To summarize, query likelihood is a simple probabilistic retrieval model that directly incorporates term frequency. The problem of coming up with effective term weights is replaced by probability estimation, which is better understood
and has a formal basis. The basic query likelihood score with Dirichlet smoothing has similar effectiveness to BM25, although it does do better on most TREC collections. If more sophisticated smoothing based on topic models is used (described further in section 7.6), query likelihood consistently outperforms BM25. This means that instead of smoothing using the collection probabilities for words, we instead use word probabilities from similar documents.
The simplicity of the language model framework, combined with the ability to describe a variety of retrieval applications and the effectiveness of the associated ranking algorithms, make this approach a good choice for a retrieval model based
on topical relevance.