MÉTRICA GH

A métrica GH é uma métrica utilizada para o calculo de uma probabilidade condicional simples,

ou seja, qual a probabilidade de uma determinada variável ocorrer dada uma outra variável que

a condiciona(P(A,B)) - > Qual a probabilidade de A ocorrer se B ocorrer

Essa métrica foi criada por dois cientistas Geiger and Heckerman(GH) ela foi feita baseada em uma

outra métrica probabilística a Cooper and Herskovits(CH)

Métrica (CH)

                                          qi                                        ri           

                          g(V,C) =  Õ  {[(ri –1)!/(Nij + ri –1)!] Õ Nijk!}

                                         j =1                                       k=1                                  

                                                        qi                                        ri           

                          log( g(V,C)) =log(  Õ  {[(ri –1)!/(Nij + ri –1)!] Õ Nijk!})

                                                        j =1                                     k=1

                            

                                                        qi                                        ri           

                          log( g(V,C)) =log(  Õ  {[(ri –1)!/(Nij + ri –1)!] Õ Nijk!})

                                                        j =1                                     k=1                                              

                                               qi                                               ri    

                         log( g(V,C)) =S{ log[(ri –1)!/(Nij + ri –1)!]  + S [log(Nijk!)]}

                                               j =1                                             k=1

                                               

                                               qi                                                           ri    

                         log( g(V,C)) =S{ log[(ri –1)!] - log[(Nij + ri –1)!]  + S [log(Nijk!)]}

                                               j =1                                                      k=1

 

Substituindo   (ri –1), (Nij + ri –1), Nijk  por R , S e T   respectivamente

 

                                               qi                             ri    

                         log( g(V,C)) =S{ logR! - logS!  + S (logT!)}

                                               j =1                         k=1

                                               qi                             ri    

                         log( g(V,C)) =S{ log R! - logS!  + S (logT!)}

                                               j =1                         k=1

                                               qi         R              S            ri         T

                         log( g(V,C)) =S{ log Õ r  - log Õ s  + S [log (Õ t)]}

                                               j =1      r=1            s=1        k=1         t=1

                                               qi     R               S                    ri     T

                         log( g(V,C)) =S   {S log(r)  - S log(s)  + S   [S log(t)]}

                                               j =1   r=1             s=1              k=1   t=1

 

                                                                                                                                             cqd.

 

Metrica GH

 

                                               qi     R               S                    ri     T

                          g(V,C)  =      S   {S log(r)  - S log(s)  + S   [S log(t)]}

                                               j =1   r=1             s=1              k=1   t=1