Industrial Statistics 

Summer school

A summer school is being planned at Danish Technical University, Denmark. The summer school is over three weeks and scheduled as last week of July and the first two weeks of August. All methods presented at the summer school have proven their success at industry. In industry the focus is on predictions. When modelling industrial data the results depend on two parts, the data used and the performance of data. In this course participants are trained in building up the mathematical model in steps, where at each step the mathematical model is optimized with respect to prediction. They are trained in getting a good prediction model by optimizing at each step the balance of improving the fit and the associated precision.
            The course consists of eight parts. They are briefly described here.

Part 1. Weighing procedures. 1 day.
Procedures are shown how we can define weighing schemes that are designed to model a data matrix. Score, loading and transformation (causal) plots are studied in order to evaluate the task at each step.

Part 2. Linear Regression. Basic methods. 3 days
The application of the basic methods for linear regression consists of three parts.

• Use of graphic tools from the first day for evaluation of the results of the regression analysis. Different methods for analysing residuals and evaluating the dimension of the model. The regression method used will be PLS regression.
• Use of CovProc methods to identify the part of data that should be used. Sensitivity analysis in low rank regression models.
• Interpretation of latent structure in linear regression. Significance testing in linear models of low rank. Covariance regression models.

Part 3. Process Control. 2 days
The course consists of two parts.

• What part of the available data should be used in the modelling task? How to use lagged variables. Study the changes in the mean level and the covariance structure.
• Mixture of modelling objective (stable regression coefficients and good fit). Dynamic version of the H-method (good predictions for recent samples). ‘Good’ response values.

Part 4. Path Modelling. 2 days
The program consists of two parts.

• How should we extend linear regression, X->Y, two three data blocks, X->Y->Z. Elementary operation on data blocks. Graphics across data blocks.
• Input and output data blocks. Building and analysing data paths.

Part 5. Classification procedures. 2 days
The program has two emphases.

• Use the weighing schemes to identify a good model for classification or classification and regression.
• Describe the class differences as found by the model. Visualise differences among groups of data. Report the performance of the model.

Part 6. Multi-way data analysis. 2 days
This part consists of two themes.

• Extension of the weighing schemes from two way data to three ways data. The use of score and loading plots to analyse the variation in data. Comparison to analysis of variance for indexed data.
• Extension to regression analysis, where X or Y or both can be multi-way data.

Part 7. Non-linear methods. 3 days
It consists of three parts.

• Linear regression can be viewed as finding a plane given by score variables and carry out regression on these score variables. This procedure is extended to finding a polynomial surface in score variables.
• The use of low rank solutions in estimation of parameters in non-linear models.
• Application of these methods to estimation of optimal response models in experimental design

Part 8. Advanced methods
The basic issues in mathematical modelling of data are collected together. This material is referred to during the course.

For a more detailed program, see here.
    Participation in the summer school presupposes some knowledge in statistics and regression analysis. Furthermore it is designed for people working with data analysis in their every day job.
    The course is based on cases. On each course day there are four hours lectures and four hours hands-on exercises. Invited teachers at the summer school have practical experience with the type of analysis studied. Participants receive a cd with all the programs that have been used at the summer school, which can be run on the participants computer. During the course it will be possible to compare the analysis with similar results from the SAS package.

     For further information you can contact: ah@ipl.dtu.dk