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The uncertainty in meteorological predictions is of interest for applications ranging from economic to recreational to public safety. One common method to estimate uncertainty is by using meteorological ensembles. These ensembles provide an easily quantifiable measure of the uncertainty in the forecast in the form of the ensemble variance. However, ensemble variance may not accurately reflect the actual uncertainty, so any measure of uncertainty derived from the ensemble should be calibrated to provide a more reliable estimate of the actual uncertainty in the forecast. A previous study introduced the linear variance calibration (LVC) as a simple method to determine the ensemble variance to error variance relationship and demonstrated this technique on real ensemble data. The LVC parameters, the slopes, and y intercepts, however, are generally different from the ideal values. This current study uses a stochastic model to examine the LVC in a controlled setting. The stochastic model is capable of simulating underdispersive and overdispersive ensembles as well as perfectly reliable ensembles. Because the underlying relationship is specified, LVC results can be compared to theoretical values of the slope and y intercept. Results indicate that all types of ensembles produce calibration slopes that are smaller than their theoretical values for ensemble sizes less than several hundred members, with corresponding y intercepts greater than their theoretical values. This indicates that all ensembles, even otherwise perfect ensembles, should be calibrated if the ensemble size is less than several hundred. In addition, it is shown that an adjustment factor can be computed for inadequate ensemble size. This adjustment factor is independent of the stochastic model and is applicable to any linear regression of error variance on ensemble variance. When applied to experiments using the stochastic model, the adjustment produces LVC parameters near their theoretical values for all ensemble sizes. Although the adjustment is unnecessary when applying LVC, it allows for a more accurate assessment of the reliability of ensembles, and a fair comparison of the reliability for differently sized ensembles. [ABSTRACT FROM AUTHOR]

Régression auto-modélisatrice de données longitudinales en présence de covariables invariantesdans le temps Les auteurs proposent l'emploi de la régression auto-modélisatrice pour l'analyse de données longitudinales en présence de covariables invariantes dans le temps. Ils modélisent l'évolution de la courbe réponse au moyen d'une régression spline pénalisée et ont recours à un modèle linéaire mixte pour transformer les échelles du temps et de la variable réponse de façon à mieux refléter les variations individuelles. L'ajustement est fait au moyen d'un algorithme itératif facile à implanter à l'aide de logiciels standard pour l'analyse de modèles linéaires et non linéaires mixtes. Leur méthode est illustrée par voie de simulation et dans le cadre d'une étude avec échantillonnage à plusieurs degrés sur la croissance des oisillons au nid chez l'hirondelle bicolore dans laquelle le traitement a été contrǒlé et une covariable a été observée. [ABSTRACT FROM AUTHOR]

Summary Both kriging and non-parametric regression smoothing can model a non-stationary regression function with spatially correlated errors. However comparisons have mainly been based on ordinary kriging and smoothing with uncorrelated errors. Ordinary kriging attributes smoothness of the response to spatial autocorrelation whereas non-parametric regression attributes trends to a smooth regression function. For spatial processes it is reasonable to suppose that the response is due to both trend and autocorrelation. This paper reviews methodology for non-parametric regression with autocorrelated errors which is a natural compromise between the two methods. Re-analysis of the one-dimensional stationary spatial data of Laslett (1994) and a clearly non-stationary time series demonstrates the rather surprising result that for these data, ordinary kriging outperforms more computationally intensive models including both universal kriging and correlated splines for spatial prediction. For estimating the regression function, non-parametric regression provides adaptive estimation, but the autocorrelation must be accounted for in selecting the smoothing parameter. [ABSTRACT FROM AUTHOR]

Discusses the measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression. Influence measures; Examples of conditional versus unconditional cook's distance; Unconditional influence and the model selection procedure; Full model statistics of unconditional influence; Conclusions.

'The statistician knows...that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world.' [ABSTRACT FROM AUTHOR]