We now validate the proposition above, that solving
for the maximum entropy
multivariate truncated exponential (MaxEnt-MTE) distribution
approximates the asymptotic distribution of MCMC-UMS
for doubly-bounded 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 sine-wave 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
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.
The sample-mean of MCMC-UMS after 10000 samples matches the
Maximum entropy mean solution as close as could be determined.
The Maximum entropy
asymptotic mean (dark line) and the sample mean
(circles). One random MCMC-UMS sample is shown (light jagged line).
The pseudo-inverse solution (dotted lin) is seen to
have values outside .