Bayesian networks for imputation

Summary.  Bayesian networks are particularly useful for dealing with high dimensional statistical problems. They allow a reduction in the complexity of the phenomenon under study by representing joint relationships between a set of variables through conditional relationships between subsets of these variables. Following Thibaudeau and Winkler we use Bayesian networks for imputing missing values. This method is introduced to deal with the problem of the consistency of imputed values: preservation of statistical relationships between variables ( statistical consistency ) and preservation of logical constraints in data ( logical consistency ). We perform some experiments on a subset of anonymous individual records from the 1991 UK population census.     

A Mixed Approach for Data Fusion of HBS and SILC

Social Indicators Research - This paper presents an effective procedure for matching data from the Italian Household Budget Survey (HBS) and the Survey on Income and Living Conditions (SILC),...     

Estimation of contingency tables in complex survey sampling using probabilistic expert systems

In this paper we explore the possibility to use a particular class of models, known as probabilistic expert systems, to define two classes of estimators of a contingency table in case of stratified sampling designs. The two classes are characterized by the different role of the sampling design: in the first, the sampling design is treated as an additional variable; in the second, it is used only for estimation purposes by means of the survey weights. The bias/variance trade off of these estimators is analyzed and the consequences of model misspecification are illustrated. Furthermore, it is shown that the Horvitz–Thompson estimator belongs to both classes of estimators. It comes out that the Horvitz–Thompson estimator is almost always inefficient but robust. Monte Carlo simulations illustrate the efficiency of the proposed estimators.     

How far from identifiability? A systematic overview of the statistical matching problem in a non parametric framework

Statistical matching consists in estimating the joint characteristics of two variables observed in two distinct and independent sample surveys, respectively. In a parametric setup, ranges of estimates for non identifiable parameters are the only estimable items, unless restrictive assumptions on the probabilistic relationship between the non jointly observed variables are imposed. These ranges correspond to the uncertainty due to the absence of joint observations on the pair of variables of interest. The aim of this paper is to analyze the uncertainty in statistical matching in a non parametric setting. A measure of uncertainty is introduced, and its properties studied: this measure studies the “intrinsic” association between the pair of variables, which is constant and equal to 1/6 whatever the form of the marginal distribution functions of the two variables when knowledge on the pair of variables is the only one available in the two samples. This measure becomes useful in the context of the reduction of uncertainty due to further knowledge than data themselves, as in the case of structural zeros. In this case the proposed measure detects how the introduction of further knowledge shrinks the intrinsic uncertainty from 1/6 to smaller values, zero being the case of no uncertainty. Sampling properties of the uncertainty measure and of the bounds of the uncertainty intervals are also proved.