Robust Bayesian Regression with Synthetic Posterior

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on $\gamma$-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.Comment: 23 pages, 5 figure

On default priors for robust Bayesian estimation with divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum $\gamma$-divergence estimator is well-known to work well estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the $\gamma$-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.Comment: 22page

Robust Bayesian graphical modeling using γ\gamma-divergence

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods such as the graphical lasso are useful to detect significant conditional independence structures. However, the estimates are affected by outliers due to the Gaussian assumption. This paper proposes a novel robust posterior distribution for inference of Gaussian graphical models using the $\gamma$-divergence which is one of the robust divergences. In particular, we focus on the Bayesian graphical lasso by assuming the Laplace-type prior for elements of the inverse covariance matrix. The proposed posterior distribution matches its maximum a posteriori estimate with the minimum $\gamma$-divergence estimate provided by the frequentist penalized method. We show that the proposed method satisfies the posterior robustness which is a kind of measure of robustness in the Bayesian analysis. The property means that the information of outliers is automatically ignored in the posterior distribution as long as the outliers are extremely large, which also provides theoretical robustness of point estimate for the existing frequentist method. A sufficient condition for the posterior propriety of the proposed posterior distribution is also shown. Furthermore, an efficient posterior computation algorithm via the weighted Bayesian bootstrap method is proposed. The performance of the proposed method is illustrated through simulation studies and real data analysis.Comment: 35 pages, 5 figure

Bayesian Boundary Trend Filtering

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the P\'olya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.Comment: 25 pages, 6 figure

Fast and Locally Adaptive Bayesian Quantile Smoothing using Calibrated Variational Approximations

Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering method to estimate non-stationary trend of quantiles. We introduce general shrinkage priors to induce locally adaptive Bayesian inference on trends and mixture representation of the asymmetric Laplace likelihood. To quickly compute the posterior distribution, we develop calibrated mean-field variational approximations to guarantee that the frequentist coverage of credible intervals obtained from the approximated posterior is a specified nominal level. Simulation and empirical studies show that the proposed algorithm is computationally much more efficient than the Gibbs sampler and tends to provide stable inference results, especially for high/low quantiles.Comment: 41 pages, 7 figures. arXiv admin note: text overlap with arXiv:2202.0953

Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures

In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where most of the underlying means are concentrated around a certain value. Unlike existing shrinkage priors, our new prior is a shape-scale mixture of inverse-gamma distributions, which has a desirable interpretation of the form of posterior mean and admits flexible shrinkage. We show that the proposed prior has two desirable theoretical properties; Kullback-Leibler super-efficiency under sparsity and robust shrinkage rules for large observations. We propose an efficient sampling algorithm for posterior inference. The performance of the proposed method is illustrated through simulation and two real data examples, the average length of hospital stay for COVID-19 in South Korea and adaptive variance estimation of gene expression data

Effective radii of deuteron induced reactions

The continuum-discretized coupled-channels method (CDCC) for exclusive reactions and the eikonal reaction theory (ERT) as an extension of CDCC to inclusive reactions are applied to deuteron induced reactions. The CDCC result reproduces experimental data on the reaction cross section for $d+^{58}$Ni scattering at 200 MeV/nucleon and ERT does data on the neutron-stripping cross section for inclusive $^7$Li$(d,n)$ reaction at 40 MeV. For deuteron induced reactions at 200 MeV/nucleon, target-dependence of the reaction, elastic-breakup, nucleon-stripping, nucleon-removal, complete- and incomplete-fusion cross sections is clearly explained by simple formulae. Accuracy of the Glauber model is also investigated.Comment: 11 pages, 11 figures, 2 table

Embryonic LTR retrotransposons supply promoter modules to somatic tissues

Long terminal repeat (LTR) retrotransposons are widely distributed across the human genome. They have accumulated through retroviral integration into germline DNA and are latent genetic modules. Active LTR promoters are observed in germline cells; however, little is known about the mechanisms underlying their active transcription in somatic tissues. Here, by integrating our previous transcriptome data set with publicly available data sets, we show that the LTR families MLT2A1 and MLT2A2 are primarily expressed in human four-cell and eight-cell embryos and are also activated in some adult somatic tissues, particularly pineal gland. Three MLT2A elements function as the promoters and first exons of the protein-coding genes ABCE1, COL5A1, and GALNT13 specifically in the pineal gland of humans but not in that of macaques, suggesting that the exaptation of these LTRs as promoters occurred during recent primate evolution. This analysis provides insight into the possible transition from germline insertion to somatic expression of LTR retrotransposons.Peer reviewe

Vegetable juice preload ameliorates postprandial blood glucose concentration in healthy women : A randomized cross-over trial

Background and Objectives: The aim of this study was to evaluate the acute effect of drinking vegetable juice 20 min before carbohydrate on postprandial blood glucose concentrations in young healthy women. Method: In this randomized controlled cross-over study, 24 women (age 21.3 ±0.6 years, HbA1c 5.4 ±0.2 %, mean ± SD) consumed either 200 g of vegetable juice, vegetable (150 g of tomato and 40 g of broccoli), or water at 20 min before consuming 200 g of boiled white rice for 3 separate days. The blood glucose concentrations were measured by self-monitoring blood glucose pre- and post-breakfast at -20, 0, 15, 30, 45, 60, 120, and 180 min. The glycemic parameters were compared among 3 days. Results: The incremental glucose peak at 45 min (vegetable juice 48.3 ± 4.1, vegetable 47.4 ± 3.3 vs. water 66.8 ± 4.3 mg/dl, respectively, both p < 0.01, mean ± SEM) and large amplitude of glycemic excursion (LAGE; vegetable juice 57.1 ± 3.1, vegetable 58.3 ± 3.6 vs. water 78.3 ± 4.3 mg/dl, respectively, both p < 0.05) in consuming vegetable juice and vegetable at 20 min before carbohydrate intake were all significantly lower than those of water. There was no significant difference between glycemic parameters of vegetable juice and vegetable. Conclusions: Drinking vegetable juice 20 min before carbohydrate ameliorates the postprandial blood glucose concentrations as well as vegetable preload, despite total amounts of energy and carbohydrate of vegetable juice or vegetable are higher than those of water