Because estimators like that for the mutual information and chi-squared involve what is best described as subset-sums, notation is now introduced to handle this situation.
The convention for indices is i, j, ij, etc. The generalization to two dimensional indices is transparent for the following notation.
Subsets of indices will be denoted using 
and 
, while the full set of indices will be denoted by 
. Union and intersection are denoted by 
and 
. Set subtraction is denoted by 
indicating the elements in not in . Two sets of indices having non-empty intersection will be called pairwise overlapping. More complicated index set intersection structure also appears. The pairwise overlap case may also occur where one index set is contained in the other, and this will be denoted the contained overlap case.
There are two basic entities that have to be summed over subsets of indices, the counts, 
, and the probabilities, 
. Define 
, 
, where 
. Also needed are 
, 
, 
and 
. The sum of all counts in the form 
is useful.
Exponents will involve the variables 
or 
, with being variables to be differentiated with respect to, and being associated with the subset . The sum of these variables will be denoted by 
.
The variables of transformation will be taken to be s, t, (associated with ), and 
.
Hypergeometric functions 
and 
are given in appendix 9.4, along with the definition of the Pockhammer symbol 
.
The product of gamma functions 
is useful.
The prior is suppressed, The subscript 
on an integral indicates that the surface of integration and weight of integration are those set by the prior, see section 9.3.6.