Residuals in fault detection and diagnosis are usually designed with directional or structured properties to facilitate fault isolation. With directional residuals, best isolation is achieved if the residual directions are orthogonal. In the presence of noise, the residuals are subjected to statistical testing. Testing conditions are ideal if the Fisher information matrix of the residuals is di...

In this paper, a strategy is proposed for alternative computations of the residual vectors in Krylov subspace methods, which improves the agreement of the computed residuals and the true residuals to the level of O(u)kAkkxk. Building on earlier ideas on residual replacement and on insights in the nite precision behaviour of the Krylov subspace methods, computable error bounds are derived for it...

Abstract Evaluation of document models for text based Information retrieval is crucial for developing document models that are appropriate for specific domains. Unfortunately, current document model evaluation methods for text retrieval provide no feedback, except for an evaluation score. To improve a model, we must use trial and error. In this article, we examine how we can provide feedback in...

The use of martingale residuals have been proposed for model checking and also to get a non-parametric estimate of the effect of an explanatory variable. We apply this approach to an epidemiological problem which presents two characteristics: the data are left truncated due to delayed entry in the cohort; the data are grouped into geographical units (parishes). This grouping suggests a natural ...

We define residuals for point process models fitted to spatial point pattern data, and propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, ke...

based on the definition of Vt. Once we have data,Rt is not the variance of our model residuals because our residuals are now conditioned on a set of observed data. There are two types of conditional model residuals used in MARSS analyses: innovations and smoothations. Innovations are the model residuals at time t using the expected value of X t conditioned on the data from 1 to t−1. Smoothation...

In this paper, a strategy is proposed for alternative computations of the residual vectors in Krylov subspace methods, which improves the agreement of the computed residuals and the true residuals to the level of O(u)‖A‖‖x‖. Building on earlier ideas on residual replacement and on insights in the finite precision behavior of the Krylov subspace methods, computable error bounds are derived for i...