This paper considers the framework of the so-called "market basket problem", in which a database of transactions is mined for the occurrence of unusually frequent item sets. In our case, "unusually frequent" involves estimates of the frequency of each item set divided by a baseline frequency computed as if items occurred independently. The focus is on obtaining reliable estimates of this measure of interestingness for all item sets, even item sets with relatively low frequencies. For example, in a medical database of patient histories, unusual item sets including the item "patient death" (or other serious adverse event) might hopefully be flagged with as few as 5 or 10 occurrences of the item set, it being unacceptable to require that item sets occur in as many as 0.1% of millions of patient reports before the data mining algorithm detects a signal. Similar considerations apply in fraud detection applications. Thus we abandon the requirement that interest...