Observation is a phenomenal instance of noticing or perceiving in the natural sciences and the acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. The term may also refer to any data collected during the scientific activity. Observations can be qualitative, that is, only the absence or presence of a property is noted, or quantitative if a numerical value is attached to the observed phenomenon by counting or measuring. Science The scientific method requires observations of natural phenomena to formulate and test hypotheses. It consists of the following steps:

Ask a question about a natural phenomenon

Make observations of the phenomenon

Formulate a hypothesis that tentatively answers the question

Predict logical, observable consequences of the hypothesis that have not yet been investigated

Test the hypoth

A global model study of ozone enhancement during the August 2003 heat wave in Europe

The European summer of 2003 was characterised by intense heat, prolonged isolation and suppressed ventilation of the boundary layer which, combined with large anthropogenic emissions and strong fires, resulted in a build up of an unprecedentedly high and long-lasting photochemical smog over large parts of the continent. In this work, a global chemistry and transport model GEOS-Chern is compared with surface O-3 concentrations observed in 2003 in order to examine the extent to which the model is capable of reproducing such an extreme event. The GEOS-Chem reproduces the temporal variation of O-3 at the Jungfraujoch mountain site, Switzerland, including the enhanced concentrations associated with the August 2003 heat wave (r = 0.84). The spatial distribution of the enhanced surface O-3 over Spain, France, Germany and Italy is also captured to some extent (r = 0.63), although the largest concentrations appear to be located over the Italian Peninsula in the model rather than over Central Europe as suggested by the surface O-3 observations. In general, the observed differences between the European averaged O-3 concentrations in the summer of 2003 to those in 2004 are larger in the observations than in the model, as the model reproduces relatively well the enhanced levels in 2003 but overestimates those observed in 2004. Preliminary contributions of various sources to the O-3 surface concentrations over Europe during the heat wave indicate that anthropogenic emissions from Europe contribute the most to the O-3 build up near the surface (40 to 50%, i.e. 30 ppb). The contribution from anthropogenic emissions from the other major source regions of the northern hemisphere, in particular North America, tends to be smaller than those of other years. The model indicates that the large fires that occurred in that year contributed up to 5% (3 ppb) to surface O-3 in close proximity to the fire regions and less elsewhere in Europe. Biogenic volatile organic compounds (VOCs) emitted by grass and forest areas contributed up to 10% (5-6 ppb) of surface O-3 over France, Germany and northern Italy, which represents a contribution that is twice as large than that found in 2004. These results in terms of contributions from various sources, particularly biogenic emissions, should be seen as preliminary, as the response of vegetation to such extreme events may not be well represented in the model.

2007

Robust Parameter Estimation for the Ornstein-Uhlenbeck Process

Sonja Rieder

In this thesis, we treat robust estimation for the parameters of the Ornstein–Uhlenbeck process, which are the mean, the variance, and the friction. We start by considering classical maximum likelihood estimation. For the simulation study, where we also investigate the choice of the time lag, we use the method of moment (MoM) estimator as initial estimator for the friction parameter of the maximum likelihood estimator (MLE). However, in several aspects the MLE is not robust. For robustification, we first derive elementary M-estimates by extending the method of M-estimation from Huber (1981). We use an intuitively robustified MoM estimate as initial estimate and compare by means of simulation the M-estimate with the MLE. This approach is, however, only ad-hoc since Huber’s minimum Fisher information and minimax asymptotic variance theory remains incomplete for simultaneous location and scale, and does not cover more general models (as for example the Ornstein–Uhlenbeck process). A more general robustness concept due to Kohl et al. (2010), Rieder (1994), and Staab (1984) is based on local asymptotic normality (LAN), asymptotically linear (AL) estimates, and shrinking neighborhoods. We then apply this concept to the Ornstein–Uhlenbeck process. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. For two kind of neighborhoods (average and average square neighborhoods) we obtain optimally robust ICs. In case of average neighborhoods, their graph exhibits surprising, redescending behavior. For average square neighborhoods the graph is between the one of the elementary M-estimates and the MLE. Finally, we discuss the estimator construction, that is, the problem of constructing an estimator from the family of optimal ICs. We carry out in our context the One-Step construction dating back to LeCam and use both an intuitively robustified MoM estimate and the elementary M-estimate as initial estimate. This results in optimally AL estimates (for average and average square neighborhoods). By means of simulation we then compare the different estimators: MLE, elementary M-estimates, and optimally AL estimates. In addition, we give an application to electricity prices.

EPFL2012

Robust parameter estimation for the Ornstein-Uhlenbeck process

Sonja Rieder

In this paper, we derive elementary M- and optimally robust asymptotic linear (AL)-estimates for the parameters of an Ornstein-Uhlenbeck process. Simulation and estimation of the process are already well-studied, see Iacus (Simulation and inference for stochastic differential equations. Springer, New York, 2008). However, in order to protect against outliers and deviations from the ideal law the formulation of suitable neighborhood models and a corresponding robustification of the estimators are necessary. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. In a first step, we extend the method of M-estimation from Huber (Robust statistics. Wiley, New York, 1981). In a second step, we apply the general theory based on local asymptotic normality, AL estimates, and shrinking neighborhoods due to Kohl et al. (Stat Methods Appl 19:333-354, 2010), Rieder (Robust asymptotic statistics. Springer, New York, 1994), Rieder (2003), and Staab (1984). This leads to optimally robust ICs whose graph exhibits surprising behavior. In the end, we discuss the estimator construction, i.e. the problem of constructing an estimator from the family of optimal ICs. Therefore we carry out in our context the One-Step construction dating back to LeCam (Asymptotic methods in statistical decision theory. Springer, New York, 1969) and compare it by means of simulations with MLE and M-estimator.

Springer-Verlag2012

A global model study of ozone enhancement during the August 2003 heat wave in Europe

2007

Robust Parameter Estimation for the Ornstein-Uhlenbeck Process

Sonja Rieder

EPFL2012