Rosario Susi

Sensitivity Analysis in Gaussian Bayesian Networks Using a Divergence Measure

This article develops a method for computing the sensitivity analysis in a Gaussian Bayesian network. The measure presented is based on the Kullback–Leibler divergence and is useful to evaluate the impact of prior changes over the posterior marginal density of the target variable in the network. We find that some changes do not disturb the posterior marginal density of interest. Finally, we describe a method to compare different sensitivity measures obtained depending on where the inaccuracy was. An example is used to illustrate the concepts and methods presented.

The Computer-Vision Symptom Scale (CVSS17): development and initial validation.

PURPOSE To develop a questionnaire (in Spanish) to measure computer-related visual and ocular symptoms (CRVOS). METHODS A pilot questionnaire was created by consulting the literature, clinicians, and video display terminal (VDT) workers. The replies of 636 subjects completing the questionnaire were assessed using the Rasch model and conventional statistics to generate a new scale, designated the Computer-Vision Symptom Scale (CVSS17). Validity and reliability were determined by Rasch fit statistics, principal components analysis (PCA), person separation, differential item functioning (DIF), and item-person targeting. To assess construct validity, the CVSS17 was correlated with a Rasch-based visual discomfort scale (VDS) in 163 VDT workers, this group completed the CVSS17 twice in order to assess test-retest reliability (two-way single-measure intraclass correlation coefficient [ICC] and their 95% confidence intervals, and the coefficient of repeatability [COR]). RESULTS The CVSS17 contains 17 items exploring 15 different symptoms. These items showed good reliability and internal consistency (mean square infit and outfit 0.88-1.17, eigenvalue for the first residual PCA component 1.37, person separation 2.85, and no DIF). Pearsons correlation with VDS scores was 0.60 (P < 0.001). Intraclass correlation coefficient for test-retest reliability was 0.849 (95% confidence interval [CI], 0.800-0.887), and COR was 8.14. CONCLUSIONS The Rasch-based linear-scale CVSS17 emerged as a useful tool to quantify CRVOS in computer workers. : Spanish Abstract.

The effect of block parameter perturbations in Gaussian Bayesian networks: Sensitivity and robustness

In this work we study the effects of model inaccuracies on the description of a Gaussian Bayesian network with a set of variables of interest and a set of evidential variables. Using the Kullback-Leibler divergence measure, we compare the output of two different networks after evidence propagation: the original network, and a network with perturbations representing uncertainties in the quantitative parameters. We describe two methods for analyzing the sensitivity and robustness of a Gaussian Bayesian network on this basis. In the sensitivity analysis, different expressions are obtained depending on which set of parameters is considered inaccurate. This fact makes it possible to determine the set of parameters that most strongly disturbs the network output. If all of the divergences are small, we can conclude that the network output is insensitive to the proposed perturbations. The robustness analysis is similar, but considers all potential uncertainties jointly. It thus yields only one divergence, which can be used to confirm the overall sensitivity of the network. Some practical examples of this method are provided, including a complex, real-world problem.

Evaluating the difference between graph structures in Gaussian Bayesian networks

In this work, we evaluate the sensitivity of Gaussian Bayesian networks to perturbations or uncertainties in the regression coefficients of the network arcs and the conditional distributions of the variables. The Kullback-Leibler divergence measure is used to compare the original network to its perturbation. By setting the regression coefficients to zero or non-zero values, the proposed method can remove or add arcs, making it possible to compare different network structures. The methodology is implemented with some case studies.

Assessing the effect of kurtosis deviations from Gaussianity on conditional distributions

The multivariate exponential power family is considered for n-dimensional random variables, Z, with a known partition Z=(Y,X) of dimensions p and n-p, respectively, with interest focusing on the conditional distribution Y|X. An infinitesimal variation of any parameter of the joint distribution produces perturbations in both the conditional and marginal distributions. The aim of the study was to determine the local effect of kurtosis deviations using the Kullback-Leibler divergence measure between probability distributions. The additive decomposition of this measure in terms of the conditional and marginal distributions, Y|X and X, is used to define a relative sensitivity measure of the conditional distribution family {Y|X=x}. Finally, simulated results suggest that for large dimensions, the measure is approximately equal to the ratio p/n, and then the effect of non-normality with respect to kurtosis depends only on the relative size of the variables considered in the partition of the random vector.

Sensitivity to hyperprior parameters in Gaussian Bayesian networks

Bayesian networks (BNs) have become an essential tool for reasoning under uncertainty in complex models. In particular, the subclass of Gaussian Bayesian networks (GBNs) can be used to model continuous variables with Gaussian distributions. Here we focus on the task of learning GBNs from data. Factorization of the multivariate Gaussian joint density according to a directed acyclic graph (DAG) provides an alternative and interchangeable representation of a GBN by using the Gaussian conditional univariate densities of each variable given its parents in the DAG. With this latter conditional specification of a GBN, the learning process involves determination of the mean vector, regression coefficients and conditional variances parameters. Some approaches have been proposed to learn these parameters from a Bayesian perspective using different priors, and therefore some hyperparameter values are tuned. Our goal is to deal with the usual prior distributions given by the normal/inverse gamma form and to evaluate the effect of prior hyperparameter choice on the posterior distribution. As usual in Bayesian robustness, a large class of priors expressed by many hyperparameter values should lead to a small collection of posteriors. From this perspective and using Kullback-Leibler divergence to measure prior and posterior deviations, a local sensitivity measure is proposed to make comparisons. If a robust Bayesian analysis is developed by studying the sensitivity of Bayesian answers to uncertain inputs, this method will also be useful for selecting robust hyperparameter values.

Five levels of performance and two subscales identified in the computer-vision symptom scale (CVSS17) by Rasch, factor, and discriminant analysis

Purpose To quantify the levels of performance (symptom severity) of the computer-vision symptom scale (CVSS17), confirm its bifactorial structure as detected in an exploratory factor analysis, and validate its factors as subscales. Methods By partial credit model (PCM), we estimated CVSS17 measures and the standard error for every possible raw score, and used these data to determine the number of different performance levels in the CVSS17. In addition, through discriminant analysis, we checked that the scales two main factors could classify subjects according to these determined levels of performance. Finally, a separate Rasch analysis was performed for each CVSS17 factor to assess their measurement properties when used as isolated scales. Results We identified 5.8 different levels of performance. Discriminant functions obtained from sample data indicated that the scales main factors correctly classified 98.4% of the cases. The main factors: Internal symptom factor (ISF) and external symptom factor (ESF) showed good measurement properties and can be considered as subscales. Conclusion CVSS17 scores defined five different levels of performance. In addition, two main factors (ESF and ISF) were identified and these confirmed by discriminant analysis. These subscales served to assess either the visual or the ocular symptoms attributable to computer use.