Conflicts Map To Kernels by Minimal Set Covering Conflicts MI=U M2=U Al=U MI=U. M2=U Al=U A2=U M3=U MI=U M3=U A2=UMI=U Al=U MI=U Ml=U∧A2=U M2=U∧M3=U Ranking Diagnoses by Probability ()=p Assume Failure and Observation Independence y=vi∈C p(clx,=v Obs)=P(x,=v lc)p(c Obs) Bayes Rule P(X=V I c)estimated using Model normalization If previous Obs, c and 4 entails z=V Then p(z=v c)=1 If previous obs, c and entails x <> V Then p(z=V c)=0 If y consistent with all values for z Then p(x=v c)is based on priors E.g. uniform prior= 1/m for m possible values of x7 A2=U M1=U A1=U M3=U A1=U, A2=U, M1=U, M3=U A1=U M1=U M2=U A1=U M1=U M1=U š A2=U M2=U š M3=U Conflicts Map To Kernels by Minimal Set Covering A1=U, M1=U , M2=U Conflicts 8 Ranking Diagnoses by Probability () ( ) i ij i ij yv c pc py v  Assume Failure and Observation Independence P(xi =vij | c) estimated using Model: ƒ If previous Obs, c and Ȍ entails z = v Then p(z = v | c) = 1 ƒ If previous obs, c and Ȍ entails x <> v Then p(z = v | c) = 0 ƒ If Ȍ consistent with all values for z Then p(x = v | c) is based on priors ƒ E.g., uniform prior = 1/m for m possible values of x ( |)(| ) (| , ) ( ) i ij i ij i ij p x v c p c Obs p c x v Obs px v Bayes’ Rule Normalization