MTB > # Chapter 1 - Example 3
MTB > # Car and Goats Problem
MTB > # Car is behind one of three doors (numbered 1, 2, 3); goats
MTB > # are behind remaining two doors.  You initially select door 1
MTB > # as hiding the car.  Monty Hall opens door 2 with a goat behind it.
MTB > # Should you switch your choice to door 3?
MTB > # Here there are three models (door 1, door 2, door 3) and three
MTB > # possible data outcomes (you see what's behind door 1, door 2, or door 3).
MTB > # You observe outcome "see 2"
MTB > 
MTB > exec 'bayes_se'
 
INPUT NUMBER OF MODELS:
DATA> 3
 
INPUT NAMES OF MODELS (ONE NAME ON EACH LINE):
DATA> door 1
DATA> door 2
DATA> door 3
 
INPUT PRIOR PROBABILITIES OF MODELS:
DATA> .33 .33 .33

WARNING:
  ************************************                                  
  INVALID PRIOR PROBABILITIES                                           
  (WILL NORMALIZE THEM IN CALCULATION)                                  
  ************************************                                  

INPUT THE NUMBER OF POSSIBLE OUTCOMES:
DATA> 3
 
INPUT THE NAME OF EACH OBSERVATION:
 (ONE OBSERVATION ON A LINE)
DATA> see 1
DATA> see 2
DATA> see 3
 
INPUT LIKELIHOODS OF EACH MODEL:

MODEL   
   1 

DATA> 0 .5 .5

MODEL   
   2 

DATA> 0 0 1

MODEL   
   3 

DATA> 0 1 0
 
OBSERVATION NAMES:

 Row            OBS  OBS_NAME
   1   OUT_1            see 1
   2   OUT_2            see 2
   3   OUT_3            see 3
 
TABLE OF PROBABILITIES OF MODELS AND OUTCOMES:

 Row  MODEL           NAME      PRIOR  OUT_1  OUT_2  OUT_3
   1      1   door 1         0.333333      0    0.5    0.5
   2      2   door 2         0.333333      0    0.0    1.0
   3      3   door 3         0.333333      0    1.0    0.0

MTB > exec 'bayes'
 
INPUT NUMBER OF OBSERVATIONS:
DATA> 1
 
INPUT OBSERVATIONS:
 (ONE OBSERVATION NAME ON A LINE:)
DATA> see 3

OUTCOME 
  see 3

 Row  MODEL           NAME      PRIOR   LIKE    PRODUCT       POST
   1      1   door 1         0.333333    0.5   0.166667   0.333333
   2      2   door 2         0.333333    1.0   0.333333   0.666667
   3      3   door 3         0.333333    0.0   0.000000   0.000000

 
SUMMARY OF PRIOR AND POSTERIOR MODEL PROBABILITIES:

 Row  OBS_NO  OUTCOMES    PROB_M1    PROB_M2    PROB_M3

   1       0             0.333333   0.333333   0.333333
   2       1     see 3   0.333333   0.666667   0.000000