Baseball Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximated Bayes and empirical Bayes confidence intervals—The known variance case

1988

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“…The adverse effect of incorrect prior specification is when the prior information did not agree with the data information which might lead to incorrect estimation or inference about the unknown parameter. Solving this problem led to the proposition of empirical Bayes in the early 1950s by Robbins as reported in Robbins (1956), Martiz (1970, Efron and Morris (1973, 1975, 1976, Morris (1983), Casella (1985, Bishop (2005), and recently in Efron (2012Efron ( , 2013Efron ( , 2014, Lee (2012), and Lesaffre and Lawson (2013).…”

Section: Priors and Prior Distributionsmentioning

confidence: 99%

Bayesian Hypothesis Testing of Two Normal Samples using Bootstrap Prior Technique

Olaniran

Yahya

2017

J. Mod. App. Stat. Meth.

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The most important ingredient in Bayesian analysis is prior or prior distribution. A new prior determination method was developed under the framework of parametric empirical Bayes using bootstrap technique. By way of example, Bayesian estimations of the parameters of a normal distribution with unknown mean and unknown variance conditions were considered, as well as its application in comparing the means of two independent normal samples with several scenarios. A Monte Carlo study was conducted to illustrate the proposed procedure in estimation and hypothesis testing. Results from Monte Carlo studies showed that the bootstrap prior proposed is more efficient than the existing method for determining priors and also better than the frequentist methods reviewed.

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“…The adverse effect of incorrect prior specification is when the prior information did not agree with the data information which might lead to incorrect estimation or inference about the unknown parameter. Solving this problem led to the proposition of empirical Bayes in the early 1950s by Robbins as reported in Robbins (1956), Martiz (1970, Efron and Morris (1973, 1976, Morris (1983), Casella (1985, Bishop (2005), and recently in Efron (2012Efron ( , 2013Efron ( , 2014, Lee (2012), and Lesaffre and Lawson (2013).…”

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confidence: 99%

Vol. 16, No. 2 (Full Issue)

2017

J. Mod. App. Stat. Meth.

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EDITORIAL ASSISTANCEJMASM (ISSN 1538−9472, http://digitalcommons.wayne.edu/jmasm) is an independent, open access electronic journal, published biannually in May and November by JMASM Inc. (PO Box 48023, Oak Park, MI, 48237) in collaboration with the Wayne State University Library System. JMASM seeks to publish (1) new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computer-intensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) the study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods.Journal correspondence (other than manuscript submissions) and requests for advertising may be forwarded to ea@jmasm.com. See back matter for instructions for authors. IntroductionComputer simulation studies represent an important tool for investigating statistical procedures difficult or impossible to study using mathematical theory or real data. Descriptors of these studies vary (e.g., statistical experiment, Monte Carlo simulation, computer experiment), but the examples of Hoaglin and Andrews (1975) and Hauck and Anderson (1984) are followed here with use of the term simulation studies. Extensive descriptions of simulation studies can be found in Lewis and Orav (1989) and Santner, Williams, and Notz (2003). In the behavioral sciences simulation studies have been used to study a wide array of statistical methods (e.g., Cribbie, Fiksenbaum, & Wilcox, 2012; Depaoli, 2012; Enders, Baraldi, & Cham, 2014; Hu & Bentler, 1999; Tomarken & Serlin, 1986). The general goal of these studies is to provide evidence of the behavior of statistical methods under a variety of data conditions that improves statistical practice and informs future statistical research. The goal here is to encourage methodological researchers to treat these studies as statistical sampling EXPERIMENTAL DESIGN AND DATA ANALYSIS IN SIMULATION 4 experiments subject to established principles of experimental design and data analysis.An underappreciated facet of simulation studies in statistics is their role in enhancing the reproducibility of scientific findings. The importance of reproducibility has gained momentum in numerous scientific arenas because of growing evidence that many findings cannot be replicated (Stodden, 2015). Concerns over reproducibility and the role of statistics were captured in Statistics and science: A report of the London workshop on the future of the statistical sciences (2014) which noted: "The reproducibility problem goes far beyond statistics, of course, because it involves the entire reward structure of the scientific enterprise. Nevertheless, statistics is a very important ingredient in both the problem and the remedy." (p. 27) Simulati...

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Parametric Empirical Bayes Inference: Theory and Applications

Cited by 1,105 publications

References 24 publications

Approximated Bayes and empirical Bayes confidence intervals—The known variance case

Approximated Bayes and empirical Bayes confidence intervals—The known variance case

Bayesian Hypothesis Testing of Two Normal Samples using Bootstrap Prior Technique

Vol. 16, No. 2 (Full Issue)

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