Bayesian shrinkage analysis is arguably the state-of-the-art technique for large-scale multiple quantitative trait locus (QTL) mapping. However, when the shrinkage model does not involve indicator variables for marker inclusion, QTL detection remains heavily dependent on significance thresholds derived from phenotype permutation under the null hypothesis of no phenotype-to-genotype association....

Latent factor models are the canonical statistical tool for exploratory analyses of lowdimensional linear structure for an observation matrix with p features across n samples. We develop a Bayesian group factor analysis (BGFA) model that extends the factor model to multiple coupled observation matrices. Our model puts a structured Bayesian hierarchical prior on the joint factor loading matrix, ...

Bayesian nonparametric regression with dependent wavelets has dual shrinkage properties: there is shrinkage through a dependent prior put on functional differences, and shrinkage through the setting of most of the wavelet coefficients to zero through Bayesian variable selection methods. The methodology can deal with unequally spaced data and is efficient because of the existence of fast moves i...

The Bayesian CART (classiication and regression tree) approach proposed by Chipman, George and McCulloch (1998) entails putting a prior distribution on the set of all CART models and then using stochastic search to select a model. The main thrust of this paper is to propose a new class of hierarchical priors which enhance the potential of this Bayesian approach. These priors indicate a preferen...

Many quantitative traits are measured repeatedly during the life of an organism. Such traits are called dynamic traits. The pattern of the changes of a dynamic trait is called the growth trajectory. Studying the growth trajectory may enhance our understanding of the genetic architecture of the growth trajectory. Recently, we developed an interval-mapping procedure to map QTL for dynamic traits ...

Latent factor models are the canonical statistical tool for exploratory analyses of lowdimensional linear structure for an observation matrix with p features across n samples. We develop a Bayesian group factor analysis (BGFA) model that extends the factor model to multiple coupled observation matrices. Our model puts a structured Bayesian hierarchical prior on the joint factor loading matrix, ...

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well some theories have proved high efficiency LISTA for solving sparse coding problems. However, existing methods are all serial connection. To address this issue, we propose a novel extragradient based (ELISTA), which residual structure and th...

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, ver...

This article studies the convergence rate of the posterior for Bayesian low rank supervised tensor modeling with multiway shrinkage priors. Multiway shrinkage priors constitute a new class of shrinkage prior distributions for tensor parameters in Bayesian low rank supervised tensor modeling to regress a scalar response on a tensor predictor with the primary aim to identify cells in the tensor p...

We investigate the posterior rate of convergence for wavelet shrinkage using a Bayesian approach in general Besov spaces. Instead of studying the Bayesian estimator related to a particular loss function, we focus on the posterior distribution itself from a nonparametric Bayesian asymptotics point of view and study its rate of convergence. We obtain the same rate as in Abramovich et al. (2004) w...