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Abstract Under mild assumptions, we show that the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis–Hastings independence sampler. We develop a new upper and lower bound on the worst-case Wasserstein distance when initialized from points. For an arbitrary point initialization, we show that the convergence rate is the same and matches the convergence rate in total variation. We derive exact convergence expressions for more general Wasserstein distances when initialization is at a specific point. Using optimization, we construct a novel centered independent proposal to develop exact convergence rates in Bayesian quantile regression and many generalized linear model settings. We show that the exact convergence rate can be upper bounded in Bayesian binary response regression (e.g. logistic and probit) when the sample size and dimension grow together. 

Abstract A Bayesian method is proposed for variable selection in high-dimensional matrix autoregressive models which reflects and exploits the original matrix structure of data to (a) reduce dimensionality and (b) foster interpretability of multidimensional relationship structures. A compact form of the model is derived which facilitates the estimation procedure and two computational methods for the estimation are proposed: a Markov chain Monte Carlo algorithm and a scalable Bayesian EM algorithm. Being based on the spike-and-slab framework for fast posterior mode identification, the latter enables Bayesian data analysis of matrix-valued time series at large scales. The theoretical properties, comparative performance, and computational efficiency of the proposed model is investigated through simulated examples and an application to a panel of country economic indicators. 

Over the past century, supernova (SN) searches have detected multiple supernovae (SNe) in hundreds of individual galaxies. So-called SN siblings discovered in the same galaxy present an opportunity to constrain the dependence of the properties of SNe on those of their host galaxies. To investigate whether there is a connection between sibling SNe in galaxies that have hosted multiple SNe and the properties of galaxies, we have acquired integrated optical spectroscopy of 59 galaxies with multiple core-collapse SNe. Perhaps surprisingly, a strong majority of host galaxy spectra fall within the composite region of the Baldwin–Phillips–Terlevich (BPT) diagram. We find a statistically significant difference (Kolmogorov–Smirnov test p-value = 0.044) between the distributions of the [Nii]λ6583/Hα of galaxies that have hosted a majority of SNe Ibc and those that have hosted a majority of Type II supernovae (SNe II), where the majority of Type Ibc supernovae (SNe Ibc) galaxies have, on average, higher ratios. The difference between the distributions of [Nii]λ6583/Hα may arise from either increased contribution from active galactic nuclei or low-ionization nuclear emission-line regions in SNe Ibc host galaxies, greater metallicity for SNe Ibc host galaxies, or both. When comparing the inferred oxygen abundance and the ionization parameter for the galaxies in the star-forming region on the BPT diagram, we find statistically significant differences between the distributions for SNe Ibc hosts and SNe II hosts (p= 0.008 and p= 0.001, respectively), as well as SNe Ib hosts and SNe II hosts (p = 0.030 and p= 0.006, respectively). We also compare the Hα equivalent width distributions, also integrated across the galaxies, and find no significant difference. 

Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an analytically intractable posterior distribution that can be sampled using a data augmentation algorithm. When the response matrix has missing entries, there are unique challenges to the application and analysis of the convergence properties of the algorithm. Conditions for geometric ergodicity are provided when the incomplete data have a “monotone” structure. In the absence of a monotone structure, an intermediate imputation step is necessary for implementing the algorithm. In this case, we provide sufficient conditions for the algorithm to be Harris ergodic. Finally, we show that, when there is a monotone structure and intermediate imputation is unnecessary, intermediate imputation slows the convergence of the underlying Monte Carlo Markov chain, while post hoc imputation does not. An R package for the data augmentation algorithm is provided. 

Researchers routinely face choices throughout the data analysis process. It is often opaque to readers how these choices are made, how they affect the findings, and whether or not data analysis results are unduly influenced by subjective decisions. This concern is spurring numerous investigations into the variability of data analysis results. The findings demonstrate that different teams analyzing the same data may reach different conclusions. This is the “many-analysts” problem. Previous research on the many-analysts problem focused on demonstrating its existence, without identifying specific practices for solving it. We address this gap by identifying three pitfalls that have contributed to the variability observed in many-analysts publications and providing suggestions on how to avoid them.