We now validate the proposition above, that solving
for the maximum entropy
multivariate truncated exponential (MaxEntMTE) distribution
approximates the asymptotic distribution of MCMCUMS
for doublybounded data.
In this experiment, we used a data size of .
The matrix in (5.1)
computed the first Coefficients of the
length DCT of .
We created a data sample using a raised sinewave plus
Gaussian noise, clipped it to the interval [0,1], then computed the feature .
The original was then discarded. We then got a starting point
for
using a linear programming solver
as previously explained, with the lower and upper bounds of 0 and .
We then maximized (6.6) over
subject to (5.12)
using the method above. Figure 6.2 shows the results.
See software/test_lin01.m.
Figure:
The Maximum entropy
asymptotic mean (dark line) and the sample mean
(circles). One random MCMCUMS sample is shown (light jagged line).
The pseudoinverse solution (dotted lin) is seen to
have values outside .

The samplemean of MCMCUMS after 10000 samples matches the
Maximum entropy mean solution as close as could be determined.
Baggenstoss
20170519