420 P. J. Rayner: Optimizing n etworks and modelerror Comparison of the predicted fluxes themselves also yields
only small differences between the two inverse calculations, especially if one normalizes the differences by the total un- certainty. This can be seen visually by considering the over- lap of the error bars for each region. In most cases the er- ror bars for each network include the central estimate for the other network. We should note that since the error bar rep- resents one standard deviation we should expect some esti- mates to differ at this level. There are four regions of appar- ently significant difference: the Southern Ocean, Australa- sia, the West Pacific and the Tropical Indian Ocean. Most of these are due to removal of specific stations between the TransCom 3 and total-76 networks, e.g. the anomalous Dar- win station. Sensitivity of the TransCom 3 inversion to this station has previously been noted by Law et al. (2003). One change is due to more systematic influences. The reduction of the Southern Ocean sink, already noted by Gurney et al. (2002), is strengthened in our optimal network. This occurs despite the great reduction in station density in this region. Roy et al. (2003) have noted that the reduction in Southern Ocean sink (relative to the prior) occurs even when almost all atmospheric observations are removed from the high south- ern latitudes. They conclude that the reduction in Southern Ocean sink is required to match large-scale atmospheric con- centration gradients rather than particular local observations. The result of the present study suggests this result is also ro- bust to the choice of atmospheric transport model.
We applying this method to a sample of 10000 quotes on calls on TOYS'R US, and document the behavior of several competing models nesting the B-S. The competing extended models are justied as expansions of a model unknown or too costly to implement. We formulate the error in relative terms (logarithms models) and in dollar terms (levels models). We show that there is indeed evidence of Black Scholes mispricing and by some criteria, the extended models dominate the B-S within sample. They reduce root mean squared errors of pricing and residuals. The im- provement is not limitless as models with12 parameters show severe degradation in performance due to the increase in parameter uncertainty. The extended models have dierent hedging and pricing implications than the B-S. We show that the failure to include modelerror in specica- tion tests results in very severe biases toward rejection. The interquartile range of a predictive distribution which in fact covers the true value 50% of the time, would be wrongly believed to cover the true value 2% of the time, thus leading to a rejection of the model.
of this last term modifies the choice of observing sites, leading to larger networks than would be chosen under the traditional estimated variance metric. Model-model dif- ferences behave like sub-grid heterogeneity and optimal networks try to average over some of this. The optimization does not, however, necessarily reject apparently di fficult sites to model. Although the results are so conditioned on the experimental set-up that
3.4 Spatial structure of the observation error
The spatial footprint of the observation error without time lag is shown by the distance correlogram in Fig. 3. Note that here we use the posterior diagnosis based on Eq. (3), which provides a better numerical stability than the prior diagno- sis of Eq. (1). Each point in Fig. 3 represents a pair of sites that have at least one year of data in common. The all-site median is calculated using 400-km bins. It shows a declining spatial structure of the correlation within the first 500 km, where it remains larger than 0.4, while it converges toward zero for larger lag distances. Since all sites present the same dominant PFT and since the spatial correlations of the mea- surement error is considered as negligible, we suggest that the inferred spatial structure of the observation error derives from the modelerror and that the correlation decline origi- nates from the meteorology. In the next section, this spatial structure is approximated by an exponential decay, with an e- folding length of 500 km in the flux space (black dotted line in Fig. 3).
3.2.4. Initiation and execution of the intended action. The action is executed. In the example, the person picks up the book and gives it back to the library.
3.2.5. The outcome evaluation. The action outcome is here evaluated in order to check whether the action has been executed as intended. The existence of this last phase is also one of the PM issues that has motivated the attempt to link error detection with PM. Ellis (1996) justiﬁes it with the necessity of some form of outcome record in order to avoid the repetition of a satisﬁed intention or to ensure the success of a postponed or failed delayed intention (i.e. avoiding the omission). One may also think that it is a key phase in which the subject may compare the actual outcome with the expected one and thus detect at least a deviation. However, the objective of this study is to go one step further by admitting that this phase may actually last quite a long time, until the actual resumption of the intention, i.e. until the individual feels, even subjectively, that his/her intended goal has been achieved.
The second type of residual-based estimation for mixed finite element discretizations gives bounds on the error in the H(div; Ω ) × L 2 (Ω )-norm. Such an estimate was first introduced by Alonso who in  obtained an upper bound of the
error only on the dual variable in the L 2 (Ω )-norm. This estimate was generalized by Carstensen who in  obtained
upper and lower bounds on the error in the natural norm for the primal and dual variables in the 2D case, by using a Helmholtz-like decomposition of vectors of H(div; Ω ). Hoppe and Wohlmuth in  gave a comparison of such estimates with hierarchical ones and estimates using resolution of local problems. In Nicaise and Creus´e  one can find a generalization to the anisotropic 2D and 3D cases of such estimates. The error estimation that we use here is based on that of  and of .
Inference for the Generalization Error *
Claude Nadeau H , Yoshua Bengio I
Résumé / Abstract
Nous considérons l'estimation par validation croisée de l'erreur de généralisation. Nous effectuons une étude théorique de la variance de ect estimateur en tenant compte de la variabilité due au choix des ensembles d'entraînement et des exemples de test. Cela nous permet de proposer deux nouveaux estimateurs de cette variance. Nous montrons, via des simulations, que ces nouvelles statistiques performent bien par rapport aux statistiques considérées dans Dietterich (1998). En particulier, ces nouvelles statistiques se démarquent des autres présentement utilisées par le fait qu'elles mènent à des tests d'hypothèses qui sont puissants sans avoir tendance à être trop libéraux.
The existence of such an error structure built from the parametric model allows to prop- agate the accuracy through calculations performed with the parameter thanks to a coherent specific differential calculus (property 1 of Γ). Moreover error calculus provides a natural frame- work concerning the study of non-injective mapping. A possible extension will be to generalize such an experimental protocol when J is singular and also to explore more precisely the con- nections between Dirichlet forms and asymptotic statistics. Finally, we wonder whether the semi-parametric and non-parametric estimation theories (see ) could lay the foundation of an infinite dimensional identification in order to get Γ on the Wiener space, using a direct functional reasoning instead of a component per component argument as above.
From a practical standpoint, our results suggest that neurophysiological measures may exhibit complex patterns that cannot be directly associated with mental workload. Future work should further investigate how the latter issue could be resolved. For instance, one option would be to calibrate a neurophysiological model of mental workload with performance at a secondary task in a simulated ROV environment. Such a calibration could be performed by machine learning algorithms in order to best capture potential non-linear relations. If successful, this model could later be used to predict mental workload in a real ROV situation.
models in simplified form by setting model coefficients to unity).
In stereovision and photogrammetry, finding elevation of a terrain object consists in 1-D search of the object image on the left(right) image along the corresponding epipolar line at the right(left) image. The epipolar line on one stereo pair image is formed by projecting all 3-D points having the same projection in the other stereo pair image . The object displacement (with respect to a reference elevation, typically Z = 0) along the epipolar line is called disparity D, which is related to elevation as Z = D(r/B), where B denotes the base-to-height ratio and r is an instrument spatial resolution . In Fig. 3, elevation Z = 0 corresponds to point A and line A–B is the corresponding epipolar line. Object E has higher elevation (and disparity) than object C and is placed farer from point A along the epipolar line. Position of the reference point A and orien- tation of the epipolar line are determined from the instrument calibration data and are subject to errors. The deviation of the estimated epipolar line from the true one is called epipolar line error . It has been shown that camera errors propagate to epipolar line error in a way dependent on disparity . As a result, SD of distance between points on the true and estimated epipolar lines is increasing with disparity: in average A − A < C − C < D − D < B − B . The object
CF-EKF RMS EKF/ADHOC 3σ
Fig. 4. Kinematics states error results.
Kalman filter statistical divergence (notice that RMS di- vergence is also observed). This precludes filter validation and usage. Suboptimal inflation of process noise could bring the filter back to statistical convergence, but the tuning strategy is often a blind and painful trial-and-error method which often yield poor overall performance. Simi- lar performance patterns are observed in misalignment and accelerometer error curves.
“In certain circumstances a man cannot make a mistake (…). If Moore were to pronounce the opposite of those propositions which he declares certain [‘I have two hands’…], we should not just not share his opinion: we should regard him as demented” (Wittgenstein, 1969-75: §155).
It would therefore be impossible to attribute such words or behavior to an error or a difference in perception. Why? On one hand, because one cannot make a mistake when there is no point in speaking of knowledge, or when doubt does not seem reasonable. On the other hand, because when we are faced with someone who extends doubt beyond reason, and attempts to prove that his doubt is justified, we will refuse – in ordinary circumstances – to accept what he presents as evidence.
The existence of such an error structure built from the parametric model allows to propagate the accuracy through calculations performed with the parameter thanks to a coherent specific differential calculus (property 1) of Γ). Moreover error calculus provides a natural framework concerning the study of non-injective mapping. A possible extension will be to generalize such an experimental protocol when J is singular and also to explore more precisely the connections between Dirichlet forms and asymptotic statistics. Finally, we wonder whether the semi-parametric and non-parametric estimation theories (see ) could lay the foundation of an infinite dimensional identification in order to get Γ on the Wiener space, using a direct functional reasoning instead of a component per component argument as above. References
2 for each relative performance measure.
The analysis employed a simple errormodel based on Gaussian statistics, as previously described. The statistical behavior of real positioning systems is more complex and highly variable between system type and conguration. Pose error is also dicult to character- ize and quantify in practice. Furthermore, each pose error eect has been studied in isolation. Multiple types of pose error in combination will interact in a non-linear manner. Nevertheless, while its limitations are acknowledged, the pose errormodel employed here should form a suitable basis for understanding pose er- ror eects and developing countermeasures.
We have seen that the generic covariance definition is based on S 2 error (Section 2). Furthermore, the
projection function p of the camera propagates this error to image error such that the uncertainty ellipses of image error are distortion ellipses of p (Section 3.1). Figure 2 shows these ellipses for our equiangular cata- dioptric camera (on the right) and two other cases: a perspective projection into a cube face (on the left) and an equirectangular projection (in the mid- dle). The equirectangular projection maps 3D point to its spherical coordinates (ϕ, θ) and is often used for panoramic imaging (Figure 2 only shows a half part of the view field). We see that the propagated image error depends on p and is not “standard” (isotropic and uniform in the whole image), especially for cam- eras with wide view fields.
An in-depth analysis of the sources of mass balance error in sequential iterative surface-subsurface ﬂow mod- els was performed. The different sources were investigated by isolating subsurface, surface, and coupling errors and by using a saturation area index and a coupling degree index to track these errors. The analyses were performed for two synthetic test cases and a complex drainage basin in northern Italy simulated by the CATHY model. A modiﬁed time step control scheme was introduced to improve model performance by con- sidering a normalized variation of the coupling index. The node-to-cell interpolation of the exchange ﬂuxes between the surface and subsurface grids was also found to be critical. A detailed analysis of the spatial distri- bution of surface error on each cell revealed that the main source of surface error arises in cells that are in transition between saturated and unsaturated state, rather than along the drainage network where the area is normally saturated. A new interpolation algorithm was therefore developed that considers the availability of water on surface cells and thus improves the description of subsurface-surface interaction. This enhancement resulted in signiﬁcantly reduced surface mass balance error, in particular during recession phases.