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ADDITIONAL EXAMPLES Bayes Rule; Conditional Probabilities Model: Bayes MODEL: SETS: ! Computing probabilities using Bayes rule; ACTUAL/1..3/:MPA;!Marginal probability of actual; FCAST/1..3/:MPF;!Marginal probability of forecast; FXA(FCAST, ACTUAL): CAGF, !Conditional prob of actual given forecast; CFGA, !Conditional prob of forecast given actual; JP; ! Joint probability of both; ENDSETS DATA: !Conditional probability of forecast, given actual; CFGA = .80 .15 .20 .10 .70 .20 .10 .15 .60; ! Marginal probabilities of actual; MPA = .5 .3 .2; ENDDATA ! The calculations; ! Marginal probabilities are the sum of joint probabilities; @FOR(ACTUAL(J): MPA(J) = @SUM(FCAST(I): JP(I, J)) ); @FOR(FCAST(I): MPF(I) = @SUM(ACTUAL(J): JP(I, J)) ); ! Bayes rule relating joint to conditional probabilities; @FOR(FXA(I, J): JP(I, J) = MPF(I) * CAGF(I, J); JP(I, J) = MPA(J) * CFGA(I, J) ); END Model: BAYES 725
