Vortragsnachmittag
am Donnerstag, 12. Juni 2008, 14:00 Uhr
SR 407, Instituts für Statistik,
Steyrergasse 17 / IV,
8010 Graz
14:00 Uhr
Two Examples of Enviromental and Medical Data Processing by Means of Generalized Linear Models
von Dr. Jaroslav Michálek
Department of Mathematics, Brno University of Technology
Abstract
The first application is the statistical analysis of the observation of dust aerosols PM10 from four monitoring stations of the city of Brno from January 1, 1998 till December 30, 2005. By means of autoregressive GLMs with gamma distribution of the response variable and log-link function to the main meteorological factors affecting air pollution are identified at each station. Additionally the influence of seasonality, weekend and working days on air pollution is considered. The suggested model can be used for a prediction of the value of PM10 at a given station using selected factors and their previous values.
The second application is based on a multivariate GLM. The power of one-way MANOVA type tests based on deviance statistics is approximated and calculated. Then the power is used for experimental design to find the genes variants which correspond to the higher level of clinical severity of sepsis states in paediatric patients. The data were obtained from patients aged 0-19 years at the University Hospital Brno, Czech Republic.
15:00 Uhr
Sparse Estimators with Applications to Time Series Forcasting and PM10 Modeling
von Dr. Vítězslav Veselý
Department of Applied Mathematics and Computer Science, Masaryk University Brno
Abstract
The conventional estimators of overparametrized models often produce parameter estimates partially or fully corrupted by round-off errors. The reason is that a great deal of information carried by the parameters is spread over a lot of small numerical values which tend to be more affected by big relative round-off errors than the larger ones. On the other hand sparse estimators concentrate the information into a few most relevant quantities reducing the information loss significantly. In both cases the model fits may look nearly equal, yet when plugging a nonsparse estimate into a parametric function (when computing forecasts etc.), fully inapplicable results may come out.
The Basic Pursuit Algorithm (BPA) [Chen & Donoho & Saunders, 2001] is now very popular for nonharmonic and nonorthogonal sparse spectral representation of signals, the brand-new hit being compressed signal sampling and reconstruction by the so-called Compressed sensing technique [Candès & Romberg & Tao, 2006].
Author's experience with BPA will be demonstrated on two selected problems related to predicting future paths from stationary time series and modeling of PM10 pollution in the city of Brno (CZ). Among others, the results show that sparse least-squares estimates obtained by BPA may significantly outperform the standard (non-sparse) maximum likelihood estimates as to the precision of forecasts from short sample paths.
Research supported by MŠMT (Ministry of Education of the Czech Republic): research contract MSM0021622418
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