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One-sided Bayes factors are obtained for the association in 2 by 2 tables, under three different sampling designs. These Bayes factors are relevant when one has a prior believe about the direction of an association. It is further shown how prior knowledge can be incorporated in determining the support of a positive association against the hypothesis of row-column independence.

Empirical Bayes estimates of the local false discovery rate can reflect uncertainty about the estimated prior by supplementing their Bayesian posterior probabilities with confidence levels as posterior probabilities. This use of coherent fiducial inference with hierarchical models generates set estimators that propagate uncertainty to varying degrees. Some of the set estimates approach estimates from plug-in empirical Bayes methods for high numbers of comparisons and can come close to the usual confidence sets given a sufficiently low number of comparisons.

In this paper we study various reliability properties of a Weibull inverse exponential distribution. The maximum likelihood and Bayes estimates of unknown parameters and reliability characteristics are obtained. Bayes estimates are obtained with respect to the squared error loss function under proper and improper prior situations. We use the Lindley method and the Metropolis–Hastings algorithm to compute the Bayes estimates. Interval estimation is also considered. Asymptotic and highest posterior density intervals of unknown parameters are constructed in this respect. We perform a numerical study to compare the performance of all methods and obtain comments based on this study. We also analyze two real data sets for illustration purposes. Finally a conclusion is presented.

The problem of estimation of the shape parameter in a generalized half-logistic distribution for progressively type-II censored samples is of interest in reliability and survival analysis. In this paper, Bayesian methods of estimation based on quadratic and Linex loss functions are proposed. Closed expressions and approximations are obtained for the Bayes and posterior risks of Bayes estimators. These results allow us to assess the performance of estimators obtained under the previously cited loss functions. An application to a real dataset and a simulation study are included where the importance of the different features involved in the progressive type-II censoring scheme is also shown.

We propose the power-log loss function plotted in Figure 1 for the restricted parameter space (0,1), which satisfies all the six properties listed in Table 1 for a good loss function on (0,1). In particular, the power-log loss function penalizes gross overestimation and gross underestimation equally, is convex in its argument, and attains its global minimum at the true unknown parameter. The power-log loss function on (0,1) is an analog of the power-log loss function on (0,∞), which is the popular Stein's loss function. We then calculate the Bayes rule (estimator) of the parameter in (0,1) under the power-log loss function, the posterior expected power-log loss (PEPLL) at the Bayes estimator, and the integrated risk under the power-log loss (IRPLL) at the Bayes estimator, which is also the Bayes risk under the power-log loss (BRPLL). We also calculate the usual Bayes estimator under the squared error loss, which has been proved to be larger than that under the power-log loss. Next, we analytically...

In this work, the problem of transformation and simultaneous variable selection is thoroughly treated via objective Bayesian approaches by the use of default Bayes factor variants. Four uniparametric families of transformations (Box–Cox, Modulus, Yeo-Johnson and Dual), denoted by T, are evaluated and compared. The subjective prior elicitation for the transformation parameter $$\lambda _T$$ , for each T, is not a straightforward task. Additionally, little prior information for $$\lambda _T$$ is expected to be available, and therefore, an objective method is required. The intrinsic Bayes factors and the fractional Bayes factors allow us to incorporate default improper priors for $$\lambda _T$$ . We study the behaviour of each approach using a simulated reference example as well as two real-life examples.

Tests with binary outcomes (e.g., positive versus negative) to indicate a binary state of nature (e.g., disease agent present versus absent) are common. These tests are rarely perfect: chances of a false positive and a false negative always exist. Imperfect results cannot be directly used to infer the true state of the nature; information about the method's uncertainty (i.e., the two error rates and our knowledge of the subject) must be properly accounted for before an imperfect result can be made informative. We discuss statistical methods for incorporating the uncertain information under two scenarios, based on the purpose of conducting a test: inference about the subject under test and inference about the population represented by test subjects. The results are applicable to almost all tests. The importance of properly interpreting results from imperfect tests is universal, although how to handle the uncertainty is inevitably case-specific. The statistical considerations not only will change the way we interpret test results, but also how we plan and carry out tests that are known to be imperfect. Using a numerical example, we illustrate the post-test steps necessary for making the imperfect test results meaningful., Conditional probability; False negative; Uncertainty; False positive; Bayes' rule; Statistics; Environmental assessment; Environmental risk assessment; Bioinformatics; Epidemiology

We consider Khamis' (1960) Laguerre expansion with gamma weight function as a class of “near-gamma” priors (K-prior) to obtain the Bayes predictor of a finite population mean under the Poisson regression superpopulation model using Zellner's balanced loss function (BLF). Kullback–Leibler (K-L) distance between gamma and some K-priors is tabulated to examine the quantitative prior robustness. Some numerical investigations are also conducted to illustrate the effects of a change in skewness and/or kurtosis on the Bayes predictor and the corresponding minimal Bayes predictive expected loss (MBPEL). Loss robustness with respect to the class of BLFs is also examined in terms of relative savings loss (RSL).

The Bayesian estimation of unknown parameters of shifted Gompertz mixture model under type-I censorship, assuming both the informative and noninformative priors is investigated using different loss functions to obtain the Bayes estimates. It is seen that the closed-form expressions for the Bayes estimators cannot be obtained under shape and scale parameters. Some properties of the model with some graphs of the mixture density are discussed. These properties include Bayes estimators, posterior risks and reliability function under simulation scheme. The prior belief of the mixture model is represented by the uniform, and gamma prior. Bayes estimates are obtained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. A detailed simulation study is carried out to investigate the performance of the proposed set of estimators of the mixture model parameters. Posterior risks of the Bayes estimators are evaluated and compared to explore the effect of prior be...

Although teaching Bayes' theorem is popular, the standard approach---targeting posterior distributions of parameters---may be improved. We advocate teaching Bayes' theorem in a ratio form where the posterior beliefs relative to the prior beliefs equals the conditional probability of data relative to the marginal probability of data. This form leads to an interpretation that the strength of evidence is relative predictive accuracy. With this approach, students are encouraged to view Bayes' theorem as an updating mechanism, to obtain a deeper appreciation of the role of the prior and of marginal data, and to view estimation and model comparison from a unified perspective.

Monitoring for disease requires subsets of the host population to be sampled and tested for the pathogen. If all the samples return healthy, what are the chances the disease was present but missed? In this paper, we developed a statistical approach to solve this problem considering the fundamental property of infectious diseases: their growing incidence in the host population. The model gives an estimate of the incidence probability density as a function of the sampling effort, and can be reversed to derive adequate monitoring patterns ensuring a given maximum incidence in the population. We then present an approximation of this model, providing a simple rule of thumb for practitioners. The approximation is shown to be accurate for a sample size larger than 20, and we demonstrate its use by applying it to three plant pathogens: citrus canker, bacterial blight and grey mould.

This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for the unknown parameters based on one's prior beliefs. It is shown that in most typical situations in psychological research (when either observing no, small, medium or large effects) default Bayes factors are asymmetric in information, i.e., they result in unequal error probabilities. The tendency to either prefer the null hypothesis or the alternative hypothesis varies for different default Bayes factors. Although this asymmetry in information is a natural property of a Bayes factor, severe cases of asymmetry may be undesirable in a default setting because the underlying default priors are not a translation of one's prior beliefs. A calibration scheme is presented to make a default Bayes factor symmetric in information under certain conditions. (C) 2015 Elsevier Inc. All rights reserved.

This paper derives Bayes shrinkage estimator of Rayleigh parameter and its associated risk based on conjugate prior under the assumption of general entropy loss function for progressive type-II censored data. Risk function of maximum likelihood estimate, Bayes estimate and Bayes shrinkage estimate have also been derived and compared. A procedure has been suggested to include a guess value in case of the Bayes shrinkage estimation. Risk function of empirical Bayes estimate and empirical Bayes shrinkage estimate have also been derived and compared. In conclusion, an illustrative example is presented to assess how the Rayleigh distribution fits a real data set.

This paper deals with the problem of testing on the equality of the scale parameters in the log-logistic distributions. We propose default Bayesian testing procedures for the scale parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be dened up to a multiplicative constant. Therefore, we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the reference priors. To justify proposed procedures, a simulation study is provided and also, an example is given.

In this paper, we suggest the Bayes linear estimator (BLE) for randomized response model (RRM) to improve the efficiency of RR estimators, only using the first and second prior moments. The randomized response model is an indirect questioning technique used to protect the privacy of respondents in a survey regarding a sensitive characteristic. Meanwhile Bayes linear estimation is useful for parameter estimation compared to the typical Bayesian method because it only uses the first and second prior knowledge of the variable of interest. Also, it has an advantage of robustness with the distribution. We suggest the Bayes linear estimators for the two-stage and the stratified RRM and find the optimal sample size to minimize the Bayes risk for the stratified RRM. Also, we show the difference in efficiency between the Bayes linear estimators and the typical non-Bayesian RR estimators by simulation study.

I emphasize some common misuses of statistics that everyone, whether you do statistics or just read what others write, should be on the lookout for. I next discuss somewhat more complicated issues in archaeological method and theory and then conclude with a qualitative explanation of Bayesian methods and why they are often preferable to the frequentist methods advocated in many introductory statistics texts.

The Bayes factor for the integral priors in the one-way random effects model has recently been developed by Cano et al. (2007). We establish the consistency of this Bayes factor when the number of groups goes to infinity, when the number of observations per group goes to infinity, and when both go to infinity.

How much more likely is a positive test to be found in a patient with a pathological condition than in a patient without it? How much more likely is a negative test to be found in a patient without...

© 2018, © 2018 American Statistical Association. We develop a Bayes factor-based testing procedure for comparing two population means in high-dimensional settings. In ‘large-p-small-n” settings, Bayes factors based on proper priors require eliciting a large and complex p × p covariance matrix, whereas Bayes factors based on Jeffrey’s prior suffer the same impediment as the classical Hotelling T2 test statistic as they involve inversion of ill-formed sample covariance matrices. To circumvent this limitation, we propose that the Bayes factor be based on lower dimensional random projections of the high-dimensional data vectors. We choose the prior under the alternative to maximize the power of the test for a fixed threshold level, yielding a restricted most powerful Bayesian test (RMPBT). The final test statistic is based on the ensemble of Bayes factors corresponding to multiple replications of randomly projected data. We show that the test is unbiased and, under mild conditions, is also locally consistent. We demonstrate the efficacy of the approach through simulated and real data examples. Supplementary materials for this article are available online.

We investigate the problem of constructing Bayesian credible sets that are honest and adaptive for the L2-loss over a scale of Sobolev classes with regularity ranging between [D; 2D], for some given D in the context of the signal-in-white-noise model. We consider a scale of prior distributions indexed by a regularity hyper-parameter and choose the hyper-parameter both by marginal likelihood empirical Bayes and by hierarchical Bayes method, respectively. Next we consider a ball centered around the corresponding posterior mean with prescribed posterior probability. We show by theory and examples that both the empirical Bayes and the hierarchical Bayes credible sets give misleading, overconfident uncertainty quantification for certain oddly behaving truth. Then we construct a new empirical Bayes method based on risk estimation, which provides the correct uncertainty quantification and optimal size., 24 pages, 3 figures

The main objective of this paper is to find a close link between the adaptive level of significance, presented here, and the sample size. We, statisticians, know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that is compared to the canonical significance levels (10%, 5% and 1%): "Raise the sample to reject the null hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. The Bayesian Lindley's paradox – "increase the sample to accept the hypothesis" – also disappears. Obviously, we present here only the beginning of a possible prominent research. The intention is to extend its use to more complex applications such as survival analysis, reliability tests and other areas. The main tools used here are the Bayes Factor and the extended Neyman-Pearson Lemma.

To apply Bayes Rule when forming expectations agents must correctly assess the inherent “process variance” of each relevant cue, and place a larger weight on those cues with a smaller process variance. We test this notion by analysing subjective probabilities inferred from odds on the outcomes of tennis matches, exploiting natural variation in process variance related to the format with which tennis matches are played. Our results are consistent with “process variance neglect”, i.e., agents are not adjusting their ex-ante probabilities sufficiently according to process variance, and thus violate Bayes Rule. The resulting biases in expectations are costly.

The problem of selecting a population according to “selection and ranking” is an important statistical problem. The ideas in selecting the best populations with some demands having optimal criterion have been suggested originally by Bechhofer (1954) and Gupta (1956, 1965). In the area of ranking and selection, the large part of literature is connected with a single criterion. However, this may not satisfy the experimenter’s demand. We follow methodology of Huang and Lai (1999) and the main focus of this article is to select a best population under Type-II progressively censored data for the case of right tail exponential distributions with a bounded and unbounded supports for μi. We formulate the problem and develop a Bayesian setup with two kinds of bounded and unbounded prior for μi. We introduce an empirical Bayes procedure and study the large sample behavior of the proposed rule. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal.

This study considers the estimation problem for the parameter and reliability function of Generalized Half logistic distribution under record Data. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Generalized Half logistic distribution. We also obtain the Empirical Bayesian Estimators for the parameter and reliability function of Generalized Half logistic distribution and considered the problem of predicting future record in a Bayesian and Empirical Bayesian approaches. Comparisons are made between the different estimators based on a simulation study.

In this paper, we develop Bayesian inference of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation in the presence of auxiliary information under the balanced loss function. We compare the performance of the optimal Bayes estimator under the balanced loss function with ones of the classical ratio estimator and the usual Bayes estimator in terms of the posterior expected losses, risks and Bayes risks.

In this article, we study the problem of selecting the best population from among several exponential populations based on interval censored samples using a Bayesian approach. A Bayes selection procedure and a curtailed Bayes selection procedure are derived. We show that these two Bayes selection procedures are equivalent. A numerical example is provided to illustrate the application of the two selection procedure. We also use Monte Carlo simulation to study performance of the two selection procedures. The numerical results of the simulation study demonstrate that the curtailed Bayes selection procedure has good performance because it can substantially reduce the duration time of life test experiment.

In this paper, we consider the Bayesian approach to the model selection problem for nested linear regression models. Common Bayesian procedures to this problem are based on Zellner's g-prior with a hyper-prior for the scaling factor g. Maruyama and George (2011) recently adopted this procedure with the beta-prime distribution for g and derived an explicit closed-form Bayes factor without integral representation which is thus easy to compute. In addition, they have studied its corresponding model selection consistency for fixed number of parameters. Over recent years, linear regression models with a growing number of unknown parameters have gained increased popularity in practical applications, such as the clustering problem. This observation motivates us to further investigate the consistency of Bayes factor with the beta-prime distribution for g under a scenario in which the number of parameters increases with the sample size. Finally, the results presented here are compared with the ones for the Bayes factor under intrinsic priors in relevant literature.

A new method is proposed for testing multiple hypotheses with equality and inequality constraints on the parameters of interest. The method is based on the fractional Bayes factor with a modification that the updated prior is centered on the boundary of the constrained parameter space under investigation. The resulting prior adjusted default Bayes factors work as an “Ockham’s razor” when testing inequality constrained hypotheses, which is not the case for the fractional Bayes factor. Two different types of prior adjusted default Bayes factors are considered. In the first type, the updated prior is based on imaginary training data. Analytical and numerical examples show that this criterion converges fastest to a true inequality constrained hypothesis. In the second type, the updated prior is based on empirical training data. This second criterion only outperforms the fractional Bayes factor in the case of small samples.Keywords: Fractional Bayes factor, Ockham’s razor, (In)equality constraints, Updated prior

A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of variables and their probabilistic independencies. Some researches often involve continuous random variables. In order to apply these continuous variables to BN models, these variables should convert into discrete variables with limited states, often two. During the discretization process, one problem that researchers faced is to decide the number of states for discretization. Does the number of states chosen for discretization impact models’ power? In this study, this issue is examined empirically. The study examines this issue in the financial distress prediction field. The sample consists of 144 firms listed in Tehran stock exchange from 1997 to 2007. In order to develop Naive Bayes models, two methods for choosing variables were used. The first method is based upon conditional correlation between variables and the second method is based upon conditional likelihood. The accuracy in predicting financial distress of the first naive Bayes model's performance that is based upon conditional correlation is 90% and the accuracy of the second naive Bayes model is 93%. Collectively, the results showed that the performance of the second naive Bayes model that based upon conditional likelihood is better than the first one. Further analyses also showed that the number of states chosen for discretization has effect on models’ performance. In comparing the model's performance when continuous variables are discretized into two, three, four and five states, the results showed that the naive Bayes model's performance increases when the number of states for discretization increases from two to three, and from three to four but when the number of states increases from four to five the model's performance decreased.

We examine the large sample properties of Bayes procedures in a general framework, where data may be dependent and models may be misspecified and nonsmooth. The posterior distribution of parameters is shown to be asymptotically normal, centered at the quasi maximum likelihood estimator, under mild conditions. In this framework, the Bayes factor for the test problem of Davies (1997, 1987), where a parameter is unidentified under the null hypothesis, is analyzed. The probability that the Bayes factor leads to a correct conclusion about the hypotheses in Davies’ problem is shown to approach to one.

In this study, the theory of statistical kernel density estimation has been applied for deriving non-parametric kernel prior to the empirical Bayes which frees the Bayesian inference from subjectivity that has worried some statisticians. For comparing the empirical Bayes based on the kernel prior with the fully Bayes based on the informative prior, the mean square error and the mean percentage error for the Weibull model parameters are studied based on these approaches under both symmetric and asymmetric loss functions, via Monte Carlo simulations. The results are quite favorable to the empirical Bayes that provides better estimates and outperforms the fully Bayes for different sample sizes and several values of the true parameters. Finally, a numerical example is given to demonstrate the efficiency of the empirical Bayes.

We use Bayes’ estimator of a consumer-surplus probit model to study the relevance of the prior in a discrete choice model. We take random subsamples of varying sizes of stated preference data regarding ultra-low emission vehicle purchases in California and focus on the willingness-to-pay for improvements in driving range. Prior information is obtained from a meta-analysis of consumer valuation of driving range. We find the posterior distribution of the willingness-to-pay using a tight and a weakly informative prior, and also analyze the nonparametric estimates of the posterior compare these with the likelihood function of the problem. It is found that the weight of the prior is relevant for very small samples, but for standard sample sizes the prior vanishes. Thus, the Bayes estimator of a static discrete choice model is in general equivalent to the maximum likelihood estimator, although for some intermediate sample sizes the prior provides more realistic values.

We show that under the null, the 2log(Bayesfactor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and the normal prior. Our results have three immediate impacts. First, we can compute analytically a p-value associated with a Bayes factor without the need of permutation. We provide a software package that can evaluate the p-value associated with Bayes factor efficiently and accurately. Second, the null distribution is illuminating to some intrinsic properties of Bayes factor, namely, how Bayes factor quantitatively depends on prior and the genesis of Bartlett’s paradox. Third, enlightened by the null distribution of Bayes factor, we formulate a novel scaled Bayes factor that depends less on the prior and is immune to Bartlett’s paradox. When two tests have an identical p-value, the test with a larger power tends to have a larger scaled Bayes factor, a desirable property that is missing for the (unscaled) Bayes factor. Supplementary materials for this article are available online.

Asymptotic cumulants of the Bayes and pseudo Bayes estimators of ability in item response theory are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. Typical estimators are treated as special cases of the (pseudo) Bayes estimator with the general weight. The asymptotic cumulants of the estimators after studentization are also derived. From the comparison of the mean square errors, the Bayes modal estimator with the standard normal prior is recommended for point estimation. For interval estimation, however, the maximum likelihood estimator is appropriate considering its small bias after studentization.

We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: Misclassication probability; linear classier; quadratic classier; Bayes risk.

We consider an Empirical Bayes method to correct for the Winner's Curse phenomenon in genome-wide association studies. Our method utilizes the collective distribution of all odds ratios (ORs) to determine the appropriate correction for a particular single-nucleotide polymorphism (SNP). We can show that this approach is squared error optimal provided that this collective distribution is accurately estimated in its tails. To improve the performance when correcting the OR estimates for the most highly associated SNPs, we develop a second estimator that adaptively combines the Empirical Bayes estimator with a previously considered Conditional Likelihood estimator. The applications of these methods to both simulated and real data suggest improved performance in reducing selection bias.

In this article, multiple forecasts given as probabilities of events are aggregated using two assumptions: calibration and conditional independence. The forecasts are treated as data and the aggregation is based on Bayes's theorem. A measure of discrimination is given and the behavior of the aggregated posterior probability is examined as the number of forecasters grows without bound. The work is motivated by recent research efforts employing large numbers of individual forecasts.

An objective Bayesian model selection procedure is proposed for the one way analysis of variance under homoscedasticity. Bayes factors for the usual default prior distributions are not well defined and thus Bayes factors for intrinsic priors are used instead. The intrinsic priors depend on a training sample which is typically a unique random vector. However, for the homoscedastic ANOVA it is not the case. Nevertheless, we are able to illustrate that the Bayes factors for the intrinsic priors are not sensitive to the minimal training sample chosen; furthermore, we propose an alternative pooled prior that yields similar Bayes factors. To compute these Bayes factors Bayesian computing methods are required when the sample sizes of the involved populations are large. Finally, a one to one relationship—which we call the calibration curve—between the posterior probability of the null hypothesis and the classical $$p$$ value is found, thus allowing comparisons between these two measures of evidence. The behavior of the calibration curve as a function of the sample size is studied and conclusions relating both procedures are stated.

This article deals with the problem of testing on the common mean of several normal populations. We propose Bayesian hypothesis testing procedures for the common normal mean under the noninformative prior. The noninformative prior is usually improper and yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

We study a Bayes factor based on a robust test statistic, MAX3, for case-control genetic association studies. MAX3 is the maximum of three trend tests derived under the recessive, additive and dominant genetic models, respectively. The proposed Bayes factor, denoted as BFM, models the asymptotic distributions of MAX3 under the null and alternative hypotheses. It is compared to an existing Bayes factor based on Bayesian model averaging (BMA). Through simulation studies, we show that both BFM and BMA are robust under genetic model uncertainty. They both depend on specifying the prior distribution for the genetic model, and have similar performance when common objective priors are used. When the prior places a large probability on the true (wrong) genetic model, BMA (BFM) is more powerful. Applications to real data from a genome-wide association study are presented to illustrate their use and show their sensitivity under genetic model uncertainty.

Multiple hypothesis testing collects a series of techniques usually based on p-values as a summary of the available evidence from many statistical tests. In hypothesis testing, under a Bayesian perspective, the evidence for a specified hypothesis against an alternative, conditionally on data, is given by the Bayes factor. In this study, we approach multiple hypothesis testing based on both Bayes factors and p-values, regarding multiple hypothesis testing as a multiple model selection problem. To obtain the Bayes factors we assume default priors that are typically improper. In this case, the Bayes factor is usually undetermined due to the ratio of prior pseudo-constants. We show that ignoring prior pseudo-constants leads to unscaled Bayes factor which do not invalidate the inferential procedure in multiple hypothesis testing, because they are used within a comparative scheme. In fact, using partial information from the p-values, we are able to approximate the sampling null distribution of the unscaled Bayes factor and use it within Efron's multiple testing procedure. The simulation study suggests that under normal sampling model and even with small sample sizes, our approach provides false positive and false negative proportions that are less than other common multiple hypothesis testing approaches based only on p-values. The proposed procedure is illustrated in two simulation studies, and the advantages of its use are showed in the analysis of two microarray experiments. Authors F. Bertolino, S. Cabras and W. Racugno were partially supported by the Italian Ministry of Education, University and Research. M.E. Castellanos was partially supported by the Spanish Ministry of Science and Technology, under grant MTM2010-19528, CAM of Spain under grant S2009/esp-1594 and the visiting professor program of Regione Autonoma della Sardegna of Italy.