Summer School in Industrial Statistics

Program

Part 1. Weighing procedures
Day 1. Modelling a data matrix using weighing procedures

• Criteria for defining weight vectors

• Score and loading plots

• Transformation (causal) vector

Part 2. Linear Regression. Basic methods
Day 2. Standard tools for regression analysis

• Graphs associated with the algorithms

• Analysis of residuals

•  Dimension analysis

 Day 3. Analysis of data for regression analysis

• CovProc Methods in linear regression

• Sensitivity analysis

• Robust methods

 Day 4. Advanced methods in regression analysis

•  Interpretation of latent structures

• Advanced models in linear regression

• Significance testing in linear models of reduced rank

 Part 3. Process Control
Day 5. Analysis of data for process control

• Selection of samples/variables to use

• Use of lagged variables

• Changes in mean levels 

• Changes in the correlation structures

Day 6. Advanced methods for process control

• Mixture of modelling objectives 

• Dynamic version of the H-method

• ‘Good’ response values

 Part 4. Path Modelling
Day 7. Multi-block methods

• Extension of linear regression to three data blocks

• Decomposition of data into data blocks  

• Elementary operations on data blocks

• Graphic analysis across data blocks

 Day 8. Data paths

• Input and output data blocks

• Building data paths

• Modelling data paths and parts of data paths

Part 5. Classification procedures
Day 9. Weighing schemes for classification

• Use of weighing scheme for classification of data into groups

• Visualize differences obtained by classification results

• Performance measures

 Day 10. Weighing schemes for combined classification and regression

• Weighing schemes for double objectives of regression and classification

• Use of tools from regression analysis

 Part 6. Multi-way data analysis
Day 11. One data block

• Weighing schemes for two-way data

• Methods for choosing weight vectors in each mode

• Graphics analysis of loading scores

• Extensions to three way-data Multi-way data structure

• Comparison to Analysis of Variance

Day 12. Regression analysis using multi-way data

• Weighing schemes for regression

• Multi-way X and/or Y

• Standard regression analysis methods

Part 7. Non-linear methods
Day 13. Procedures for finding low-dimensional polynomial surface

• Criteria for finding polynomials in score vectors

• Study of the curvature in data

• Use of tools from regression analysis

Day 14. Gauss-Newton estimation of parameters in a non-linear function

• The Gauss-Newton procedure

• Low rank approximation to the iterative solution

• Use of tools from regression analysis

Day 15. Applications of non-linear methods. Optimal response methods.  

• Optimal response in experimental design

• Use of CovProc methods for models with many variables to improve solution estimates

• Sensitivity analysis

Part 8. Advanced methods

• Prediction variance. Estimates and simulations.

• Fit and model variation. Independence of 'tools' and 'results'.

• Mean squared error. Cross-validation and bootstrapping.

• Forward analysis of data. Model revisions.

• Likelihood ratio procedures. Tests and simplifications.

• Simplification of loading structures. Interpretation and tests.

• Search in data. Variable selection.

• Model validation. On-line models.

• Analysis of residuals. Procedures.