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GraphicalModels :: identifyParameters

identifyParameters -- solving the identifiability problem: expressing each parameter in terms of covariances

Synopsis

Description

If H#p contains a linear equation a*p+b where a is always nonzero, then p is identifiable.

If H#p contains a linear equation a*p+b where a may be zero, then p is generically identifiable.

If H#p contains a polynomial in p of degree d, then p is algebraically d-identifiable.

If H#p does not contain any polynomial in p, then p is not generically identifiable.
i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}})

o1 = MixedGraph{Bigraph => Bigraph{a => set {d}}   }
                                   d => set {a}
                Digraph => Digraph{b => set {c, d}}
                                   c => set {d}
                                   d => set {}
                Graph => Graph{}

o1 : MixedGraph
i2 : R = gaussianRing G

o2 = R

o2 : PolynomialRing
i3 : H = identifyParameters(R,G)

o3 = HashTable{l    => ideal (s   , s   , l   s    - s   )                                                                        }
                b,c            a,c   a,b   b,c b,b    b,c
                                               2
               l    => ideal (s   , s   , l   s    - l   s   s    + s   s    - s   s   )
                b,d            a,c   a,b   b,d b,c    b,d b,b c,c    b,d c,c    b,c c,d
                                               2
               l    => ideal (s   , s   , l   s    - l   s   s    - s   s    + s   s   )
                c,d            a,c   a,b   c,d b,c    c,d b,b c,c    b,c b,d    b,b c,d
               p    => ideal (s   , s   , p    - s   )
                a,a            a,c   a,b   a,a    a,a
               p    => ideal (s   , s   , p    - s   )
                a,d            a,c   a,b   a,d    a,d
               p    => ideal (s   , s   , p    - s   )
                b,b            a,c   a,b   b,b    b,b
                                                      2
               p    => ideal (s   , s   , p   s    + s    - s   s   )
                c,c            a,c   a,b   c,c b,b    b,c    b,b c,c
                                               2                     2                              2      2
               p    => ideal (s   , s   , p   s    - p   s   s    - s   s    + 2s   s   s    - s   s    - s   s    + s   s   s   )
                d,d            a,c   a,b   d,d b,c    d,d b,b c,c    b,d c,c     b,c b,d c,d    b,b c,d    b,c d,d    b,b c,c d,d

o3 : HashTable

See also

Ways to use identifyParameters :