Sampling-importance-resampling

Example:  y is distributed binomial(n, p)
suppose that you know that .2 < p < .4 and you place a uniform prior on this set
observe 3 successes and 17 failures -- want posterior

MTB > # first simulate 1000 values uniformly distributed on (.2, .4)
MTB > rand 1000 c1;
SUBC> unif .2 .4.
MTB > # compute likelihood for each simulated value
MTB > let c2=c1**3*(1-c1)**17
MTB > # convert likelihoods to probabilities
MTB > let c2=c2/sum(c2)
MTB > # now sample with replacement from prior sample with probabilities
MTB > # proportional to the likelihoods
MTB > rand 1000 c3;
MTB > discrete c1 c2.
----------------------------------------------------------------------------------

Using the program 'mod_cont':
 
MTB > name c1 'prior_s'
MTB > rand 1000 'prior_s';
SUBC> unif .2 .4.
MTB > exec 'mod_cont'

INPUT THE NUMBER OF THE LIKELIHOOD:
(1-Binomial P, 2-Normal M, 3-Poisson L, 4-Hypergeometric S,
 5-Discrete Uniform N, 6-Capture/Recapture N, 7-Exponential M)
DATA> 1

INPUT   
  (number of successes, number of failures)                        
DATA> 3 17
 
Input number of simulated values:
DATA> 1000

                                         :
                      .                  :     :  ..
              .  . ...:: .   :  :: .  .  : . : :: ::. . . . :.
              :: : ::::: :. .: .::::. :. :::.: ::.::: :.:::.::.
              :::::::::: :::::.::::::::: :::::::::::: :::::::::
             .::::::::::::::::::::::::::.::::::::::::::::::::::.
             :::::::::::::::::::::::::::::::::::::::::::::::::::
             :::::::::::::::::::::::::::::::::::::::::::::::::::
          ---+---------+---------+---------+---------+---------+---prior_s 

              .. :   .
              :: :   : :
              :: : :::::
              ::.: :::::    :.
             .:::::::::: . :::        :
             :::::::::::.::::: .: .:. :  :
             ::::::::::::::::: :::::: :. ::: :
             ::::::::::::::::::::::::.:::::: :.. ::::..   .
             :::::::::::::::::::::::::::::::.::::::::::::.::::.
          ---+---------+---------+---------+---------+---------+---POST_S  
         0.200     0.240     0.280     0.320     0.360     0.400