MODEL CHECKING BY USE OF THE POSTERIOR PREDICTIVE DISTRIBUTION - SPEED OF LIGHT DATA

light   
   28    29    24    37    36    26    29    26    22    20    25    23    32 
   27    33    24    36    28    27    32    28    24    21    32    26    27 
   24    29    34    25    36    30    28    39    16   -44    30    28    32 
   27    28    23    27    23    25    36    21    24    16    29    21    26 
   27    25    40    31    28    30    26    32    -2    19    29    22    33 
   25

                                                         :
                                                       : :
                                                       : :
                                                     ..::: .  .
                                                    ::::::::. :
            .                         .          : .::::::::: :..
         +---------+---------+---------+---------+---------+-------light   
       -48       -32       -16         0        16        32


FIRST WE SIMULATE FROM THE POSTERIOR DISTRIBUTION OF (MU, SIGMA^2)

MTB > let k1=mean(c1)
MTB > let k2=std(c1)
MTB > let k3=count(c1)
MTB > name c2 'chisq' c3 's2' c4 'mu'
MTB > let k4=count(c1)-1
MTB > rand 1000 'chisq';
SUBC>   chisq k4.
MTB > let 's2'=k4*k2**2/'chisq'
MTB > rand 1000 'mu';
SUBC>   normal 0 1.
MTB > let 'mu'=mean(c1)+sqrt('s2')/sqrt(k3)*'mu'

THEN WE SIMULATE 1000 SAMPLES Y1, ..., Y66 FROM THE PREDICTIVE DISTRIBUTION

MTB > store
STOR>    rand 1000 'yrep';
STOR>      normal 0 1.
STOR>    let 'yrep'='mu'+sqrt('s2')*'yrep'
STOR>    let k11=k11+1
STOR>    copy 'yrep' ck11
STOR> end
MTB > let k11=10
MTB > exec 66

FIND DISTRIBUTION OF T(Y) = MIN(Y1,...,Y66)

MTB > name c77 'y_min'
MTB > rmin c11-c76 'y_min'
MTB > dotplot 'y_min'
                                                .
                                                : :
                                             .  : :  ..
                                           :::: : :::::
                                        .  :::: ::::::::  .
                                        ::.:::::::::::::. :
                                   ..  ::::::::::::::::::::.:
                                  .::::::::::::::::::::::::::.
          .        .  .. . ..::::::::::::::::::::::::::::::::::...
          -------+---------+---------+---------+---------+---------y_min   
             -21.0     -14.0      -7.0       0.0       7.0      14.0

OBSERVED VALUE MIN(Y1,...,Y66) = -44 - THIS IS RARE RELATIVE TO THE POST. PRED. DIST.