Dear All,
I have been struggling for some time to implement the Maximum Entropy
(or Generalized Maximum Entropy) method in a range of software
platforms.
The intention is to use these to reconstruct transaction values in an
input-output matrix subject to the constraints of known row and column
totals and in a way which maximises the Shannon entropy function. This
method follows Golan, A.; Judge, G.; et al.(1996).Maximum Entropy
Econometrics: robust estimation with limited data. Chichester, John
Wiley& Sons (amongst one of many).
The intention is then to use these reconstructed values as a conjugate
Dirichlet prior for Multinomial data from another source in a larger
model.
The question is - is there any way I can do the Maximum Entropy, Gen Max
Ent, or some comparable procedure for data reconstruction within
WinBUGS?
Alternatively - has anybody else managed to implement Max Ent (for
something other than image reconstruction) in another package
(preferably Mathematica)?
Any help greatly appreciated.
David.

Dr David Shipworth
Coordinator: External Environments Research Division
School of Construction Management and Engineering
The University of Reading
Ph: (direct) +44 (0)118 378 7177
Ph: (office) +44 (0)118 378 8201
Fax:(office) +44 (0)118 931 3856

Further information on Maximum Entropy reconstruction:

The aim is to reconstruct values pjk in the matrix below so that:
1. The columns sum to the given column totals
2. The rows sum to the given row totals
3. The sum of the pjk values across the rows equals 1
4. The sum of the pjk values down the columns equals 1
5. The values selected for the pjk maximise the 'entropy function' which
takes the general form: -

In the general case:


n*m table
Col 1
Col k
Col m
Row Marginals

Row 1
pjk
pjk
pjk
TotRow 1

Row j
pjk
pjk
pjk
TotRow j

Row n
pjk
pjk
pjk
TotRow n

Column Marginals
TotCol 1
TotCol k
TotCol m
S S
Summary from below:
MaxEnt equation  =
Constraint equation =
Summation equation =
Constraint: 0 * p(jk) * 1, p * R


-------------------------------------------------------------------
This list is for discussion of modelling issues and the BUGS software.
For help with crashes and error messages, first mail <a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind03%26L%3DBUGS%26E%3D7bit%26P%3D580836%26B%3D------%253D_NextPart_001_0019_01C33FEF.3D4C9AB0%26T%3Dtext%252Fplain%3B%2520charset%3Dus-ascii%26attachment%3Dq" target="_parent" >[log in to unmask]</a>

To mail the BUGS list, mail to <a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind03%26L%3DBUGS%26E%3D7bit%26P%3D580836%26B%3D------%253D_NextPart_001_0019_01C33FEF.3D4C9AB0%26T%3Dtext%252Fplain%3B%2520charset%3Dus-ascii%26attachment%3Dq" target="_parent" >[log in to unmask]</a>
Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html
Please do not mail attachments to the list.

To leave the BUGS list, send LEAVE BUGS to <a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind03%26L%3DBUGS%26E%3D7bit%26P%3D580836%26B%3D------%253D_NextPart_001_0019_01C33FEF.3D4C9AB0%26T%3Dtext%252Fplain%3B%2520charset%3Dus-ascii%26attachment%3Dq" target="_parent" >[log in to unmask]</a>
If this fails, mail <a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind03%26L%3DBUGS%26E%3D7bit%26P%3D580836%26B%3D------%253D_NextPart_001_0019_01C33FEF.3D4C9AB0%26T%3Dtext%252Fplain%3B%2520charset%3Dus-ascii%26attachment%3Dq" target="_parent" >[log in to unmask]</a>, NOT the whole list