An exploration of aspects of Bayesian multiple testing

By James G. Scott, James O. Berger. 2006

363 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6b9f7f214abbe504b8ba69be77c030eb1fc44412

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In Management Science and Operations Research

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Citations in the corpus

Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction (2012, background): “Many of this framework's asymptotic properties are well understood, both as the number of means (p) and the number of replicated observations (n) grow [Johnstone and Silverman, 2004, Scott and Berger, 2006, 2010, Muller et al., 2006, Bogdan et al., 2008a,b].”
A Nearby Repeating Fast Radio Burst in the Direction of M81 (2021, methodology): “Bayesian hypothesis testing is another method proposed to avoid the problem of multiple testing (Scott & Berger 2006; Gelman et al. 2012).”
A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing (2008, methodology): “To compute the posterior probability of H0i (see formula (9) of Scott and Berger [25]) Markov chain Monte Carlo (MCMC) is applied, which according to our simulations is more stable than the importance sampling suggested in Scott and Berger [25].”
Bayesian analysis of neuroimaging data in FSL (2009, background): “…when we are looking to threshold posterior probability maps of GLM regression parameters, but is not generally true (e.g. when the thresholding is explicitly contained within the model itself via classification parameters; Scott and Berger, 2006; Woolrich et al., 2005; Woolrich and Behrens, 2006).”
Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective (2014, methodology): “(2012) with uniform model probabilities, and (iii) a g-prior with g = n and model probabilities as suggested in Scott and Berger (2006). Withp = 15 < 30, we are able to evaluate marginal likelihoods for all models under the model selection priors (ii) and (iii).”
Asymptotic Properties of Bayes Risk of a General Class of Shrinkage Priors in Multiple Hypothesis Testing Under Sparsity (2013, methodology): “Fully Bayesian approaches towards mul- tiple testing based on the two-groups model by placing hyperpriors on the underlying model parameters are available in the literature, see, for example, Scott and Berger (2006) and Bogdan et al. (2008).”
On the half-cauchy prior for a global scale parameter (2011, background): “An example of a situation in which formal noninformative priors for λ should not be used on mathematical grounds is when β is expected to be sparse; see Scott and Berger (2006) for a discussion of this issue in the context of multiple-testing.”
Handling Sparsity via the Horseshoe (2009, background): “The former allows large signals to be accommodated, while the latter allows the model to adapt to the overall level of sparsity in β, automatically handling the implied multiple-testing problem (Scott and Berger, 2006).”
CONSISTENCY OF A RECURSIVE ESTIMATE OF MIXING DISTRIBUTIONS (2009, background): “A fully Bayesian analysis can be difficult in these applications: the results are very sensitive to the choice of hyperparameters (π,fac) [4, 29].”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, background): “, [6, 12, 31] and [35]) have also been proposed and are used extensively in such problems.”