Information matrix

An analytical description of the photon-economy and additive noise could be carried out by the estimation of the Fisher-information matrix of the used estimators [34],... 

Information state y and the information matrix Y associated with an observation estimate x, and the covariance of the observation estimate P at time instant k are given by [16]... 

In [16], it is shown that by means of sufficient statistics, an observation cp contributes i( ) to the information state y and I( ) to the information matrix Y where... 

Just before the data at time k are collected, if we are given the observations up to the time k — 1, the predicted information state and the information matrix at time k can be calculated from... 

The algorithm employed by a sensor for tracking targets in a collaborative manner within the distributed data fusion framework is depicted in Fig. 7. The information state and the information matrix are defined by (5). The predicted information state and the information matrix are computed by (7). The sensor s current belief is updated by its own... 

Furthermore, under symplectic transformations, it is relatively easy to show, using the Hessian formula for calculating the Fisher information matrix, that the measurement covariance matrix transforms as... 

C Information matrix. .t u Element of the fcth power of matrix R... 

RECONSTRUCTION OF MEASUREMENT INFORMATION MATRIX TO REFLECT CORRELATIONS... 

Lastly, we have developed two KNIME nodes to select parameters based on mutual information (24). The Parameter Mutual Information computes the mutual information matrix for all parameters. The Group Mutual Information computes the mutual information between two reference populations for a set of selected parameters. In this manner it is possible to select parameters and discover new phenotypes in a screen. 

The elements of fhe vector y are the reference values of the response variable, used for building the model. The uncertainty on the coefficient estimation varies inversely with the determinant of the information matrix (X X) which, in the case of a unique predictor, corresponds to its variance. In multivariate cases, the determinant value depends on the variance of fhe predictors and on their intercorrelation a high correlation gives a small determinant of the information matrix, which means a big uncertainty on the coefficients, that is, unreliable regression results. 

Another advantage of simplex-lattice designs having special cubic order or lower order is that they are D-optimal. Namely, they have the maximum value of the determinant of the information matrix in the case of mixtures, XTX. Another common advantage of simplex-lattice designs is the possibility of generating component contour plots showing the behavior of the model in a three-dimensional space. 

The design that maximizes the determinant of the information matrix, det M([Pg.304]

An experimental design with extended design matrix F is referred to as D-optimal if its information matrix fulfills the condition ... 

The determinant of the information matrix of the D-optimal design has a maximum value among all possible designs. Based on this criterion, the design with information matrix M is better than the design with information matrix M if the following condition holds ... 

An experimental design with an information matrix M is G-optimal if the following condition holds,... 

Also, we use SL to denote a set of L experimental points in the same factor space, called candidate points. The set of candidate points will be used as a source of points that might possibly be included in the experimental design, XN. The information matrix of the /V-point design, XN, will be denoted as above by Mw = FT where Mw is the information matrix for some model (Equation 8.59). By the following formula, we denote the variance of the prediction at point x-. 

Using the notation of experimental design, F represents the extended design matrix, where the elements of its k x I row-vectors, f, are known functions of x. The matrix (FT) is the Fisher information matrix and its inverse, (FT)-1, is the dispersion matrix of the regression coefficients. 

By minimizing the maximum eigenvalue of the information matrix, M, we will be assured that M will be invertible. This would be impossible if the design matrix X and, subsequently, the information matrix M were ill conditioned. A variant of the previously mentioned E-optimality criterion is shown in Equation 8.90,... 

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