Data Analysis - statistical evaluation of process data and environmental investigations

Robust methods

The development of statistical data analysis has run in parallel with the development of modern science and technology. Many calculations are nowadays easy to accomplish with a personal computer, but it is also important to remember the assumptions behind. One assumption is often that the errors should be independently and normally distributed, but it is common with outliers that disturb the analysis. Similarly, it is almost a rule that process disturbances and contamination levels in the environment does not follow the normal frequency distribution. These kinds of obstacles can be avoided with robust methods and resampling (bootstrapping), permitting that these data are evaluated without further pre-processing.

Example from regression analysis with the ordinary least squares method (LS) respectively with a robust method (LMS) that is not affected by the outlying object.

Multivariate data analysis

Most problems in the world around us demand that we consider the whole picture, but in a way that we can comprehend. Multivariate data analysis let us simultaneously evaluate the correlation pattern between hundreds, or even thousands, of variables. The results from these calculations can often be visualised in a few pictures (diagrams). By examining these mathematical windows we can then interpret reality and come to important conclusions.

Principal component analysis is a very useful multivariate
technique.
Example of a "mathematical window", prepared by principal component analysis (PCA). In this case showing differences and similarities in structure between the 209 possible congeners of the persistent environmental pollutant PCB.

Literature

Davies, O. L. and P. L. Goldsmith (1986). Statistical methods in research and production. London, Longman.
Draper, N. R. and H. Smith (1998). Applied regression analysis. New York, Wiley.
Efron, B. and R. Tibshirani (1993). An introduction to the bootstrap. New York, Chapman & Hall/CRC.
Gilbert, R. O. (1987). Statistical methods for environmental pollution monitoring. New York, Van Nostrand Reinhold Co.
Jackson, J. E. (1991). A user's guide to principal components. New York, Wiley.
Martens, H. and T. Næs (1989). Multivariate calibration. Chichester, Wiley.
Rousseeuw, P. J. and A. M. Leroy (1987). Robust regression and outlier detection. New York, Wiley.

My toolbox

There are many techniques for data analysis. My "toolbox" contains both standard statistical software and the latest algorithms from the research frontier.

You will find many examples of applications in the lists of articles, lectures and public reports. I am always interested in finding new clients and I will be happy to take assignments within this field of expertise. Please review my resume and my Ph.D. thesis with applications in environmental science.


Swedish homepage	© Tomas Öberg Konsult AB Site Map Contact

Home : Data Analysis