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Nowadays there is increasing availability of good quality official statistics data. The construction of multivariate statistical models possibly leading to the identification of causal relationships is of interest. In this context Bayesian networks play an important role. A crucial step consists in learning the structure of a Bayesian net- work. One of the most widely used procedures is the PC algorithm consisting in carrying out several independence tests on the available data set and in building a Bayesian network according to the tests results. The PC algorithm is based on the irremissible assumption that data are independent and identically distributed. Unfortunately, official statistics data are generally collected through complex sampling designs, then the aforementioned assumption is not met. In such a context the PC algorithm fails in learning the structure. To avoid this, the sample selection must be taken into account in the structural learning process. In this paper, a modified version of the PC algorithm is proposed for inferring causal structure from complex survey data. It is based on resampling techniques for finite populations. A simulation experiment showing the robustness with respect to departures from the assumptions and the good performance of the proposed algorithm is carried out.

The goal of statistical matching, at a macro level, is the estimation of the joint distribution of variables separately observed in independent samples. The lack of joint information on the variables of interest leads to uncertainty about the data generating model. In this paper we propose the use of graphical models to deal with the statistical matching uncertainty for multivariate categorical variables. The use of Bayesian networks in the statistical matching context allows both to introduce extra sample information on the dependence structure between the variables of interest and to use such an information to factorize the joint probability distribution according to the graph decomposition of a multivariate dependence in lower dimension components. This representation of the joint probability distribution, taking advantage of local relationships, allows to simplify both parameters estimation and statistical matching quality evaluation in a multivariate context. A simulation experiment is performed in order to evaluate the performance of the proposed methodology with and without auxiliary information, as well as to compare it with the saturated multinomial model, in terms of uncertainty reduction. Finally, an application to a real case is provided. Results show a considerable improvement in the quality of statistical matching when the dependence structure is taken into account.

In this paper a procedure for measurement error correction based on nonparametric Bayesian networks is proposed. The performance of the proposed method is evaluated using a validation sample collected by Banca d’Italia and a major Italian bank group to investigate the measurement error mechanism in the main financial variables amounts observed in the Banca d’Italia survey on Household Income and Wealth. Specifically, in this paper attention is focused on the bond amounts. By means of Uninet’s programmatic engine working directly from R, data can be corrected unit by unit by sampling from the nonparametric Bayesian network. Thanks to the validation sample, the distances between the true and the imputed values are computed and the procedure is evaluated.

In this paper Object-Oriented Bayesian networks are proposed as a tool to model measurement errors in a categorical variable due to respondent. A mixed measurement error model is presented and an Object-Oriented Bayesian network implementing such a model is introduced. The insertion of evidence represented by the observed value and its propagation throughout the network yields for each unit the probability distribution of the true value given the observed. Two methods are used to predict the individual true value and their performance is evaluated via simulation.

In this paper the quality of data produced by national statistical institutes and by governmental institutions is considered. In particular, the problem of measurement error is analysed and an integrated Bayesian network decision support system based on non parametric Bayesian networks is proposed for its detection and correction. Non parametric Bayesian networks are graphical models expressing dependence structure via bivariate copulas associated to the edges of the graph. The network structure and the misreport probability are estimated using a validation sample. The Bayesian network model is proposed to decide: i) which records have to be corrected; ii) the kind and amount of correction to be adopted. The proposed correction procedure is applied to the Banca d’Italia Survey on Household Income and Wealth and, specifically, the bond amounts are analysed. Finally, the sensitivity of the conditional distribution of the true value random variable given the observed one to different evidence configurations is studied.

In this paper we propose to use the object-oriented Bayesian networks (OOBNs) architecture to model measurement errors in the Italian survey on household income and wealth (SHIW) 2008 when the variable of interest is categorical. The network is used to stochastically impute microdata for households. Imputation is performed both assuming a misreport probability constant over all the population and learning a Bayesian network for estimating such a probability. Finally, potentialities and possible extensions of this approach are discussed.

In this paper we propose to use the object-oriented Bayesian network (OOBN) architecture to model measurement errors. We then apply our model to the Italian survey on household income and wealth (SHIW) 2008. Attention is focused on errors caused by the respondents. The parameters of the error model are estimated using a validation sample. The network is used to stochastically impute micro data for households. In particular imputation is performed also using an auxiliary variable. Indices are calculated to evaluate the performance of the correction procedure and show that accounting for auxiliary information improves the results. Finally, potentialities and possible extensions of the Bayesian network approach both to the measurement error context and to official statistics problems in general are discussed.