This is the standard disputed
paternity/maternity case given that genotype of the second parent is
available. The number of children involved can be arbitrary. 

The difference with the previous
scenario is that the second parent is untyped and only genotypes of the
children are available. 

Genotypes of one or both parents
are known for Person X. 

Genotypes of one or more
siblings of Person X are known. Optionally the genotypes of one or both
parents can be known as well. 

Generalization of the previous
case. Analysis can include additionally the genotypes of half siblings. 

Typical scenario for missed person case. Any combination of the genotypes of children/parent(s)/sibling(s)/spouse of Person X can be used.  
Single Person X Random Alternative  This option is the generalization of all scenarios above and should be used if your case does not fit any predefined templates. It is assumed that we have a single person (Person X) and an arbitrary group of other persons G. Hypothesis Hp states some specific relationships between Person X and G; alternative hypothesis Hd declares that Person X is unrelated to G. 
General Case 
This
option should be used if there is no “central person” (i.e. Person X)
at all: we
just have a group of persons and make two different assumptions Hp and
Hd about
kinship relationships inside this group. 
Besides Likelihood Ratio LR and Match Probability MP (usually in the context of
paternity analysis the exclusion probability 1MP is used),
Grape also calculates Pvalues
(or observed significance levels)
for both
hypotheses. Pvalues analysis is
one of the most
classical and well known approach in hypotheses testing in mathematical
statistics. It was used before in connection with DNA
typing (see, for example, exact tests for loci independence Evett
I.W., Weir B.S. Interpreting DNA
Evidence, Sinauer Associates, MA,