Concepts
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function
...One important reason for having estimation rules different from the simple x n,is that this is rather unrealistic for small samples
...0 <p <1
...This is really as much as I wish to say about estimation rules,and therefore I shall not push the technical discussion on this points any further;the interested reader should consult the readily accessible statistical literature
...Recapitulation At this point I should like to summarise the formal argument thus far so that we may reduce it to simple English
...The first point to make then,is that,we have been trying to estimate P relevance document,that is,the probability of relevance for a given document
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D 1 and D 2 can be shown to be equivalent under certain conditions
...[P x w 1 P w 1 >P x w 2 P w 2 >x is relevant,x is non relevant]D 3 Notice that P x has disappeared from the equation since it does not affect the outcome of the decision
...[R w 1 x <R w 2 x][[equivalence]][l 21 l 11 P x w 1 P w 1 >l 12 l 22 P x w 2 P w 2]When a special loss function is chosen,namely,which implies that no loss is assigned to a correct decision quite reasonable and unit loss to any error not so reasonable,then we have [R w 1 x <R w 2 x [[equivalence]]P x w 1 P w 1 >P x w 2 P w 2]which shows the equivalence of D 2 and D 3,and hence of D 1 and D 2 under a binary loss function
...This completes the derivation of the decision rule to be used to decide relevance or non relevance,or to put it differently to retrieve or not to retrieve
...Form of retrieval function The previous section was rather abstract and left the connection of the various probabilities with IR rather open
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