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.     

Bayesian Model Selection: Measuring the χ2 Discrepancy with the Uniform Distribution

In the last years, many articles have been written about Bayesian model selection. In this article, a different and easier method is proposed and analyzed. The key idea of this method is based on the well-known property that, under the true model, the cumulative distribution function is distributed as a uniform distribution over the interval (0, 1). The method is first introduced for the continuous case and then for the discrete case by smoothing the cumulative distribution function. Some asymptotical properties of the method are obtained by developing an alternative to Helly's theorems. Finally, the performance of the method is evaluated by simulation, showing a good behavior.     

On the Use of Bayes Factor in Frequentist Testing of a Precise Hypothesis

This article deals with Bayes factors as useful Bayesian tools in frequentist testing of a precise hypothesis. A result and several examples are included to justify the definition of Bayes factor for point null hypotheses, without merging the initial distribution with a degenerate distribution on the null hypothesis. Of special interest is the problem of testing a proportion (joint with a natural criterion to compare different tests), the possible presence of nuisance parameters, or the influence of Bayesian sufficiency on this problem. The problem of testing a precise hypothesis under a Bayesian perspective is also considered and two alternative methods to deal with are given.     

Some Asymptotic Properties of Ridge Regression in a System of Seemingly Unrelated Regression Equations

A discussion is made of asymptotic properties of an Operational Ordinary Ridge Regression estimator and comparison is made with the Operational Generalized Least Squares estimator. Also, some simulation experiments are carried showing efficiency gains can be made through the use of de Ridge estimator.     

Confidence Intervals for a New Characteristic of Central Tendency of Distributions

The t-mean is a new characteristic of the central tendency of continuous distributions. In this article, we introduce a t-difference in the sample space, which is used for a construction of confidence intervals for the t-mean.     

Properties and Inference on the Skew-Curved-Symmetric Family of Distributions

In this article, we study some results related to a specific class of distributions, called skew-curved-symmetric family of distributions that depends on a parameter controlling the skewness and kurtosis at the same time. Special elements of this family which are studied include symmetric and well-known asymmetric distributions. General results are given for the score function and the observed information matrix. It is shown that the observed information matrix is always singular for some special cases. We illustrate the flexibility of this class of distributions with an application to a real dataset on characteristics of Australian athletes.     

The Effect of Verification Bias in the Naïve Estimators of Accuracy of a Binary Diagnostic Test

The assessment of a binary diagnostic test requires a knowledge of the disease status of all the patients in the sample through the application of a gold standard. In practice, the gold standard is not always applied to all of the patients, which leads to the problem of partial verification of the disease. When the accuracy of the diagnostic test is assessed using only those patients whose disease status has been verified using the gold standard, the estimators obtained in this way, known as Naïve estimators, may be biased. In this study, we obtain the explicit expressions of the bias of the Naïve estimators of sensitivity and specificity of a binary diagnostic test. We also carry out simulation experiments in order to study the effect of the verification probabilities on the Naïve estimators of sensitivity and specificity.     

Records Properties of Non Stationary Time Series

This article proposes an asymptotic expansion for the Studentized linear discriminant function using two-step monotone missing samples under multivariate normality. The asymptotic expansions related to discriminant function have been obtained for complete data under multivariate normality. The result derived by Anderson (1973 Anderson , T. W. ( 1973 ). An asymptotic expansion of the distribution of the Studentized classification statistic W . The Annals of Statistics 1 : 964 – 972 .[Crossref], [Web of Science ®] , [Google Scholar]) plays an important role in deciding the cut-off point that controls the probabilities of misclassification. This article provides an extension of the result derived by Anderson (1973 Anderson , T. W. ( 1973 ). An asymptotic expansion of the distribution of the Studentized classification statistic W . The Annals of Statistics 1 : 964 – 972 .[Crossref], [Web of Science ®] , [Google Scholar]) in the case of two-step monotone missing samples under multivariate normality. Finally, numerical evaluations by Monte Carlo simulations were also presented.     

A Detrended Range Unit Root (DRUR) Test

We extend the Range Unit Root test in two directions. First, we consider the process with time trend and prove that the modified standardized number of new records converges to a sum of two Rayleigh distributions. Second, more general structures of autocorrelated disturbances are also taken into account. Monte Carlo experiments show the good sample properties of this nonparametric unit root test.     

Readouts for echo-state networks built using locally regularized orthogonal forward regression

Echo state network (ESN) is viewed as a temporal expansion which naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the teacher output and we propose to determine the importance of the echo-regressors by a joint calculation of the individual variance contributions and Bayesian relevance using the locally regularized orthogonal forward regression (LROFR). This information can be advantageously used in a variety of ways for an analysis of an ESN structure. We present a locally regularized linear readout built using LROFR. The readout may have a smaller dimensionality than the ESN model itself, and improves robustness and accuracy of an ESN. Its main advantage is ability to determine what type of an additional readout is suitable for a task at hand. Comparison with PCA is provided too. We also propose a radial basis function (RBF) readout built using LROFR, since flexibility of the linear readout has limitations and might be insufficient for complex tasks. Its excellent generalization abilities make it a viable alternative to feed-forward neural networks or relevance-vector-machines. For cases where more temporal capacity is required we propose well studied delay&sum readout.