From: SIMONOFB@WMAVM7.VNET.IBM.COM
Newsgroups: comp.ai
Subject: Dempster Schafer
Date: 8 Apr 92 13:40:50 GMT

Hi, I am hoping to find some people who understand Dempster-Schafer
Theory, a mechanism for reasoning under uncertainty.  I am currently
taking a graduate course which has covered Dempster-Schafer Theory,
but gave no indication of how to pick the basic probability assignment
(bpa).  I decided to set up an experiment and see what happens under
certain circumstances.  The following is the experiment:

We have a Martian coin (a coin which looks and is shaped a bit funny).
Based on the shape, I believe that m(HEADS) = 0.1 meaning that I start
out thinking that if the tail comes up heads by belief in a heads
biased coin increases by a mass of 0.1.  I also believe that
m(TAILS)=0.05 which leaves m(THETA) = 0.85.

In reality, the coin's outcomes are equiprobable.  The following are
the first two flips of the coin and the last two flips of the coin
complete with the combination of evidence table and updated masses.

  Starting masses:
      m[HEADS]=0.0
      m[TAILS]=0.0
      m[THETA]=0.0



                                        New Evidence  (Heads)
                            {Heads}           {Tails}           Theta
                            0.100000          0.000000          0.900000
                        +-----------------------------------------------
      {Heads}  0.100000 |   0.010000          0.000000          0.090000
  M1  {Tails}  0.100000 |   0.010000          0.000000          0.090000
      Theta    0.800000 |   0.080000          0.000000          0.720000

      m[HEADS]=0.180000/0.990000 = 0.181818
      m[TAILS]=0.090000/0.990000 = 0.090909
      m[THETA]=0.720000/0.990000 = 0.727273

                                        New Evidence  (Tails)
                            {Heads}           {Tails}           Theta
                            0.000000          0.050000          0.950000
                        +-----------------------------------------------
      {Heads}  0.181818 |   0.000000          0.009091          0.172727
  M1  {Tails}  0.090909 |   0.000000          0.004545          0.086364
      Theta    0.727273 |   0.000000          0.036364          0.690909

      m[HEADS]=0.172727/0.990909 = 0.174312
      m[TAILS]=0.127273/0.990909 = 0.128440
      m[THETA]=0.690909/0.990909 = 0.697248




                                        New Evidence  (Heads)
                            {Heads}           {Tails}           Theta
                            0.100000          0.000000          0.900000
                        +-----------------------------------------------
      {Heads}  0.999979 |   0.099998          0.000000          0.899981
  M1  {Tails}  0.000021 |   0.000002          0.000000          0.000019
      Theta    0.000000 |   0.000000          0.000000          0.000000

      m[HEADS]=0.999979/0.999998 = 0.999981
      m[TAILS]=0.000019/0.999998 = 0.000019
      m[THETA]=0.000000/0.999998 = 0.000000

                                        New Evidence  (Tails)
                            {Heads}           {Tails}           Theta
                            0.000000          0.050000          0.950000
                        +-----------------------------------------------
      {Heads}  0.999981 |   0.000000          0.049999          0.949982
  M1  {Tails}  0.000019 |   0.000000          0.000001          0.000018
      Theta    0.000000 |   0.000000          0.000000          0.000000

      m[HEADS]=0.949982/0.950001 = 0.999980
      m[TAILS]=0.000019/0.950001 = 0.000020
      m[THETA]=0.000000/0.950001 = 0.000000


The question I have is what does it mean that the masses converged to
approximately 1.0 for HEADS and 0.0 for TAILS.  I understand that
m[THETA] = 0.0 means that all of the unknowns are accounted for, but I
expected m[HEADS] = M[TAILS] = 0.5 to be the result.

Any help in this matter would be GREATLY appreciated.

Thanks
Bob Simonoff