An experimentally confirmed statistical model on arm movement.

The purpose of this research work was to develop a methodology to model arm movement in normal subjects and neurologically impaired individuals through the application of a statistical modelling method. Thirteen subjects with Parkinson's disease and 29 normal controls were recruited to participate in an arm motor task. An infrared optoelectronic kinematic movement analysis system was employed to record arm movement at 50 times per second. This study identified the modified extended Freundlich model as one that could be used to describe this task. Results showed that this model fit the data well and that it has a good correspondence between the observed and the predicted data. However, verification of the model showed that the residuals contained a sizeable autocorrelation factor. The Cochrane and Orcutt method was applied to remove this factor, which improved the fit of the model. Results showed that Parkinson's disease subjects had a higher autocorrelation coefficient than the normal subjects for this task. A positive correlation (r(s) = 0.72, p < 0.001) was found between the Langton-Hewer stage and the autocorrelation coefficient of PD subjects. This finding suggests that if autocorrelation is positively correlated with disease progression, clinicians in their clinical practice might use the autocorrelation value as a useful indicator to quantify the progression of a subjects' disease. Significant differences in model parameters were seen between normal and Parkinson's disease subjects. The use of such a model to represent and quantify movement patterns provides an important base for future study.

Multivariate stochastic modelling of grass fluoride and airborne fluorides.

Stochastic modelling was used to investigate the influence of airborne fluorides (in the case of grass fluoride) and meteorological factors on both grass and airborne fluoride levels, taking into consideration lagged dependence. Using rigorous grass sampling methods, there were indications of a negative relationship between volume of rainfall and grass fluoride concentrations, but no apparent relationship between the time which the leaf was visibly wet and grass fluoride levels. No evidence was found that rainfall washed airborne fluoride from the atmosphere or that wind variables influenced grass fluoride. For one particular experimental site, a multivariate stochastic model, which accounts for 81% of the total variation of the grass fluoride series, is developed.

Autocorrelation and univariate time series modelling for grass fluoride and airborne fluoride concentrations.

The dependence of observed fluoride levels-grass, gaseous air and particulate air-on previous levels was investigated in the field situation. Autocorrelation was found in grass fluoride observations, and to a lesser extent was present in both gaseous and particulate airborne fluorides. Univariate time series models were obtained which accounted for 56-66% of total variation in grass fluoride, 31% in gaseous airborne and 26% in particulate airborne fluorides. The large amount of variation unexplained by the models was thought to be due to the influence of environmental and meteorological factors not included in the models, and random variation due to day-to-day and plot-to-plot variation.