100 G. Busca et al. Given any two estimated models, the model with the lower value of BIC is the one to be preferred. The BIC generally depends on the size of n and relative magnitude of n and k. It is important to keep in mind that the BIC can be used to compare models based on different probability distributions [4]. 10.2.3 Mahalanobis Distance The Mahalanobis distance is the feature that is used in this paper to estimate the supposed unusual behaviour of the tested structure [2]. The Mahalanobis distance is a measurement of the distance between a point P and a distribution D. It is a multi-dimensional generalization of the idea of measuring how many standard deviations P is away from the mean of D. It has many advantages such as: it takes into account the fact that the variances in each direction are different, it considers the covariance between variables, and it becomes the Euclidean distance for uncorrelated variables with unit variance. This distance is zero if P is at the mean of the D, and it grows as P moves away from the mean. Along each principal component axis, it measures the number of standard deviations between P and the mean of D. In the following ¯ denotes a vector, otherwise D denotes a matrix. The Mahalanobis distance of the observations x D .x1; x2; x3; : : : ;xn / from a group of observation with mean D . 1; 2; 3; : : : ; n / and covariance matrix S, is defined as: DistMahalanobis x Dr x T S 1 x (10.9) In this paper the observations (Qx) are the parameters (˚i) of the model for many different days, each one having its mean, grouped in the same vector ( Q . Moreover, we compute the covariance matrix (S) of all these parameter (˚i). 10.3 G. Meazza Statium The Meazza stadium consists of a number of different substructures, subject to continuous modifications, enlargements and reinforcements, see Figs. 10.1 and 10.2. The main substructures are the rings and the roofing structures. The first ring is the oldest substructure, it was built in 1927, and permitted to reach the capacity of 35,000 seats. The second ring was built in Fig. 10.1 Inside view of the stadium
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