scholarly journals Bayesian Modelling by Method of Normal Regression: A Case of Modelling Gluten Content in terms of Protein Content in a Variety of Wheat

2015 ◽  
Vol 19 (1) ◽  
pp. 121-128
Author(s):  
Ram Prasad Khatiwada
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Protein Content ◽  
Simulated Data ◽  
Bayesian Modelling ◽  
Simple Linear Regression ◽  
Normal Regression ◽  
Gluten Content ◽  
Regression Parameters ◽  
Credible Sets

This article is about the Bayesian modelling of the parameters of a simple linear regression with normal errors. It studies the use of non-informative normal priors to the regression parameters. It has an application on modelling gluten content in terms of protein content of a variety of wheat. The exact estimations of credible sets of the regression parameters obtained from real and simulated data by using MCMC. The posterior estimates of the gluten content in terms of protein content are better in this regression model with normal non-informative prior.Journal of Institute of Science and Technology, 2014, 19(1): 121-128

scholarly journals Credibility in the Regression case Revisited (A Late Tribute to Charles A. Hachemeister)

1997 ◽  
Vol 27 (1) ◽  
pp. 83-98 ◽  
Author(s):  
H. Bühlmann ◽  
A. Gisler
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Regression Line ◽  
Good Choice ◽  
Design Matrix ◽  
Simple Linear Regression ◽  
One Dimensional ◽  
Regression Parameters ◽  
Definition Of ◽  
General Regression

AbstractMany authors have observed that Hachemeisters Regression Model for Credibility – if applied to simple linear regression – leads to unsatisfactory credibility matrices: they typically ‘mix up’ the regression parameters and in particular lead to regression lines that seem ‘out of range’ compared with both individual and collective regression lines. We propose to amend these shortcomings by an appropriate definition of the regression parameters:–intercept–slopeContrary to standard practice the intercept should however not be defined as the value at time zero but as the value of the regression line at the barycenter of time. With these definitions regression parameters which are uncorrected in the collective can be estimated separately by standard one dimensional credibility techniques.A similar convenient reparametrization can also be achieved in the general regression case. The good choice for the regression parameters is such as to turn the design matrix into an array with orthogonal columns.

Online estimation of VFA, alkalinity and bicarbonate concentrations by electrical conductivity measurement during anaerobic fermentation

2012 ◽  
Vol 65 (7) ◽  
pp. 1281-1289 ◽  
Author(s):  
Cesar-Arturo Aceves-Lara ◽  
Eric Latrille ◽  
T. Conte ◽  
Jean-Philippe Steyer
Keyword(s):  
Electrical Conductivity ◽  
Hydrogen Production ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Anaerobic Fermentation ◽  
Simple Linear Regression ◽  
Conductivity Measurements ◽  
Bicarbonate Concentration ◽  
On Line

This paper describes the use of electrical conductivity for measurement of volatile fatty acids (VFA), alkalinity and bicarbonate concentrations, during the anaerobic fermentation process. Two anaerobic continuous processes were studied: the first was a laboratory reactor for hydrogen production from molasses and the second was a pilot process for anaerobic digestion (AD) of vinasses producing methane. In the hydrogen production process, the total VFA concentration, but not bicarbonate concentration, was well estimated from the on-line electrical conductivity measurements with a simple linear regression model. In the methane production process, the bicarbonate concentration and the VFA concentration were well estimated from the simultaneous on-line measurements of pH and electrical conductivity by means of non-linear regression with neural network models. Moreover, the total alkalinity concentration was well estimated from electrical conductivity measurements with a simple linear regression model. This demonstrates the use of electrical conductivity for monitoring the AD processes.

scholarly journals New Algorithms for L1 Norm Regression

2019 ◽  
Vol 1 (1) ◽  
pp. 1-18
Author(s):  
Bijan Bidabad
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Simple Linear Regression ◽  
L1 Norm ◽  
Median Problem ◽  
Regression Parameters ◽  
Multiple Regression Models ◽  
Weighted Median ◽  
Weighted Median Problem ◽  
New Algorithms

In this paper, we propose four algorithms for L1 norm computation of regression parameters, where two of them are more efficient for simple and multiple regression models.  However, we start with restricted simple linear regression and corresponding derivation and computation of the weighted median problem. In this respect, a computing function is coded.  With discussion on the m parameters model, we continue to expand the algorithm to include unrestricted simple linear regression, and two crude and efficient algorithms are proposed. The procedures are then generalized to the m parameters model by presenting two new algorithms, where the algorithm 4 is selected as more efficient. Various properties of these algorithms are discussed.

scholarly journals PM2.5 Concentration Estimation Based on Image Processing Schemes and Simple Linear Regression

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2423 ◽  
Author(s):  
Jiun-Jian Liaw ◽  
Yung-Fa Huang ◽  
Cheng-Hsiung Hsieh ◽  
Dung-Ching Lin ◽  
Chin-Hsiang Luo
Keyword(s):  
Image Processing ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Simple Linear Regression ◽  
Simple Linear Regression Model ◽  
Concentration Estimation ◽  
Single Feature ◽  
The Difference ◽  
Pm2.5 Concentration

Fine aerosols with a diameter of less than 2.5 microns (PM2.5) have a significant negative impact on human health. However, their measurement devices or instruments are usually expensive and complicated operations are required, so a simple and effective way for measuring the PM2.5 concentration is needed. To relieve this problem, this paper attempts to provide an easy alternative approach to PM2.5 concentration estimation. The proposed approach is based on image processing schemes and a simple linear regression model. It uses images with a high and low PM2.5 concentration to obtain the difference between these images. The difference is applied to find the region with the greatest impact. The approach is described in two stages. First, a series of image processing schemes are employed to automatically select the region of interest (RoI) for PM2.5 concentration estimation. Through the selected RoI, a single feature is obtained. Second, by employing the single feature, a simple linear regression model is used and applied to PM2.5 concentration estimation. The proposed approach is verified by the real-world open data released by Taiwan’s government. The proposed scheme is not expected to replace component analysis using physical or chemical techniques. We have tried to provide a cheaper and easier way to conduct PM2.5 estimation with an acceptable performance more efficiently. To achieve this, further work will be conducted and is summarized at the end of this paper.

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