MTB > # summarizing a beta density
MTB > #
MTB > # suppose I want to learn about p=Prob(coin lands heads)
MTB > # I use a uniform prior and toss the coin 100 times, getting
MTB > # 108 heads and 92 tails
MTB > #
MTB > # posterior density is beta(109, 93)
MTB > # I want to compute P(.48<p<.52) and find a 90% interval estimate
MTB > # for p
MTB > 
MTB > exec 'p_beta'
 
INPUT VALUES OF BETA PARAMETERS A AND B:
DATA> 109 93
 
TYPE 'y' TO SEE A PLOT OF THE BETA DENSITY:
y
         -                           * *
     10.5+
         -
 density -
         -
         -                           *  *
      7.0+
         -
         -
         -
         -                          *   *
      3.5+
         -
         -
         -                         *      *
         -                        *        *
      0.0+ ******* *2* **2 ***2 **          ******************
           +---------+---------+---------+---------+---------+------P       
        0.00      0.20      0.40      0.60      0.80      1.00
         
TYPE 'y' TO COMPUTE CUMULATIVE PROBABILITIES:
----------------------------------------------------------------
  Input values of P of interest.  The output is the column of
  values P and the column of cumulative probabilities PROB_LT.
----------------------------------------------------------------
y
DATA> .48 .52
DATA> end

 Row      P    PROB_LT

   1   0.48   0.044889
   2   0.52   0.287360

 TYPE 'y' TO COMPUTE PERCENTILES:
----------------------------------------------------------------
  Input probabilities for which you wish to compute percentiles.
  The output is the probabilities in the column PROB and the
  corresponding percentiles in the column PERCNTLE.
----------------------------------------------------------------
y
DATA> .05 .95
DATA> end

 Row   PROB   PERCNTLE

   1   0.05   0.481819
   2   0.95   0.596941