Thank you very much Michael for your answer.
Below the extra information you asked for, and a sample result

QUERY INFORMATION
query=covid
back query = *:*
fore query = mitochondria
sample gene id ="57506" / "54205"

facet code:
"json.facet": "{'titles_gene': {'type': 'terms', 'field': 
'titles_gene_pubtator_annotation_ids', 'limit': 10, 'sort': {'rtitles0': 
'desc'}, 'facet': {'rtitles0': 'relatedness($fore,$back)'}}

CARDINALITY
q=157120
back=157120
fore=321385
fore & back=343

"57506" & back=8
"57506" & fore & back=5

"54205" & back=5
"54205" & fore & back=5

RESULTS
titles_gene
        "val": "57506",
        "count": 8,
        "rtitles0": {
          "relatedness": 0.69182,
          "foreground_popularity": 1e-05,
          "background_popularity": 1e-05
        }
abstracts_gene
        "val": "54205",
        "count": 5,
        "rabstracts0": {
          "relatedness": 0.94975,
          "foreground_popularity": 0.00025,
          "background_popularity": 0.00043
        }



Here it looks like that the fpopularity and bpopularity are the same for 
titles_gene (but I expected 5/343 and 8/157120  instead..)
but the relatedness of 0.69182 (it should range between -1 and 1) suggests me 
that "57506" is strongly "characteristic"
(meaning that it is occourring more in the fore than in the back, that is a 
superset of fore)
to the fore corpus with respect to the back corpus.


I would like to ask:

  1.  is my interpretation of relatedness correct?
  2.  why foreground_popularity and background_popularity are like this?
  3.  how should I change my json.facet query to require a min_popularity? 
should this solve the strange relatedness values?
  4.  is it possible to 'test' (statistically) the significativity of a 
z-score, like we do with a p-value?


thank you
D


Danilo Tomasoni

Fondazione The Microsoft Research - University of Trento Centre for 
Computational and Systems Biology (COSBI)
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