Bayesian Variable Selection for Mixture Process Variable Design Experiment

This paper discussed Bayesian variable selection methods for models from split-plot mixture designs using samples from Metropolis-Hastings within the Gibbs sampling algorithm. Bayesian variable selection is easy to implement due to the improvement in computing via MCMC sampling. We described the Bayesian methodology by introducing the Bayesian framework, and explaining Markov Chain Monte Carlo (MCMC) sampling. The Metropolis-Hastings within Gibbs sampling was used to draw dependent samples from the full conditional distributions which were explained. In mixture experiments with process variables, the response depends not only on the proportions of the mixture components but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomisation force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first-factor group is set and combinations of the other factors are run. We discussed the computational algorithm for the Stochastic Search Variable Selection (SSVS) in linear mixed models. We extended the computational algorithm of SSVS to fit models from split-plot mixture design by introducing the algorithm of the Stochastic Search Variable Selection for Split-plot Design (SSVS-SPD). The motivation of this extension is that we have two different levels of the experimental units, one for the whole plots and the other for subplots in the split-plot mixture design.

The pathway and fate of the heavy metal mixture in Xiamen marine experiment enclosures

The pathway and fate of heavy metals were studied in 10m3 enclosures at Xiamen Bay in 1985. The dissolved metals added are removed rather quickly during the first days, and their half-removal times ( t1/2) (d) are as follows: Pb 5. 4-5. 8, Hg 6. 7-14, Zn 11-22, Cu 16 - 29, and Cd 30-89. Zinc is transferred biologically to particles during phytoplankton bloom. The main Fate of added metals after 27 days is as follows; over 80% Cd and 60% Cu remain in dissolved phase, more than 60% Pb and 50% Hg transfer to settling settlement, while Zn is equally distributed in dissolved phase and settling settlement. The wall uptake is less than 2% of the total metals added. Organic materials play an essential role in the partition and the transfer of heavy metals in water column. Terrigenous and autochthonous particles show different affinities to different metals. Most heavy metals associate weakly with zooplankton. The Binding of Cd, Pb, Zn and Cu to the particles shows distinctive features related to the diagenetic alteration.

Discovering optimal weights in weighted‑scoring stock‑picking models: a mixture design approach

Certain literature that constructs a multifactor stock selection model adopted a weighted-scoring approach despite its three shortcomings.First,it cannot effectively identify the connection between the weights of stock-picking concepts and portfolio performances.Second,it cannot provide stock-picking concepts’optimal combination of weights.Third,it cannot meet various investor preferences.Thus,this study employs a mixture experimental design to determine the weights of stock-picking concepts,collect portfolio performance data,and construct performance prediction models based on the weights of stock-picking concepts.Furthermore,these performance prediction models and optimization techniques are employed to discover stock-picking concepts’optimal combination of weights that meet investor preferences.The samples consist of stocks listed on the Taiwan stock market.The modeling and testing periods were 1997–2008 and 2009–2015,respectively.Empirical evidence showed(1)that our methodology is robust in predicting performance accurately,(2)that it can identify significant interactions between stock-picking concepts’weights,and(3)that which their optimal combination should be.This combination of weights can form stock portfolios with the best performances that can meet investor preferences.Thus,our methodology can fill the three drawbacks of the classical weighted-scoring approach.

Formula Optimization of Wheat Germ Solid Beverage

[Objectives]This study was conducted to develop a health-care product with smooth taste and high nutrition.[Methods]With natural wheat germ powder as the main raw material and maltodextrin,white sugar,compound stabilizer and other materials as auxiliary materials,the formula of wheat germ solid beverage was optimized using sensory evaluation value as an index,through the mixture experiment method and fuzzy mathematical analysis.[Results]The optimal formula of wheat germ solid beverage was:sugar 11.51%,maltodextrin 37.89%,wheat germ powder 50%,compound stabilizer 0.6%(arabic gum 0.3%,xanthan gum 0.3%),soya bean lecithin 0.2%,ethyl maltol 0.002%,and vanillin 0.003%.[Conclusions]This study provides a theoretical basis for expanding the market-oriented production and application of wheat germ.

Effects of Different Material Ratios on the Dissolution of Tongmai Pills

[Objectives]To study the effects of different material ratios on the dissolution of Tongmai pills.[Methods]Based on mixture uniform experiment design,the fiber,starch and grease-resin materials in Tongmai pills were proportioned.The contents of strychnine,brucine,paeoniflorin,calycosin,ferulic acid,hesperidin and salvianolic acid B in the solution were determined by HPLC,and the content of total flavonoids was determined by ultraviolet spectrophotometry.The weight coefficient of index components was determined by analytic hierarchy process,and the SAS software was used to optimize the dissolution model and calculate the dissolution parameter T40.MATLAB was used to establish a mathematical model and realize the data visualization between material ratio and dissolution parameter T40.[Results]The mathematical model between material ratio and dissolution parameter was T40=8.93-5.31X1-5.83X2+17.67X1X3(X1,X2,X3 are fiber,starch and grease-resin materials respectively,r2=0.9706,P=0.01,RMSE=0.5696).[Conclusions]Fiber can effectively promote the dissolution(P<0.05).Starch can promote the dissolution,but the effect is not obvious(P=0.05).The interaction between fiber and grease-resin can inhibit the dissolution,but was not significant(P=0.07).