Delusions are one of the most classical symptoms described in schizophrenia. However, despite del... more Delusions are one of the most classical symptoms described in schizophrenia. However, despite delusions are often emotionally charged, they have been investigated using tasks involving non-affective material, such as the Beads task. In this study we compared 30 patients with schizophrenia experiencing delusions with 32 matched controls in their pattern of responses to two versions of the Beads task within a Bayesian framework. The two versions of the Beads task consisted of one emotional and one neutral, both with ratios of beads of 60:40 and 80:20, considered, respectively, as the “difficult” and “easy” variants of the task. Results indicate that patients showed a greater deviation from the normative model, especially in the 60:40 ratio, suggesting that more inaccurate probability estimations are more likely to occur under uncertainty conditions. Additionally, both patients and controls showed a greater deviation in the emotional version of the task, providing evidence of a reasoni...
To quantify the levels of performance (symptom severity) of the computer-vision symptom scale (CV... more 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. 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 scale's 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. We identified 5.8 different levels of performance. Discriminant functions obtained from sample data indicated that the scale's main factors correctly classified 98.4% of the cases. The main factors: Internal symptom factor (ISF) and external symptom fact...
Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mea... more Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mean vector and the covariance matrix that specify the joint distribution of the variables in the nodes of a Gaussian Bayesian network (GBN). Nevertheless, uncertainty about the alternative conditional specification of GBN based on the regression coefficients of each variable given its parents in the directed acyclic graph (DAG), has received low attention in the literature. In this line, we focus on evaluating the e¤ect of regression coefficients misspecification by means of the Kullback-Leibler (KL) divergence.
To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is ne... more To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is necessary to study the sensitivity of the model. With this aim we propose a sensitivity analysis based on comparing two different models: the original model with the initial parameters assigned to the Gaussian Bayesian network and the perturbed model obtained after perturbing a set of inaccurate parameters with specific characteristics. The network’s outputs obtained for both models, after the evidence propagation, are going to be compared with the Kullback-Leibler divergence. This measure is useful to discriminate between two probability distributions, comparing the whole behavior of the considered probability distributions. Depending on the set of parameters that are going to be perturbed, different expressions for the Kullback-Leibler are obtained. It is possible to determine the set of parameters that mostly disturb the network’s output, detecting the variables that must be accurately ...
This article maybe used for research, teaching and private study purposes. Any substantial or sys... more This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
BACKGROUND AND OBJECTIVE The aim of this study was to describe the lipid profile, the levels of s... more BACKGROUND AND OBJECTIVE The aim of this study was to describe the lipid profile, the levels of serum total cholesterol (TC), LDL cholesterol (C-LDL), HDL cholesterol (C-HDL) and triglyceride (TG), to compare these levels between geographical areas and to estimate the prevalence of dyslipidemia in elderly residents (65 years and older) from urban and rural areas of Spain. PATIENTS AND METHOD Epidemiological, observational, multicentre study of Spanish elderly people residents (>or= 65 years old) of 3 communities in 3 Spanish regions: Arévalo (Avila) and Begonte (Lugo) as rural areas and Lista (Central Madrid) as urban area. Stratified randomized sample by age and sex from population census of each area. The participation rate was: 84.6%. At-home interviews (phase 1) (n = 4522): with determination of capillary blood cholesterol levels (Reflotron) and clinical visit (phase 2) (1/3 selected randomly, n = 1907): determination of serum TC levels (enzymatic colorimetric method CHOP-PAD...
To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is ne... more To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is necessary to study the sensitivity of the model. With this aim we propose a sensitivity analysis based on comparing two different models: the original model with the initial parameters assigned to the Gaussian Bayesian network and the perturbed model obtained after perturbing a set of inaccurate parameters with specific characteristics. The network’s outputs obtained for both models, after the evidence propagation, are going to be compared with the Kullback-Leibler divergence. This measure is useful to discriminate between two probability distributions, comparing the whole behavior of the considered probability distributions. Depending on the set of parameters that are going to be perturbed, different expressions for the Kullback-Leibler are obtained. It is possible to determine the set of parameters that mostly disturb the network’s output, detecting the variables that must be accurately ...
Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mea... more Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mean vector and the covariance matrix that specify the joint distribution of the variables in the nodes of a Gaussian Bayesian network (GBN). Nevertheless, uncertainty about the alternative conditional speci cation of GBN based on the regression coe¢ cients of each variable given its parents in the directed acyclic graph (DAG), has received low attention in the literature. In this line, we focus on evaluating the e¤ect of regression coe¢ cients misspeci cation by means of the Kullback-Leibler (KL) divergence. 1 Introduction GBNs are de ned as Bayesian networks (BNs) where the joint probability density of X = (X1; X2; :::; Xp) T is a multivariate normal distribution Np( ; ) with the p dimensional mean vector and the p p positive de nite covariance matrix using a directed acyclic graph (DAG) to represent the dependence structure of the variables. As in BNs, the joint density can be factorized...
This article develops a method for computing the sensitivity analysis in a Gaussian Bayesian netw... more 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.
En este trabajo se introduce una f ormula recursiva que permite calcular la matriz de covarianzas... more En este trabajo se introduce una f ormula recursiva que permite calcular la matriz de covarianzas de una red Bayesiana Gaussiana dados los par ametros
Al definirse una red Bayesiana Gaussiana (RBG) es posible trabajar con la distribuci�on conjunta ... more Al definirse una red Bayesiana Gaussiana (RBG) es posible trabajar con la distribuci�on conjunta normal multivariante de las variables del problema o definir las distribuciones normales de cada variable condicionada por sus padres en el Grafo Ac��íclico Dirigido que recoge la estructura de dependencia de las variables de la red. La caracterí��stica de las redes Bayesianas es que permiten introducir evidencia en algunas variables del modelo y determinar, mediante la salida de la red, la distribuci�on a posteriori del resto de variables del problema, actuando as�� como sistema experto. En trabajos previos hemos estudiado la sensibilidad y robustez del modelo cuando la RBG se define con su distribuci�on conjunta y se ha determinado el comportamiento de la salida red para distintas perturbaciones asociadas a los par�ametros inciertos. En este trabajo se extiende la metodolog��a anterior considerando perturbaciones en otros aspectos de la distribuci�on. ISBN 978-84-691-8159-1
En Redes Bayesianas Gaussianas (RBGs) se ha estudiado la sensibilidad del modelo a cambios en los... more En Redes Bayesianas Gaussianas (RBGs) se ha estudiado la sensibilidad del modelo a cambios en los parámetros, comparando las salidas de la red tras la propagación de la evidencia, y a cambios en la estructura de la red en la fase inicial, es decir, sin propagar la evidencia. En este trabajo se evalúan cambios en la estructura de la red estudiando la salida de la misma tras la propagación de la evidencia con el objetivo de encontrar una red más sencilla que facilite el proceso de inferencia en el modelo. Para ello, proponemos un análisis de sensibilidad que permita determinar como de sensible es la RBG cuando se eliminan arcos de la misma, así, si la red no es sensible a eliminar un arco se puede trabajar con la red simplificada. Para estudiar la sensibilidad utilizamos la divergencia de Kullback-Leibler que permite comparar las salidas de la red tras la propagación de la evidencia entre la RBG definida inicialmente y la RBG de estructura simplificada.
ABSTRACT In this work, we introduce an n-way sensitivity analysis for Gaussian Bayesian networks ... more ABSTRACT In this work, we introduce an n-way sensitivity analysis for Gaussian Bayesian networks (GBNs) to study uncertainties in the mean vector and in the regression coefficients and the conditional variances of each variable given its parents in the graph (DAG). These parameters describe the quantitative part of the GBN and determine the structure of the qualitative part of the model, given by the DAG. The study of variations in these parameters leads us to compare different dependence structures of the network, adding or removing arcs. This analysis is useful in order to study the sensitivity of the network to variations in the qualitative part of the model. We perform the analysis by calculating the Kullback-Leibler divergence measure between the reference GBN and another one with misspecified mean vector, regression coefficients or conditional variances. Finally, some examples are analysed using the proposed methodology.
En este trabajo se introduce una f�ormula recursiva que permite calcular la matriz de covarianzas... more En este trabajo se introduce una f�ormula recursiva que permite calcular la matriz de covarianzas de una red Bayesiana Gaussiana dados los par�ametros de la especi�caci�on condicionada de la parte cuantitativa del modelo. Adem�as, se determinan las varianzas y las covarianzas del problema considerando los distintos caminos que aparecen en el grafo que recoge la parte cualitativa de la red. Se aplicar�an los conceptos introducidos en este trabajo a un ejemplo real.
Delusions are one of the most classical symptoms described in schizophrenia. However, despite del... more Delusions are one of the most classical symptoms described in schizophrenia. However, despite delusions are often emotionally charged, they have been investigated using tasks involving non-affective material, such as the Beads task. In this study we compared 30 patients with schizophrenia experiencing delusions with 32 matched controls in their pattern of responses to two versions of the Beads task within a Bayesian framework. The two versions of the Beads task consisted of one emotional and one neutral, both with ratios of beads of 60:40 and 80:20, considered, respectively, as the “difficult” and “easy” variants of the task. Results indicate that patients showed a greater deviation from the normative model, especially in the 60:40 ratio, suggesting that more inaccurate probability estimations are more likely to occur under uncertainty conditions. Additionally, both patients and controls showed a greater deviation in the emotional version of the task, providing evidence of a reasoni...
To quantify the levels of performance (symptom severity) of the computer-vision symptom scale (CV... more 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. 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 scale's 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. We identified 5.8 different levels of performance. Discriminant functions obtained from sample data indicated that the scale's main factors correctly classified 98.4% of the cases. The main factors: Internal symptom factor (ISF) and external symptom fact...
Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mea... more Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mean vector and the covariance matrix that specify the joint distribution of the variables in the nodes of a Gaussian Bayesian network (GBN). Nevertheless, uncertainty about the alternative conditional specification of GBN based on the regression coefficients of each variable given its parents in the directed acyclic graph (DAG), has received low attention in the literature. In this line, we focus on evaluating the e¤ect of regression coefficients misspecification by means of the Kullback-Leibler (KL) divergence.
To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is ne... more To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is necessary to study the sensitivity of the model. With this aim we propose a sensitivity analysis based on comparing two different models: the original model with the initial parameters assigned to the Gaussian Bayesian network and the perturbed model obtained after perturbing a set of inaccurate parameters with specific characteristics. The network’s outputs obtained for both models, after the evidence propagation, are going to be compared with the Kullback-Leibler divergence. This measure is useful to discriminate between two probability distributions, comparing the whole behavior of the considered probability distributions. Depending on the set of parameters that are going to be perturbed, different expressions for the Kullback-Leibler are obtained. It is possible to determine the set of parameters that mostly disturb the network’s output, detecting the variables that must be accurately ...
This article maybe used for research, teaching and private study purposes. Any substantial or sys... more This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
BACKGROUND AND OBJECTIVE The aim of this study was to describe the lipid profile, the levels of s... more BACKGROUND AND OBJECTIVE The aim of this study was to describe the lipid profile, the levels of serum total cholesterol (TC), LDL cholesterol (C-LDL), HDL cholesterol (C-HDL) and triglyceride (TG), to compare these levels between geographical areas and to estimate the prevalence of dyslipidemia in elderly residents (65 years and older) from urban and rural areas of Spain. PATIENTS AND METHOD Epidemiological, observational, multicentre study of Spanish elderly people residents (>or= 65 years old) of 3 communities in 3 Spanish regions: Arévalo (Avila) and Begonte (Lugo) as rural areas and Lista (Central Madrid) as urban area. Stratified randomized sample by age and sex from population census of each area. The participation rate was: 84.6%. At-home interviews (phase 1) (n = 4522): with determination of capillary blood cholesterol levels (Reflotron) and clinical visit (phase 2) (1/3 selected randomly, n = 1907): determination of serum TC levels (enzymatic colorimetric method CHOP-PAD...
To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is ne... more To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is necessary to study the sensitivity of the model. With this aim we propose a sensitivity analysis based on comparing two different models: the original model with the initial parameters assigned to the Gaussian Bayesian network and the perturbed model obtained after perturbing a set of inaccurate parameters with specific characteristics. The network’s outputs obtained for both models, after the evidence propagation, are going to be compared with the Kullback-Leibler divergence. This measure is useful to discriminate between two probability distributions, comparing the whole behavior of the considered probability distributions. Depending on the set of parameters that are going to be perturbed, different expressions for the Kullback-Leibler are obtained. It is possible to determine the set of parameters that mostly disturb the network’s output, detecting the variables that must be accurately ...
Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mea... more Some sensitivity analyses have been developed to evaluate the impact of uncertainty about the mean vector and the covariance matrix that specify the joint distribution of the variables in the nodes of a Gaussian Bayesian network (GBN). Nevertheless, uncertainty about the alternative conditional speci cation of GBN based on the regression coe¢ cients of each variable given its parents in the directed acyclic graph (DAG), has received low attention in the literature. In this line, we focus on evaluating the e¤ect of regression coe¢ cients misspeci cation by means of the Kullback-Leibler (KL) divergence. 1 Introduction GBNs are de ned as Bayesian networks (BNs) where the joint probability density of X = (X1; X2; :::; Xp) T is a multivariate normal distribution Np( ; ) with the p dimensional mean vector and the p p positive de nite covariance matrix using a directed acyclic graph (DAG) to represent the dependence structure of the variables. As in BNs, the joint density can be factorized...
This article develops a method for computing the sensitivity analysis in a Gaussian Bayesian netw... more 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.
En este trabajo se introduce una f ormula recursiva que permite calcular la matriz de covarianzas... more En este trabajo se introduce una f ormula recursiva que permite calcular la matriz de covarianzas de una red Bayesiana Gaussiana dados los par ametros
Al definirse una red Bayesiana Gaussiana (RBG) es posible trabajar con la distribuci�on conjunta ... more Al definirse una red Bayesiana Gaussiana (RBG) es posible trabajar con la distribuci�on conjunta normal multivariante de las variables del problema o definir las distribuciones normales de cada variable condicionada por sus padres en el Grafo Ac��íclico Dirigido que recoge la estructura de dependencia de las variables de la red. La caracterí��stica de las redes Bayesianas es que permiten introducir evidencia en algunas variables del modelo y determinar, mediante la salida de la red, la distribuci�on a posteriori del resto de variables del problema, actuando as�� como sistema experto. En trabajos previos hemos estudiado la sensibilidad y robustez del modelo cuando la RBG se define con su distribuci�on conjunta y se ha determinado el comportamiento de la salida red para distintas perturbaciones asociadas a los par�ametros inciertos. En este trabajo se extiende la metodolog��a anterior considerando perturbaciones en otros aspectos de la distribuci�on. ISBN 978-84-691-8159-1
En Redes Bayesianas Gaussianas (RBGs) se ha estudiado la sensibilidad del modelo a cambios en los... more En Redes Bayesianas Gaussianas (RBGs) se ha estudiado la sensibilidad del modelo a cambios en los parámetros, comparando las salidas de la red tras la propagación de la evidencia, y a cambios en la estructura de la red en la fase inicial, es decir, sin propagar la evidencia. En este trabajo se evalúan cambios en la estructura de la red estudiando la salida de la misma tras la propagación de la evidencia con el objetivo de encontrar una red más sencilla que facilite el proceso de inferencia en el modelo. Para ello, proponemos un análisis de sensibilidad que permita determinar como de sensible es la RBG cuando se eliminan arcos de la misma, así, si la red no es sensible a eliminar un arco se puede trabajar con la red simplificada. Para estudiar la sensibilidad utilizamos la divergencia de Kullback-Leibler que permite comparar las salidas de la red tras la propagación de la evidencia entre la RBG definida inicialmente y la RBG de estructura simplificada.
ABSTRACT In this work, we introduce an n-way sensitivity analysis for Gaussian Bayesian networks ... more ABSTRACT In this work, we introduce an n-way sensitivity analysis for Gaussian Bayesian networks (GBNs) to study uncertainties in the mean vector and in the regression coefficients and the conditional variances of each variable given its parents in the graph (DAG). These parameters describe the quantitative part of the GBN and determine the structure of the qualitative part of the model, given by the DAG. The study of variations in these parameters leads us to compare different dependence structures of the network, adding or removing arcs. This analysis is useful in order to study the sensitivity of the network to variations in the qualitative part of the model. We perform the analysis by calculating the Kullback-Leibler divergence measure between the reference GBN and another one with misspecified mean vector, regression coefficients or conditional variances. Finally, some examples are analysed using the proposed methodology.
En este trabajo se introduce una f�ormula recursiva que permite calcular la matriz de covarianzas... more En este trabajo se introduce una f�ormula recursiva que permite calcular la matriz de covarianzas de una red Bayesiana Gaussiana dados los par�ametros de la especi�caci�on condicionada de la parte cuantitativa del modelo. Adem�as, se determinan las varianzas y las covarianzas del problema considerando los distintos caminos que aparecen en el grafo que recoge la parte cualitativa de la red. Se aplicar�an los conceptos introducidos en este trabajo a un ejemplo real.
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