Suprateek Kundu, Bani K. Mallick, Veera Baladandayuthapani.

Source: Bayesian Analysis, Volume 14, Number 2, 449--476.

Abstract:
There has been an intense development in the Bayesian graphical model literature over the past decade; however, most of the existing methods are restricted to moderate dimensions. We propose a novel graphical model selection approach for large dimensional settings where the dimension increases with the sample size, by decoupling model fitting and covariance selection. First, a full model based on a complete graph is fit under a novel class of mixtures of inverse–Wishart priors, which induce shrinkage on the precision matrix under an equivalence with Cholesky-based regularization, while enabling conjugate updates. Subsequently, a post-fitting model selection step uses penalized joint credible regions to perform model selection. This allows our methods to be computationally feasible for large dimensional settings using a combination of straightforward Gibbs samplers and efficient post-fitting inferences. Theoretical guarantees in terms of selection consistency are also established. Simulations show that the proposed approach compares favorably with competing methods, both in terms of accuracy metrics and computation times. We apply this approach to a cancer genomics data example.

Luis Gutiérrez, Eduardo Gutiérrez-Peña, Ramsés H. Mena.

Source: Bayesian Analysis, Volume 14, Number 2, 427--447.

Abstract:
This work presents a Bayesian predictive approach to statistical shape analysis. A modeling strategy that starts with a Gaussian distribution on the configuration space, and then removes the effects of location, rotation and scale, is studied. This boils down to an application of the projected normal distribution to model the configurations in the shape space, which together with certain identifiability constraints, facilitates parameter interpretation. Having better control over the parameters allows us to generalize the model to a regression setting where the effect of predictors on shapes can be considered. The methodology is illustrated and tested using both simulated scenarios and a real data set concerning eight anatomical landmarks on a sagittal plane of the corpus callosum in patients with autism and in a group of controls.

Haolun Shi, Guosheng Yin.

Source: Bayesian Analysis, Volume 14, Number 2, 399--425.

Abstract:
Bayesian approaches to phase II clinical trial designs are usually based on the posterior distribution of the parameter of interest and calibration of certain threshold for decision making. If the posterior probability is computed and assessed in a sequential manner, the design may involve the problem of multiplicity, which, however, is often a neglected aspect in Bayesian trial designs. To effectively maintain the overall type I error rate, we propose solutions to the problem of multiplicity for Bayesian sequential designs and, in particular, the determination of the cutoff boundaries for the posterior probabilities. We present both theoretical and numerical methods for finding the optimal posterior probability boundaries with $alpha$ -spending functions that mimic those of the frequentist group sequential designs. The theoretical approach is based on the asymptotic properties of the posterior probability, which establishes a connection between the Bayesian trial design and the frequentist group sequential method. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. We apply least-square fitting to find the $alpha$ -spending function closest to the target. We discuss the application of our method to single-arm and double-arm cases with binary and normal endpoints, respectively, and provide a real trial example for each case.

Daniela Pauger, Helga Wagner.

Source: Bayesian Analysis, Volume 14, Number 2, 341--369.

Abstract:
We propose a Bayesian approach to obtain a sparse representation of the effect of a categorical predictor in regression type models. As this effect is captured by a group of level effects, sparsity cannot only be achieved by excluding single irrelevant level effects or the whole group of effects associated to this predictor but also by fusing levels which have essentially the same effect on the response. To achieve this goal, we propose a prior which allows for almost perfect as well as almost zero dependence between level effects a priori. This prior can alternatively be obtained by specifying spike and slab prior distributions on all effect differences associated to this categorical predictor. We show how restricted fusion can be implemented and develop an efficient MCMC (Markov chain Monte Carlo) method for posterior computation. The performance of the proposed method is investigated on simulated data and we illustrate its application on real data from EU-SILC (European Union Statistics on Income and Living Conditions).

Daniele Durante, Tommaso Rigon.

Source: Statistical Science, Volume 34, Number 3, 472--485.

Abstract:
Variational Bayes (VB) is a common strategy for approximate Bayesian inference, but simple methods are only available for specific classes of models including, in particular, representations having conditionally conjugate constructions within an exponential family. Models with logit components are an apparently notable exception to this class, due to the absence of conjugacy among the logistic likelihood and the Gaussian priors for the coefficients in the linear predictor. To facilitate approximate inference within this widely used class of models, Jaakkola and Jordan ( Stat. Comput. 10 (2000) 25–37) proposed a simple variational approach which relies on a family of tangent quadratic lower bounds of the logistic log-likelihood, thus restoring conjugacy between these approximate bounds and the Gaussian priors. This strategy is still implemented successfully, but few attempts have been made to formally understand the reasons underlying its excellent performance. Following a review on VB for logistic models, we cover this gap by providing a formal connection between the above bound and a recent Pólya-gamma data augmentation for logistic regression. Such a result places the computational methods associated with the aforementioned bounds within the framework of variational inference for conditionally conjugate exponential family models, thereby allowing recent advances for this class to be inherited also by the methods relying on Jaakkola and Jordan ( Stat. Comput. 10 (2000) 25–37).

Bradley Efron.

Source: Statistical Science, Volume 34, Number 2, 234--235.

Yixin Wang, Andrew C. Miller, David M. Blei.

Source: Statistical Science, Volume 34, Number 2, 229--233.

Eitan Greenshtein, Ya’acov Ritov.

Source: Statistical Science, Volume 34, Number 2, 224--228.

Abstract:
We present some personal reflections on empirical Bayes/ compound decision (EB/CD) theory following Efron (2019). In particular, we consider the role of exchangeability in the EB/CD theory and how it can be achieved when there are covariates. We also discuss the interpretation of EB/CD confidence interval, the theoretical efficiency of the CD procedure, and the impact of sparsity assumptions.

Wenhua Jiang.

Source: Statistical Science, Volume 34, Number 2, 219--223.

Abstract:
This is a contribution to the discussion of the enlightening paper by Professor Efron. We focus on empirical Bayes interval estimation. We discuss the oracle interval estimation rules, the empirical Bayes estimation of the oracle rule and the computation. Some numerical results are reported.

Aad van der Vaart.

Source: Statistical Science, Volume 34, Number 2, 214--218.

Nan Laird.

Source: Statistical Science, Volume 34, Number 2, 206--208.

Thomas A. Louis.

Source: Statistical Science, Volume 34, Number 2, 202--205.

Bradley Efron.

Source: Statistical Science, Volume 34, Number 2, 177--201.

Abstract:
This article concerns the Bayes and frequentist aspects of empirical Bayes inference. Some of the ideas explored go back to Robbins in the 1950s, while others are current. Several examples are discussed, real and artificial, illustrating the two faces of empirical Bayes methodology: “oracle Bayes” shows empirical Bayes in its most frequentist mode, while “finite Bayes inference” is a fundamentally Bayesian application. In either case, modern theory and computation allow us to present a sharp finite-sample picture of what is at stake in an empirical Bayes analysis.

Many complex human traits exhibit differences between sexes. While numerous factors likely contribute to this phenomenon, growing evidence from genome-wide studies suggest a partial explanation: that males and females from the same population possess differing genetic architectures. Despite this, mapping gene-by-sex (GxS) interactions remains a challenge likely because the magnitude of such an interaction is typically and exceedingly small; traditional genome-wide association techniques may be underpowered to detect such events, due partly to the burden of multiple test correction. Here, we developed a local Bayesian regression (LBR) method to estimate sex-specific SNP marker effects after fully accounting for local linkage-disequilibrium (LD) patterns. This enabled us to infer sex-specific effects and GxS interactions either at the single SNP level, or by aggregating the effects of multiple SNPs to make inferences at the level of small LD-based regions. Using simulations in which there was imperfect LD between SNPs and causal variants, we showed that aggregating sex-specific marker effects with LBR provides improved power and resolution to detect GxS interactions over traditional single-SNP-based tests. When using LBR to analyze traits from the UK Biobank, we detected a relatively large GxS interaction impacting bone mineral density within ABO, and replicated many previously detected large-magnitude GxS interactions impacting waist-to-hip ratio. We also discovered many new GxS interactions impacting such traits as height and body mass index (BMI) within regions of the genome where both male- and female-specific effects explain a small proportion of phenotypic variance (R² < 1 x 10^–4), but are enriched in known expression quantitative trait loci.

Oxford : Oxford University Press, 2019.

Singapore : Springer, c2019.

Gelman, Andrew, author

Online Resource

Dewey Library - QH438.4.S73 B53 2019

Dewey Library - QA279.5.S67 2019

Dewey Library - QA278.2.F53 2020

Dewey Library - QA279.5.C66 2020

Hayden Library - QB462.3.C26 2018

Cham : Springer International Publishing : Imprint: Springer, 2014

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014

Pittsburgh, PA : International Society for Bayesian Analysis, c2006-

New York, NY : Springer, 2007

Paris : Springer-Verlag France, Paris, 2006