Topic 18:  Learning About a Mean Using Discrete Models

 

Minitab Local Macro m_disc

 

Computes the posterior distribution for a mean M using a discrete set of models (sampling standard deviation h known).

 

 

TO RUN:

 

Name two Minitab columns 'm' and 'prior'.  Place the values of the mean M in 'm' and the prior probabilities in 'prior'.  In the college student study on page 426, the following values of M and prior probabilities were used:

 

 Row      m    prior

 

   1    6.0   0.0625

   2    6.1   0.0625

   3    6.2   0.0625

   4    6.3   0.0625

   5    6.4   0.0625

   6    6.5   0.0625

   7    6.6   0.0625

   8    6.7   0.0625

   9    6.8   0.0625

  10    6.9   0.0625

  11    7.0   0.0625

  12    7.1   0.0625

  13    7.2   0.0625

  14    7.3   0.0625

  15    7.4   0.0625

  16    7.5   0.0625

 

Place the data in a column named 'data'.  and suppose that the standard deviation is .5.  In this example 'data' contains the sleeping times for 28 students:

 

MTB > prin 'data'

 

data

    8.0    6.0    6.5    7.0    7.0    6.5    6.5    6.0    7.0    7.0

    6.0    6.0    7.5    6.0    7.0    7.0    6.5    6.0    6.5    6.5

    9.0    9.0    7.0    5.0    8.0    6.5    6.0    6.0

 

To compute the posterior probabilities for M, type the following command in the Minitab Session Window.  A graph of the prior, likelihood and posterior probabilities is also created.

 

MTB >  %m_disc 'm' 'prior' .5 'data';

SUBC> plot.

 

PRIOR AND POSTERIOR DENSITIES OF M:

 

Row      M    PRIOR       LIKE   PRODUCT      POSTR

 

   1    6.0   0.0625          0       0.0   0.000000

   2    6.1   0.0625          0       0.0   0.000000

   3    6.2   0.0625          0       0.0   0.000000

   4    6.3   0.0625         14       0.9   0.000005

   5    6.4   0.0625       1207      75.4   0.000443

   6    6.5   0.0625      34735    2171.0   0.012749

   7    6.6   0.0625     326280   20392.5   0.119759

   8    6.7   0.0625    1000000   62500.0   0.367044

   9    6.8   0.0625    1000000   62500.0   0.367044

  10    6.9   0.0625     326280   20392.5   0.119759

  11    7.0   0.0625      34735    2171.0   0.012749

  12    7.1   0.0625       1207      75.4   0.000443

  13    7.2   0.0625         14       0.9   0.000005

  14    7.3   0.0625          0       0.0   0.000000

  15    7.4   0.0625          0       0.0   0.000000

  16    7.5   0.0625          0       0.0   0.000000

 

PRIOR MEAN OF M:

 

MEAN    6.75000

 

POSTERIOR MEAN OF M:

 

MEAN    6.75000

 

 

Other subcommands:

 

The full macro command is

 

%m_disc M1 PRI PS DATA;

 summ;

 store pos;

 plot.

 

Use the 'summ' subcommand when the data vector 'data' contains the mean x and the sample size n.

 

The 'store' subcommand stores the posterior probabilities in the column 'pos'.