Assuming that statistics are entered consistently from the same corpus, we can take advantage of the monotonicity of the n-gram event space to place upper bounds on the frequencies of events to be retrieved from the filter prior to querying it, thereby reducing the a priori probability of a negative and consequently the error rate.
since the log-frequency BF scheme will never underestimate an item's frequency, we can apply the following inequality recursively and bound the frequency of an n-gram by that of its least frequent subsequence, We use this to reduce the error rate of an interpolated BF language model described below.