Bayesian shrinkage analysis is the state-of-the-art method for whole genome analysis of quantitative traits. It can estimate the genetic effects for the entire genome using a dense marker map. The technique is now called genome selection. A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300–500 individuals. In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low. As a Bayesian method, no significance test is needed. However, it is still desirable to put some confidences on the estimated QTL effects. We proposed to use the permutation test to draw empirical thresholds to declare significance of QTL under a predetermined genome wide type I error. With the permutation test, Bayesian shrinkage analysis can be routinely used for QTL detection.

Many biological traits are discretely distributed in phenotype but continuously distributed in genetics because they are controlled by multiple genes and environmental variants. Due to the quantitative nature of the genetic background, these multiple genes are called quantitative trait loci (QTL). When the QTL effects are treated as random, they can be estimated in a single generalized linear mixed model (GLMM), even if the number of QTL may be larger than the sample size. The GLMM in its original form cannot be applied to QTL mapping for discrete traits if there are missing genotypes. We examined two alternative missing genotype-handling methods: the expectation method and the overdispersion method. Simulation studies show that the two methods are efficient for multiple QTL mapping (MQM) under the GLMM framework. The overdispersion method showed slight advantages over the expectation method in terms of smaller mean-squared errors of the estimated QTL effects. The two methods of GLMM were applied to MQM for the female fertility trait of wheat. Multiple QTL were detected to control the variation of the number of seeded spikelets. (Henderson, 1950). This technique has been used to map genes controlling the variation of quantitative traits (Xu and Yi, 2000;Boer et al, 2007). The LMM methodology cannot be directly applied to traits with discrete distributions. Wedderburn (1974) proposed a linear predictor and a link function to handle discrete traits. The linear predictor is simply a linear model combining information from the independent variables. The link function is used to describe the relationship between the linear predictor and the expectation of the response variable. This approach eventually leads to a special area of statistics called the generalized linear model (GLM) (McCullagh and Nelder, 1989).Xu and Hu (2010) recently developed a GLM approach to interval mapping (IM) for traits with discrete distribution. The purpose of that study was to investigate the efficiencies of two different methods for handling missing genotypes: (1) the heterogeneous residual variance method and (2) the mixture model method. In the first method (heterogeneous residual variance method), we replaced the missing genotypes of quantitative trait loci (QTL) by the conditional expectations of the genotype indicator variables and then took into account the heterogeneous residual variances of different genotypes due to heterogeneous information contents. In the second method (the mixture model method), we fully utilized the conditional distributions of the missing genotypes. Theoretically, the mixture model approach should be optimal. In practice, the heterogeneous residual variance method is more efficient because it is robust to departure from the assumed normal distribution of the residuals. On the contrary, the

The bearing is an important basic mechanical part for supporting a shaft. A flywheel storage system needs a type of noncontact support bearing to enhance the speed of the axis. A magnetic suspension bearing is one type of noncontact bearing but has electromagnetic interference to other electric equipment. Based on the performance research of ultrasonic levitation technology, a novel noncontact bearing called ultrasonic bearing is presented, which consists of a special piezoelectric vibrator supporting the load. Experiments are carried out to study the relationships among the amplitude of the vibrator and levitation clearance, the highest speed of the axis, and the frictional moment of the axis. Results show that the levitation clearance becomes smaller gradually with increasing load; the rotation speed is up to 8946 r/min, and the friction moment is only 2.095Â10 -5 N$m when the levitation clearance is 8.53 μm. The ultrasonic bearing is highlighted because of its simple structure, strong levitation ability, and low friction moment.

Che, X. and Xu, S. 2010. Bayesian data analysis for agricultural experiments. Can. J. Plant Sci. 90: 575Á603. Data collected in agricultural experiments can be analyzed in many different ways using different models. The most commonly used models are the linear model and the generalized linear model. The maximum likelihood method is often used for data analysis. However, this method may not be able to handle complicated models, especially multiple level hierarchical models. The Bayesian method partitions complicated models into simple components, each of which may be formulated analytically. Therefore, the Bayesian method is capable of handling very complicated models. The Bayesian method itself may not be more complicated than the maximum likelihood method, but the analysis is time consuming, because numerical integration involved in Bayesian analysis is almost exclusively accomplished based on Monte Carlo simulations, the so called Markov Chain Monte Carlo (MCMC) algorithm. Although the MCMC algorithm is intuitive and straightforward to statisticians, it may not be that simple to agricultural scientists, whose main purpose is to implement the method and interpret the results. In this review, we provide the general concept of Bayesian analysis and the MCMC algorithm in a way that can be understood by non-statisticians. We also demonstrate the implementation of the MCMC algorithm using professional software packages such as the MCMC procedure in SAS. Three datasets from agricultural experiments were analyzed to demonstrate the MCMC algorithm.

In order to assure the accuracy of pump test rig and stability of measurement, it would be equipped with flow meter of high precision and calibration system. A volume-weight method for in-situ calibration is brought out to achieve bidirectional calibration. The two way calibration can be done on the pump test rig. According to the design objective, the pump, weight tank, pool, commutator and standard measuring cylinder were calculated and selected. Based on measurement uncertainty method, the system uncertainty consisted of uncertainty of standard measuring cylinder, calculagraph, commutator and calibration sensor of volume method. The calculation formulas of these uncertainties are presented. The total expanded uncertainty of system is 0.136% and the stability of flowrate is 0.0212%. Results from calculation and pressure pulse experiment indicate that the combination of the convert-frequency facility with invariableness’ pool can maintain the pressure stability of test. The volume-weight calibration method, which combined with the weight method and volume method, can assure the accuracy and also reduce the expensive. It could be applied in similar test rigs.