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Gi, i 1, 2, ., s, are the usual constraints associated with iterative proportional fitting, then each conditional maximization is in closed form. if the constraints defining the subregion r are vlpsoh wkhq hdfk ri wkh v wkdw sxoo vxffhvvlyh hvwlpdwhv edfn wr wkh erxqgdu\ ri 5 duh dovr lq closed form. the initiao hvwlpdwh 0 must be in r. there is no restriction to r, then the emh algorithm corresponds to the mcecm algorithm of meng and rubin 1993 ; . rather than find a maximum at each cm-vwhs lw lv vxiilflhqw wr ilqg p + 1 gliihuhqw iurp p so that the likelihood lqfuhdvhv 7r dvvxuh wkdw vrph p + 1 duh gliihuhqw iurp p, computer code should monitor that the likelihood strictly increases on some of the cm-steps. 3. record linkage background this section contains background on the previous applications of the em to give insight into why the new methods were developed. the first subsection summarizes earlier em-applications to record linkage and the second describes the empirical data. 3.1. previous applications of em in most record linkage applications, parameter estimates associated with equation 1.1 ; have been obtained under a conditional independence assumption. when conditional independence is assumed winkler 1988, jaro 1989, winkler 1989a, b ; , the em algorithm does not yield accurate estimates of the parameters associated with the underlying probability distributions. if such parameters are used, then decision rules are not optimal and error rates can not be accurately determined. to improve decision rules, independent probabilities have been adjusted based on prior knowledge of similar files winkler and thibaudeau 1991 ; . the main reason that existing parameter-estimation procedures fail to yield optimal decision rules is that the conditional independence assumption is not valid. thibaudeau 1993 ; observed that, when files contain name and address information, strong dependencies between agreements on fields such as surname, house number, street name, and phone number occur on the set on nonmatches u. winkler 1992 ; showed that, instead of ahb naturally dividing into the desired two classes m and u, ahb can be naturally partitioned into three classes: c1- matches agreeing on name and address, c2- nonmatches agreeing on address, and c3- nonmatches not agreeing on address. in the decision rules, classes c2 and c3 are combined into u. the primary reason the 2class em procedure fails is that it divides the set of pairs into those agreeing on address and those not. if the 3-class em algorithm is applied under the independence assumption, reasonable decision rules are obtained when matching decision thresholds are obtained manually winkler, 1992 ; . error rates, however, cannot be estimated accurately. an alternative error-rate estimation procedure belin and rubin 1993, rubin and belin 1991 ; can yield accurate estimated false match rates winkler and thibaudeau 1991 ; in some cases but is not applicable to the situations of this paper. winkler 1992 ; applied 3-class em algorithms under models in which all 3-way interactions were allowed. while the interactions gave dramatically lower chi-square values and the overall fits as given by the estimated cumulative probability distributions appeared acceptable, both probability estimates for individual agreement patterns and the estimated proportion of pairs in class c1 could differ substantially from the true values. the em-type procedures arbitrarily classify sets of pairs into classes according to the variables that are agreeing in the patterns and according to interactions being fit. when a set of matching variables contains many associated 6.
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Ight mega-high rollers arrived in style at the ritzy borgata casino the first week of june. they were all packing, loaded to the gills with cartridges of cash, ready to attack the high-stakes hold'em games spread across the floor of the borgata's giant texas poker rules room. their plan was to fatten up their bankrolls and then invade the tables at atlantic city's richest poker tournament, the borgata summer open, which was to begin in two weeks. the championship event boasted a , 000 entry fee and a cool half-million to the winner. and there would be more lucrative side games running parallel to the tournament. but the most lucrative game of all was high above the borgata's poker room, its existence made known by two classy grifters who carefully selected these eight high rollers to be their victims. one by one they told them of a super high-stakes cash game taking place in a penthouse suite. the game was open to those select players who had both the requisite bankroll, at least 0, 000 cash, and the.
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