The New England Journal of Statistics in Data Science

Discussion of “Four types of frequentism and their interplay with Bayesianism” by Jim Berger.

Platform trials are multiarm clinical studies that allow the addition of new experimental arms after the activation of the trial. Statistical issues concerning “adding new arms”, however, have not been thoroughly discussed. This work was motivated by a “two-period” pediatric osteosarcoma study, starting with two experimental arms and one control arm and later adding two more pre-planned experimental arms. The common control arm will be shared among experimental arms across the trial. In this paper, we provide a principled approach, including how to modify the critical boundaries to control the family-wise error rate as new arms are added, how to re-estimate the sample sizes and provide the optimal control-to-experimental arms allocation ratio, in terms of minimizing the total sample size to achieve a desirable marginal power level. We examined the influence of the timing of adding new arms on the design’s operating characteristics, which provides a practical guide for deciding the timing. Other various numerical evaluations have also been conducted. A method for controlling the pair-wise error rate (PWER) has also been developed. We have published an R package, PlatformDesign, on CRAN for practitioners to easily implement this platform trial approach. A detailed step-by-step tutorial is provided in Appendix A.2.

Bayesian model averaging (BMA) provides a coherent way to account for model uncertainty in statistical inference tasks. BMA requires specification of model space priors and parameter space priors. In this article we focus on comparing different model space priors in the presence of model uncertainty. We consider eight reference model space priors used in the literature and three adaptive parameter priors recommended by Porwal and Raftery [37]. We assess the performance of these combinations of prior specifications for variable selection in linear regression models for the statistical tasks of parameter estimation, interval estimation, inference, point and interval prediction. We carry out an extensive simulation study based on 14 real datasets representing a range of situations encountered in practice. We found that beta-binomial model space priors specified in terms of the prior probability of model size performed best on average across various statistical tasks and datasets, outperforming priors that were uniform across models. Recently proposed complexity priors performed relatively poorly.

We highlight points of agreement between Meng’s suggested principles and those proposed in our 2019 editorial in The American Statistician. We also discuss some questions that arise in the application of Meng’s principles in practice.

Joint species distribution modeling is attracting increasing attention in the literature these days, recognizing the fact that single species modeling fails to take into account expected dependence/interaction between species. This short paper offers discussion that attempts to illuminate five noteworthy technical issues associated with such modeling in the context of plant data. In this setting, the joint species distribution work in the literature considers several types of species data collection. For convenience of discussion, we focus on joint modeling of presence/absence data. For such data, the primary modeling strategy has been through introduction of latent multivariate normal random variables.

This contribution is a series of comments on Prof. Xiao-Li Meng’s article, “Double Your Variance, Dirtify Your Bayes, Devour Your Pufferfish, and Draw Your Kidstogram”. Prof. Meng’s article offers some radical proposals and not-so-radical proposals to improve the quality of statistical inference used in the sciences and also to extend distributional thinking to early education. Discussions and alternative proposals are presented.

Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data, such as spatio-temporal or functional observations. We first introduce Gaussian processes (GPs) for modeling correlated data and highlight the computational challenge, where the computational complexity increases cubically fast along with the number of observations. We then review the connection between the state space model and GPs with Matérn covariance for temporal inputs. The Kalman filter and Rauch-Tung-Striebel smoother were introduced as a scalable marginalization technique for computing the likelihood and making predictions of GPs without approximation. We introduce recent efforts on extending the scalable marginalization idea to the linear model of coregionalization for multivariate correlated output and spatio-temporal observations. In the final part of this work, we introduce a novel marginalization technique to estimate interaction kernels and forecast particle trajectories. The computational progress lies in the sparse representation of the inverse covariance matrix of the latent variables, then applying conjugate gradient for improving predictive accuracy with large data sets. The computational advances achieved in this work outline a wide range of applications in molecular dynamic simulation, cellular migration, and agent-based models.