The identification of changes in observational data relating to the climate change hypothesis remains a topic of paramount importance. In particular, scientifically sound and rigorous methods for detecting changes are urgently needed. In this paper, we develop a Bayesian approach to nonparametric function estimation. The method is applied to blossom time series of Prunus avium L., Galanthus nivalis L. and Tilia platyphyllos SCOP. The functional behavior of these series is represented by three different models: the constant model, the linear model and the one change point model. The one change point model turns out to be the preferred one in all three data sets with considerable discrimination of the other alternatives. In addition to the functional behavior, rates of change in terms of days per year were also calculated. We obtain also uncertainty margins for both function estimates and rates of change. Our results provide a quantitative representation of what was previously inferred from the same data by less involved methods.

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This report describes the Bayesian approach to probability theory with emphasis on the application to the evaluation of experimental data. A brief summary of Bayesian principles is given, with a discussion of concepts, terminology and pitfalls. The step from Bayesian principles to data processing involves major numerical efforts. We address the presently employed procedures of numerical integration, which are mainly based on the Monte Carlo method. The case studies include examples from electron spectroscopies, plasma physics, ion beam analysis and mass spectrometry. Bayesian solutions to the ubiquitous problem of spectrum restoration are presented and advantages and limitations are discussed. Parameter estimation within the Bayesian framework is shown to allow for the incorporation of expert knowledge which in turn allows the treatment of under-determined problems which are inaccessible by the traditional maximum likelihood method. A unique and extremely valuable feature of Bayesian theory is the model comparison option. Bayesian model comparison rests on Ockham's razor which limits the complexity of a model to the amount necessary to explain the data without fitting noise. Finally we deal with the treatment of inconsistent data. They arise frequently in experimental work either from incorrect estimation of the errors associated with a measurement or alternatively from distortions of the measurement signal by some unrecognized spurious source. Bayesian data analysis sometimes meets with spectacular success. However, the approach cannot do wonders, but it does result in optimal robust inferences on the basis of all available and explicitly declared information.

The impact of climate change on the advancement of plant phenological events has been heavily studied in the last decade. Although the majority of spring plant phenological events have been trending earlier, this is not universally true. Recent work has suggested that species that are not advancing in their spring phenological behavior are responding more to lack of winter chill than increased spring heat. One way to test this hypothesis is by evaluating the behavior of a species known to have a moderate to high chilling requirement and examining how it is responding to increased warming. This study used a 60-year data set for timing of leaf-out and male flowering of walnut (Juglans regia) cultivar 'Payne' to examine this issue. The spring phenological behavior of 'Payne' walnut differed depending on bud type. The vegetative buds, which have a higher chilling requirement, trended toward earlier leaf-out until about 1994, when they shifted to later leaf-out. The date of male bud pollen shedding advanced over the course of the whole record. Our findings suggest that many species which have exhibited earlier bud break are responding to warmer spring temperatures, but may shift into responding more to winter temperatures (lack of adequate chilling) as warming continues.

Bayesian probability theory is employed to derive robust, outlier tolerant methods for the estimation of a quantity and the determination of the uncertainty associated with this estimation given a set of data. The procedure is applied to the estimate of the Newtonian constant of gravitation G yielding This value is in good agreement with the recently published value of the 2002 CODATA adjustment but offers a four-fold reduced, rigorously calculated uncertainty. The uncertainty reflects—unlike results from the conventional least squares analysis—the quoted uncertainties of the data as well as the data scatter.