The authors study the efficiency of the linear–functional strategy, as introduced by Anderssen (1986), for inverse problems with observations blurred by Gaussian white noise with known intensity δ. The optimal accuracy is presented and it is shown how this can be achieved by a linear–functional strategy based on the noisy observations. This optimal linear–functional strategy is obtained from Ti...

For complex processes whose evolution is described by partial differential equations, the identification of failures often difficult. In thermal systems, for example, when one or more heating sources fail, sensors placed at a distance perceive effect with delay. From these noisy observations, it then necessary to determine precision moment failure and possible restart heating. As inverse heat c...

To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs assessed for each node. It generally has the complexity exponential on n. Noisy-OR reduces the complexity to linear, but can only represent reinforcing causal interactions. The non-impeding noisy-AND (NIN-AND) tree is the first causal model that explicitly expresses reinforc...

Combined state and parameter estimation of dynamical systems plays a crucial role in extracting system response from noisy measurements. A wide variety of methods have been developed to deal with the joint state-parameter estimation of nonlinear dynamical systems. The Extended Kalman Filter method is a popular approach for the joint systemparameter estimation of nonlinear systems. This method c...

Ala~traet--Errors-in-variables problems are considered for the case of three variables, where the underlying relations among the noise-free variables are linear, and covariance information for the noisy variables is available. The static problem where the variables are complex (which can arise when narrowband filtering is used) is analysed in detail. Some results are also presented for the case...