" 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: Z Information about the dataset CLASSTYPE: numeric CLASSINDEX: none specific " "0" "disclosure-Z" 31.0036 58.3615 49.4349 40.8756 30.3865 21.5148 52.7983 42.5571 32.5011 82.0342 53.8209 35.45 35.9738 17.2844 47.8475 40.3432 48.942 50.7841 70.3172 40.096 71.2564 49.1559 30.1088 60.1086 73.6491 23.0957 74.5065 53.3902 60.1781 49.0703 59.3095 38.139 37.8643 40.934 48.8354 61.1532 54.8328 49.3105 33.2429 59.5954 32.7776 30.0051 36.5834 46.2388 43.8624 42.6943 39.813 30.1693 47.5691 72.0344 40.9626 65.7171 66.7765 60.8371 27.3167 32.8046 30.708 29.0028 37.5941 34.4269 17.0791 34.3645 59.2687 31.8921 37.5611 55.9898 40.2849 30.4691 66.0368 34.2131 27.3764 53.2317 45.9278 54.1808 38.0177 43.598 53.0908 29.9927 32.8793 51.4109 47.9779 35.5583 29.141 29.6195 44.6602 20.1133 46.1571 47.3507 51.1065 48.2732 38.5025 53.2833 49.3197 38.0076 53.3615 35.7549 56.6458 28.0502 24.4364 36.7415 38.4464 51.6043 36.2939 49.3156 42.526 45.0354 53.5897 50.8731 29.3276 43.2337 47.9702 44.6505 40.8824 60.2047 65.1552 32.2022 37.1728 30.4406 35.8637 30.6316 42.6076 57.7396 31.3831 58.1354 35.8288 68.8825 46.7065 31.1265 42.6687 31.6108 56.331 39.3374 48.9115 56.4765 56.266 58.6993 25.3111 57.0078 53.2853 60.5304 33.5588 43.6155 35.0767 39.5785 37.4968 42.5291 50.0261 37.9267 44.0767 45.4356 40.4984 61.0541 35.7904 28.6115 38.6191 30.4302 34.2519 47.0255 36.0865 36.1636 51.2764 34.3374 39.0298 14.5449 40.8243 56.7861 53.0299 31.4988 50.2341 53.9918 34.0723 56.196 60.2291 38.6807 22.1778 45.0585 39.8498 25.4305 44.7656 73.3673 56.3736 41.0308 45.6459 56.1439 34.7905 44.7584 42.7917 55.4171 23.3213 42.295 51.2786 16.7886 26.2422 27.756 61.6023 74.0202 50.8826 54.2211 35.3178 29.0586 29.5181 55.3401 42.9132 51.7228 48.8175 37.5191 31.5446 65.7917 48.0201 58.5623 44.4871 14.5795 58.3122 40.2588 51.2914 69.5723 53.572 44.9688 41.5281 28.7646 35.0527 38.6193 48.0554 24.5027 25.7073 54.2629 48.959 45.0932 38.2903 41.7139 52.0312 41.7135 54.0999 65.2101 46.4079 52.4793 53.4575 56.0257 52.0503 93.0684 44.5446 67.7523 38.0118 57.7712 63.8483 44.4782 35.7237 60.5194 58.2007 57.496 40.1502 33.1316 61.1682 44.7241 23.1977 44.6663 52.7552 26.2309 70.2956 62.5918 42.1919 40.4478 54.3031 64.4944 56.6593 48.9814 28.3315 51.7456 37.0818 29.7513 42.7251 55.6016 70.2845 55.6793 38.509 49.3152 69.7461 43.5284 31.9415 19.3804 27.0884 39.3895 55.0253 13.6345 14.8075 27.2985 54.6379 37.2194 29.9059 34.2316 57.4236 56.7221 52.9421 62.2051 59.8002 46.7338 63.6733 34.9797 54.8173 14.5955 34.1725 24.9502 36.7774 50.6506 76.2365 33.474 39.2487 15.1181 34.9117 16.5236 29.7111 27.7019 58.2325 23.8382 52.0517 48.7015 52.1087 64.7632 26.7035 40.9338 26.282 45.4611 36.5862 38.7788 22.6336 30.0977 19.0932 30.0619 26.2614 35.6999 52.9805 44.865 32.8632 32.9136 32.8348 26.4878 13.358 36.0884 36.7333 61.2792 43.5326 29.3158 43.6663 38.4668 69.4455 35.6456 28.0112 27.2208 42.8062 38.4935 35.178 28.7975 36.3029 8.24574 53.7241 51.0068 19.8019 34.6468 39.0937 31.5581 40.633 15.4643 39.5607 17.8051 15.7956 16.3712 41.1335 38.2574 40.2756 47.7856 45.045 24.298 32.003 29.6021 34.5685 34.2642 30.876 21.1334 22.3642 12.1879 28.0844 20.8008 29.8858 29.1609 21.7268 50.1482 28.2435 36.9189 20.5964 78.7453 18.8253 44.2498 45.4391 68.2976 9.13272 44.2786 38.9043 36.11 18.3747 39.5534 54.9354 47.2167 26.3631 21.8845 23.4885 33.9036 39.9907 31.9516 31.8448 20.9821 16.3956 48.0376 19.5111 28.2813 26.3969 27.692 25.3553 24.2833 15.4303 55.9808 32.7412 36.1192 37.497 28.5326 43.0735 25.2787 15.2815 37.9868 25.5965 22.1848 50.4227 38.8559 33.5308 18.4319 56.9755 28.9978 27.438 34.4965 48.1103 27.0701 30.1586 28.4537 16.9893 49.1107 56.9506 32.9216 46.7131 65.6233 18.7979 50.0063 61.7599 86.6564 27.4597 50.7692 46.0104 48.9263 29.4061 43.4882 67.9443 39.1813 42.4411 60.6224 20.9585 40.1842 23.622 26.4685 29.5228 37.3448 27.602 26.0713 13.4175 21.9903 48.9259 36.5812 54.0202 50.8168 17.2121 21.6974 16.9185 44.4046 30.8094 38.0239 40.9679 28.6575 34.4354 41.431 31.5418 37.4679 38.301 54.3516 30.1698 38.1373 24.9041 45.4683 5.30908 44.6183 66.577 22.3056 37.7673 48.7327 40.6537 45.4238 43.4793 84.541 58.6281 48.0152 59.8585 49.1978 47.2729 45.0325 35.7621 25.1042 29.702 25.1471 39.4605 34.9855 10.5191 21.6388 51.8945 23.1702 49.6756 67.2874 45.0139 49.7003 38.4101 14.4445 23.1793 52.5971 16.3728 22.3684 44.5875 48.8001 48.1333 73.9298 54.6935 57.3607 54.7468 45.8372 36.5168 42.2494 78.332 46.9744 37.6475 38.0702 53.9548 50.6016 48.5477 56.7445 27.0765 69.5987 41.5488 34.1171 53.83 49.3495 62.0799 71.0153 66.1778 58.0138 68.9779 87.4219 69.0604 53.4943 60.773 37.141 76.9411 27.594 26.6993 40.194 44.8108 56.9331 67.3363 68.1672 51.5518 35.2971 40.8775 31.3525 20.8048 32.429 56.9458 49.7972 41.2717 41.2037 26.5908 36.9401 29.7136 80.6023 24.8348 53.9361 40.6141 43.0688 42.1751 43.7242 23.0466 45.7103 39.5234 29.2722 41.6976 52.2637 36.8166 54.1334 79.5876 38.7679 33.7397 54.2971 29.7928 31.8526 72.3268 29.6401 32.608 65.0726 42.5278 34.2956 31.0722 50.3411 59.3226 50.0817 57.4995 49.9621 48.1774 54.7575 54.2296 53.0586 52.5986 89.0694 51.7022 55.1168 46.2084 34.4247 60.117 34.6461 35.8018 65.5874 12.1416 93.3807 45.3852 59.3356 37.3927 35.7437 33.9531 34.9874 41.4036 66.8231 45.9017 64.7722 52.1143 59.4581 59.1975 30.4524 65.8459 36.5825 42.9177 57.3563 24.5218 30.7051 52.5646 52.1954 46.748 71.772 63.049 36.0142 51.997 59.8536 23.2669 17.7601 14.584 16.5454 14.0927 14.6278 16.2054 21.2623 20.8397 18.7095 24.9092 14.9864 18.2698 19.2816 21.9185 17.0729 23.2828 20.5517 20.4365 16.5574 22.0532 25.2985 20.5194 21.4254 23.0483 23.1428 26.6755 18.147 23.9173 15.7657 22.5068 23.4555 24.3587 17.9462 21.7873 15.4596 21.481 23.7948 19.6217 20.1955 17.3604 20.7241 20.623 24.3239 23.7402 19.549 19.3315 18.7583 19.2721 21.7376 19.0252 21.57 17.3168 16.9944 18.364 12.071 11.0736 10.808 18.3053 21.6165 20.1779 17.9097 19.403 16.9841 19.205 21.6252 14.2111 21.1559 21.203 24.8147 16.9752 26.2803 16.018 20.0823 21.1553 12.0541 18.5457 20.6895 19.3303 27.1745 13.4511 19.4097 13.933 17.2811 21.0597 15.4328 20.1889 21.0383 20.1309 10.3783 19.2983 12.421 19.5302 22.6231 8.13724 21.9678 23.8379 16.4253 12.8664 28.7013 17.499 23.2566 28.2196 12.7544 15.2599 15.9106 17.4792 24.0916 19.5291 20.9966 20.2342 27.3285 24.6681 20.1988 21.9496 14.8269 22.7837 25.1385 19.8407 16.0195 21.6023 12.3059 15.6366 18.1064 19.424 22.0902 16.8852 21.2499 18.2725 11.2343 26.1855 18.0021 29.1331 17.9839 9.46595 18.4361 17.8456 21.8643 16.5476 22.4608 9.94441 23.2258 20.8637 21.3864 19.4436 13.5095 22.0019 22.0565 18.7237 6.67357 17.009 20.5656 17.4603 12.2198 22.2765 15.1755 17.393 12.6681 23.1413 21.4825 18.1549 8.79327 22.9896 18.7893 15.8666 19.6898 19.5261 19.0249 19.7877 12.5789 14.7071 16.5035 12.4947 22.0787 14.6422 24.094 19.7034 15.4295 23.9739 11.7332 9.9064 16.898 15.7765 21.0365 14.7825 16.6809 19.9069 10.9502 13.1889 20.4297 15.2457 9.06328 17.0899 20.453 19.2475 17.0406 22.1558 14.426 27.4235 14.891 18.3535 19.2312 17.7015 19.4164 15.3399 10.7125 22.9572 11.8862 17.3746 21.9673 6.31506 11.2378 23.1035 16.0208 21.3106 14.5728 15.9184 23.2292 23.4864 21.3277 14.9794 15.3222 22.3675 14.7292 20.8084 22.4126 11.6039 15.2662 18.4846 15.8596 18.6115 14.9375 19.3864 20.5934 20.1098 17.4724 18.4564 15.2693 15.0397 19.4964 23.5136 14.7208 15.6107 19.5648 22.1701 16.4659 20.9614 25.5369 21.9407 9.35638 26.5823 15.5013 21.8714 13.6957 16.3269 13.3503 6.07204 9.11729 15.6698 17.1307 12.3766 15.2022 12.82 18.6693 27.1642 20.3904 20.0739 20.7315 22.4119 15.5306 13.6189 15.7725 24.1127 18.8217 18.1483 22.5076 12.276 21.6318 24.6694 11.8601 20.4306 22.501 17.3778 14.6509 17.9023 24.0572 23.6477 16.1781 24.7437 20.4442 23.8985 17.7697 16.3422 19.9429 22.9552 15.6894 17.6211 10.6776 21.6909 19.8282 13.0225 16.0517 20.2461 23.1959 17.9905 22.7482 20.8898 9.56674 6.67954 14.999 14.8119 17.1098 25.5076 26.048 18.0265 21.1008 22.716 23.2638 18.3547 19.3137 20.9986 24.6226 22.8512 12.3155 24.2697 18.5333 21.2238 20.5232 18.5259 14.0642 19.592 18.2824 18.4542 19.6808 12.1851 18.8722 20.7817 18.9932 18.6389 18.7974 17.1951 15.6822 18.9776 23.0493 11.1586 14.7387 14.1146 20.3285 24.1461 21.1334 17.1389 24.7965 17.5391 19.5823 24.1172 16.0404 19.119 14.8761 15.1858 10.1721 19.7361 17.5125 22.4506 14.6493 13.3923 19.4272 18.3293 13.5135 15.2746 24.3833 14.1008 4.79777 19.6911 24.22 23.9629 25.0372 10.6724 13.4407 15.7544 17.6019 19.4108 14.3173 13.2411 18.3574 22.5171 22.41 19.389 16.5905 20.9454 16.1126 18.9345 18.7582 16.5302 17.9751 18.3697 16.3624 21.9565 15.5288 18.7044 17.8986 20.7685 20.6996 12.9103 17.3539 14.1593 22.6485 17.6662 16.494 22.0782 16.2188 19.0106 19.8774 20.5217 13.8991 21.4048 19.0587 16.3005 15.9954 21.4861 19.4555 12.9756 18.9902 20.9253 21.0698 18.2465 20.0555 14.4647 18.7608 16.9425 14.8234 24.561 15.4038 15.4548 26.3903 23.9497 24.5827 15.8734 17.4227 22.2943 14.357 4.82449 21.395 21.7492 17.7682 21.8754 20.8175 20.7757 18.1686 24.2127 16.1927 25.206 20.7413 16.0936 15.9694 19.4193 20.8475 19.6938 17.3992 22.0932 19.8667 24.2467 19.4019 17.3191 19.3392 15.5442 22.0688 19.694 21.6479 21.288 23.5144 20.562 20.291 17.011 16.402 12.6376 17.1201 17.1627 17.0703 23.6792 21.2058 22.4036 17.7092 8.34471 18.14 16.1738 17.9793 21.8581 26.2897 17.8481 22.4182 20.9021 22.3538 21.9084 22.025 26.0577 13.5034 21.2556 15.2608 16.6016 18.0837 22.6204 11.9251 19.3663 18.6609 22.1001 19.1441 20.1233 15.7153 18.8919 17.9478 17.6218 13.9167 23.3042 21.1925 18.4889 17.8003 21.6307 16.8437 15.7571 14.4537 20.2894 20.2848 6.02411 20.0464 20.4701 15.6393 17.496 24.7883 18.8587 24.7891 21.4843 28.7287 13.7442 14.72 15.1191 14.6659 11.4993 14.1001 6.80669 8.56396 6.10581 12.1398 8.62311 8.33367 5.99211 24.5704 11.0011 10.6048 19.2206 17.6479 10.0793 11.8198 21.945 14.7657 24.4385 12.1782 14.2957 9.04292 23.6258 26.631 6.72379 14.1668 19.5962 18.2863 14.0502 6.85552 19.4473 17.5045 11.1511 17.126 14.4365 8.57495 6.94706 21.5831 14.4725 5.6807 16.264 12.9921 12.7358 16.6432 18.1535 13.6839 21.1123 6.54604 9.66702 21.5609 17.6055 14.7916 13.9614 12.322 10.0661 9.62355 22.4264 12.0722 25.4704 19.5151 19.1044 16.2025 13.4714 11.5864 10.2047 19.3971 19.6568 21.5128 15.4718 12.6532 10.806 20.947 10.8768 11.9778 14.4373 10.0563 22.3789 16 16.0714 19.8888 13.6993 19.3652 10.9613 16.3432 8.53224 10.2366 23.5455 16.7331 20.998 24.3336 10.0547 15.5073 19.2801 18.5691 9.86567 14.349 16.2231 17.4922 14.1985 10.3657 15.8643 12.5448 19.5606 16.2461 16.4902 18.2821 6.11869 14.055 12.4391 17.8618 19.6181 25.1577 16.5019 10.4418 21.5291 16.294 14.7324 16.718 14.9328 23.1001 23.5319 19.9863 12.4682 10.861 22.3037 25.3856 7.2308 4.48085 7.63242 9.44896 10.8281 14.206 5.88176 5.63254 14.8433 7.30971 11.1784 8.15064 9.7015 11.7709 9.64362 9.56918 7.0514 3.19045 8.28228 7.5925 4.74507 9.40216 9.7619 8.32909 8.91468 8.28364 5.60768 9.13196 8.10808 8.047 16.31 9.24219 5.07225 10.7898 7.37043 12.0158 9.21009 6.10541 8.77989 10.6432 7.75334 12.0474 11.447 4.46272 9.87681 5.31879 10.3983 11.6002 9.87405 6.55889 11.6471 11.8369 12.036 11.6674 7.86162 4.00571 5.30105 9.06707 4.02582 11.538 8.94857 11.1541 6.94356 7.4516 6.58665 9.48103 11.6217 8.37223 7.65446 9.82317 9.04212 12.119 4.80196 8.73789 4.20877 11.7457 11.7962 7.72954 8.94066 18.3299 11.1321 9.94524 8.97143 12.038 13.0705 9.89517 9.89287 10.7222 7.55944 12.4644 7.38819 7.89504 8.82771 12.5179 6.99412 9.81363 5.93552 6.25448 6.41657 8.1298 13.7887 9.16286 8.96365 4.90109 3.75303 9.67398 6.59321 7.94012 10.9618 6.99948 7.15481 14.4821 11.9888 10.2738 10.5857 9.21841 7.31516 12.5623 6.63511 7.51452 17.0867 9.00786 10.5255 16.4866 7.30962 14.8644 9.01801 11.6975 9.761 6.70918 9.93447 11.848 9.50142 4.97203 12.3451 11.034 7.29637 8.63718 11.538 13.1847 11.1127 9.68971 6.41271 10.5674 7.1814 6.11971 3.77773 5.76418 7.39069 11.401 5.81838 8.52238 11.6337 8.81026 7.37814 9.92232 8.57501 12.7004 2.60821 8.22758 12.7123 9.92647 11.5816 7.40259 13.0356 8.02219 12.1091 8.89615 5.53303 13.0956 4.89592 13.3857 7.50179 10.6182 7.21792 9.99022 11.6991 7.09361 5.93367 10.9955 5.21127 7.65252 10.1003 11.8828 6.67772 8.76647 11.6037 8.8799 7.66212 8.40832 9.45157 11.9973 11.8377 11.3506 11.3616 10.0408 9.48959 11.4462 8.19675 8.47255 7.18133 9.58297 7.06344 9.00558 8.73985 11.296 12.2594 11.8444 7.79675 9.25762 9.81171 8.27931 6.08624 7.44575 5.45586 12.1027 7.84454 14.8415 10.5261 12.0997 14.0928 6.47276 10.6641 8.9337 12.411 10.9894 5.82876 8.00859 6.21186 7.77361 8.2645 9.32729 5.54141 7.16843 11.2877 11.6575 13.3872 9.6829 12.4018 13.4521 8.2341 14.866 9.08302 10.0245 11.5347 16.2829 8.92008 7.83099 9.32822 9.65729 12.4509 8.24169 10.0631 7.69702 6.48415 11.1899 12.0799 7.32945 16.6458 11.9461 11.2018 10.7317 12.6171 10.1015 10.5554 7.00198 13.1669 12.2888 9.74591 12.6694 4.82553 7.19259 11.0458 10.3699 17.0524 9.17828 8.4917 10.871 9.43186 11.6221 6.84555 11.0766 11.967 11.5948 12.4116 9.90057 12.341 8.59113 6.57858 12.0671 11.8841 8.54153 8.72545 6.33177 11.148 12.9838 10.365 3.58906 10.1829 13.5964 13.4799 7.84826 9.4723 8.34073 10.7252 8.40201 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