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