On the Convergence of Bayesian Regression Models

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this model with different priors, including splines and Gaussian process priors. The results are based on the general ones on the rates of convergence of posterior distributions for independent, non-identically distributed observations, and are established for both of the cases with random covariates, and deterministic covariates. We also illustrate that the results can be achieved for all levels of regularity, which means they are adaptive

Letter to the Editor

The paper by Alfons, Croux and Gelper (2013), Sparse least trimmed squares regression for analyzing high-dimensional large data sets, considered a combination of least trimmed squares (LTS) and lasso penalty for robust and sparse high-dimensional regression. In a recent paper [She and Owen (2011)], a method for outlier detection based on a sparsity penalty on the mean shift parameter was proposed (designated by "SO" in the following). This work is mentioned in Alfons et al. as being an "entirely different approach." Certainly the problem studied by Alfons et al. is novel and interesting.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS640 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Overexpression of the FBA and TPI genes promotes high production of HDMF in Zygosaccharomyces rouxii

4-Hydroxy-2,5-dimethyl-3 (2H)-furanone (HDMF) is widely used in the food industry as a spice and flavoring agent with high market demand. In this study, fructose-1,6-bisphosphate aldolase (FBA) and triose phosphate isomerase (TPI) were overexpressed in Zygosaccharomyces rouxii in the form of single and double genes, respectively, via electroporation. High-yield HDMF-engineered yeast strains were constructed by combining the analysis of gene expression levels obtained by real-time fluorescence quantitative PCR technology and HDMF production measured by HPLC. The results showed that there was a significant positive correlation between the production of HDMF and the expression levels of the FBA and TPI genes in yeast; the expression levels of the FBA and TPI genes were also positively correlated (p < 0.05). Compared with the wild type (WT), the engineered strains F10-D, T17-D, and TF15-A showed marked increases in HDMF production and FBA and TPI gene expression (p < 0.05) and exhibited great genetic stability with no obvious differences in biomass or colony morphology. In addition, the exogenous addition of d-fructose promoted the growth of Z. rouxii. Among the engineered strains, when fermented in YPD media supplemented with d-fructose for 5 days, TF15-A (overexpressing the FBA and TPI genes) generated the highest HDMF production of 13.39 mg/L, which is 1.91 times greater than that of the wild-type strain. The results above indicated that FBA and TPI, which are key enzymes involved in the process of HDMF biosynthesis by Z. rouxii, positively regulate the synthesis of HDMF at the transcriptional level. d-fructose can be used as a precursor for the biosynthesis of HDMF by engineered yeast in industrial production

Bayesian quantile regression for semiparametric models

Quantile regression has recently received a great deal of attention in both theoretical and empirical research. It can uncover different structural relationships between covariates and responses at the upper or lower tails, which is sometimes of significant interest in econometrics, educational and medicine applications. The methodologies of quantile regression for linear models have been well developed in both frequentist and Bayesian contexts. However, there has been relatively less work focusing on quantile regression for nonparametric models or semiparametric models, especially from a Bayesian perspective. The principal goal of this work is to propose efficient approaches to implement Bayesian quantile regression with two kinds of semiparametric modes, single-index models and partially linear additive models, using an asymmetric Laplace distribution which provides a mechanism for Bayesian inference of quantile regression. With carefully selected priors, we build hierarchical Bayesian models and design effective Markov chain Monte Carlo algorithms for posterior inference. We compare the proposed methods with some existing methods through simulation studies and real data applications.DOCTOR OF PHILOSOPHY (SPMS

Variable selection in a partially linear proportional hazards model with a diverging dimensionality

We consider the problem of simultaneous variable selection and estimation in partially linear proportional hazards models when the number of covariates in the linear part diverges with the sample size. We apply the smoothly clipped absolute deviation (SCAD) penalty to select the significant covariates in the linear part. Some simulations and a real data set are presented

Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty

In this paper, we consider the problem of simultaneous variable selection and estimation for varying-coefficient partially linear models in a “small n , large p ” setting, when the number of coefficients in the linear part diverges with sample size while the number of varying coefficients is fixed. Similar problem has been considered in Lam and Fan (Ann Stat 36(5):2232–2260, 2008) based on kernel estimates for the nonparametric part, in which no variable selection was investigated besides that p was assume to be smaller than n . Here we use polynomial spline to approximate the nonparametric coefficients which is more computationally expedient, demonstrate the convergence rates as well as asymptotic normality of the linear coefficients, and further present the oracle property of the SCAD-penalized estimator which works for p almost as large as exp{n1/2} under mild assumptions. Monte Carlo studies and real data analysis are presented to demonstrate the finite sample behavior of the proposed estimator. Our theoretical and empirical investigations are actually carried out for the generalized varying-coefficient partially linear models, including both Gaussian data and binary data as special case

SiC-on-insulator based lateral power device and it’ s analytical models

This paper proposes the concept of SiC-on-insulator (SiCOI) lateral power device and its analytical models. The SiCOI technology provides dielectric isolation and improves the vertical breakdown. The analytical models provide the physic insight of the surface potential and electric field distributions for both full and partial depletion cases. The optimal breakdown voltage and doping concentration are deduced to analyze the breakdown mechanism qualitatively. The specific on-resistance in the drift region was also calculated to analyze the conduction characteristics. The influences of the structure parameters on the performances of the SiCOI lateral power device are investigated by the analytical model and numerical simulation. The analytical results of the proposed model are well agreement with the numerical results, confirming the validity of the proposed unified analytical model. Both the analytical and numerical results provide the physical explanation and effective solution for optimizing the electric field and improving breakdown voltage for the SiCOI lateral power device

Rare Earth Ion Doped Luminescent Materials: A Review of Up/Down Conversion Luminescent Mechanism, Synthesis, and Anti-Counterfeiting Application

With the rapid development of modern technology and information systems, optical anti-counterfeiting and encryption have recently attracted considerable attention. The demand for optical materials is also constantly increasing, with new requirements proposed for performance and application fields. Currently, rare earth ion doped materials possess a unique electronic layer structure, underfilled 4f5d electronic configuration, rich electronic energy level, and long-life excited state, which can produce a variety of radiation absorption and emission. The distinctive properties of rare earth are beneficial for using in diverse optical output anti-counterfeiting. Design is essential for rare earth ion doped materials with multiple responsiveness and multi-channel optical information anti-counterfeiting in the field of information security. Therefore, this mini review summarizes the luminescent mechanisms, preparation methods, performance characteristics and anti-counterfeiting application of rare earth doped materials. In addition, we discuss some critical challenges in this field, and potential solutions that have been or are being developed to overcome these challenges