disclosure_x_bias.arff

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StatLib/numeric/disclosure_x_bias.arff
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2009-11-10 13:09:41
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Data Used in "A BAYESIAN APPROACH TO DATA DISCLOSURE: OPTIMAL INTRUDER BEHAVIOR FOR CONTINUOUS DATA" by Stephen E. Fienberg, Udi E. Makov, and Ashish P. Sanil
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%       Data Used in "A BAYESIAN APPROACH TO DATA DISCLOSURE: OPTIMAL 
%       INTRUDER BEHAVIOR FOR CONTINUOUS DATA"
% 	by Stephen E. Fienberg, Udi E. Makov, and Ashish P. Sanil
% 
% Background:
% ==========
% In this paper we develop an approach to data disclosure in survey settings by
% adopting a probabilistic definition of disclosure due to Dalenius. Our approach
% is based on the principle that a data collection agency must consider
% disclosure from the perspective of an intruder in order to efficiently evaluate
% data disclosure limitation procedures. The probabilistic definition and our
% attempt to study optimal intruder behavior lead naturally to a Bayesian
% formulation.  We apply the methods in a small-scale simulation study using data
% adapted from an actual survey conducted by the Institute for Social Research at
% York University. (See Sections 1-3 of the paper for details oF the model
% formulation and related issues.)
% 
% The Data:
% ========
% Our case study uses data from the survey data Elite Canadian
% Decision-Makers collected by the Institute for Social Research at York
% University.  This survey was conducted in 1981 using telephone
% interviews and there were 1348 respondents, but many of these did not
% supply complete data.  We have extracted data on 12 variables, each of which
% was measured on a 5-point scale:
% 
% Civil-liberties:
% - ---------------
% C1 - Free speech is just not worth it.
% C2 - We have gone too far in pushing equal rights in this country.
% C3 - It is better to live in an  orderly  society  than  to  allow people so
%      much freedom.
% C5 - Free speech ought to be allowed for all political groups.
% 
% Attitudes towards Jews:
% - ----------------------
% A15 - Most Jews don't care what happens to people who are not Jews.
% A18 - Jews are more willing than others to use shady practices  to
%       get ahead.
% 
% Canada-US relationship:
% - ----------------------
% CUS1 - Ensure independent Canada.
% CUS5 - Canada should have free trade with the USA.
% CUS6 - Canada's way of life is influenced strongly by USA.
% CUS7 - Canada benefits from US investments.
% 
% 
% In addition, we have data on two approximately continuous variables:
% 
% Personal information:
% - --------------------
% Income - Total family income before taxes (with top-coding at \$80,000).
% Age - Based on year of birth.
% 
% 
% We transformed the original survey data  as follows in order to create
% a database of approximately continuous variables:
%  
% [A]  We add categorical  variables  (all  but  income) to increase the number
% of levels. (When necessary we reversed the order of levels of a response  to a
% question.)  The new variables are defined as follows:
% 
% Civil     = C1 + C2 + C3 + (8 - C5)
% Attitude  = A15 + A18
% Can/US    = (5 - CUS1) + CUS5 + (5 - CUS6) + CUS7
% 
% After we removed cases with missing observations and  two  cases involving 
% young children, we had a  data-base consisting of 662 observations.
% 
% [B]  In order to enhance continuity, we took the following measures:
% 
% Age:  We added normal  distributed  variates,  with  0   mean  and
%       variance 4 to all observations.
% Income: We added uniform variates on the range of $0 - $10,000 to all incomes
%         below $80,000.  Since all cases of incomes exceeding $80,000 were
%         lumped together  in  the  survey,  we simulated their values by means
%         of a t(8) distribution. Drawing values from the upper 38% tail of t(8),
%         we evaluated the values of income as $60,000 + 25,000*t(8).
% Other variables: We added  normal distributed variates, with 0 mean and
%                  variance  0.5 to the variables. 
% 
% We assume that the agency releases information about all
% variables, except for Attitudes (towards Jews), which  is unavailable to
% the intruder and is at the center of the intruder's investigation.
% 
% We denote the released data by 
% 
% 	Z = (( z(i,j) ))   with i=1,..,662; j=1,2,3,4.
% 
% We assume that the intruder's data, X, are accurate and are related to Z via
% the following transformation:
% 	x(0,j) = z(i,j)*theta(i,j) + xi(j),
% 
% where theta(i,j) is a bias removing parameter normally distributed with mean 1 
% and variance  v(j), and xi(j) is normally distributed disturbance with 0  mean
% and variance sigma2(j).   
% 
% The following table provides the values of 
% v(j), sigma2(j) used in the study:
% 
% 	                            v(j)     sigma2(j)
% 	Civil                      0.1732       25
% 	Can/US                     0.1732       25
% 	Age                        0.1732       9
% 	Income (in $10000's)       0.1732       4
% 
% 
% We first generated several realizations of the above transformation on small
% subsets of the data to ascertain the impact of the process of the error
% on the data. In Table 4-1 in the paper we present 10 records the the intruder's
% accurate data, X, and the biased and corrupted released data, Z, which we
% obtained from one realization of the transformation.
% 
% Section 4.2 of the paper contains details of the implementation of our Bayesian
% model.
% 
% Data Used in the Computations:
% =============================
% We conducted a complete simulation of the procedures for the complete set of
% 662 cases.  We considered four different scenarios for the simulation. (The
% names of datasets used in each of the scenarios appear in brackets below. The
% datasets are appended to this text.)
% 
%  * The released data contains no bias or noise (i.e. v(j)=0 and sigma2(j)=0 for
%    all j). [Z.DATA]
%  * The released data contains only noise (i.e., v(j)=0 for all j and 
%    and $sigma2(j)$ as given in the above Table). [X_NOISE.DATA]
%  * The released data contains only bias (i.e., sigma2(j)=0 for all j and v(j)
%    as given in the above Table). [X_BIAS.DATA]
%  * The released data contains both bias and noise (i.e., v(j) and sigma2(j) as
%    given in the above Table). [X_TAMPERED.DATA]
% 
% We took each individual in turn as the object of the intruder's efforts and
% carried out the calculations.
% 
% Structure of the Datasets:
% - -------------------------
% Each attached dataset consists of four space-separated columns containing the
% data on Age, Civil, Can/US and Income ($) respectively.
% 
% 
%
% Dataset: X_BIAS
%
%
% Information about the dataset
% CLASSTYPE: numeric
% CLASSINDEX: none specific
%

@relation disclosure-X_BIAS

@attribute Age REAL
@attribute Civil REAL
@attribute Can/US REAL
@attribute Income REAL

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93.99088,17.748609,7.658539,44230.13
43.84731,14.117052,11.936831,58074.50
57.83679,9.985611,10.537891,64736.50
38.23766,16.438464,10.395084,63195.30
34.11756,12.142494,9.680467,48884.28
33.14464,20.660905,7.895700,80950.57
35.39177,16.140709,11.041448,112306.93
39.99518,16.703584,8.163300,38774.80
68.08147,19.044630,8.047868,104283.44
46.13650,6.187768,10.065113,44205.52
65.04837,13.974927,10.471450,52533.41
51.55560,11.401461,6.831264,36720.32
59.88922,17.886024,18.943859,52069.92
58.77503,19.508409,10.812176,49691.23
30.23897,25.419706,2.182963,61786.85
64.77486,16.374177,7.301397,50129.51
37.45922,10.384960,5.598704,42285.02
43.51985,21.420880,7.031803,59104.48
55.96206,16.219207,8.724610,43224.20
24.66040,15.177828,8.172126,68359.07
31.11619,16.335860,9.948593,43367.14
51.23527,15.119345,9.142088,63984.42
54.01389,23.028090,7.998225,65140.55
46.00692,22.604297,6.029858,57816.09
74.06681,19.778401,5.228373,90170.06
57.16693,12.51609,7.117733,121299.50
37.22166,11.14363,9.368991,59062.25
52.94066,23.15644,9.315394,79888.12
56.36546,26.19698,8.945167,82617.26

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