Preliminary Results

An Monte Carlo simulation was performed to compare the three estimators ``WF87'', ``WF87obs'' and ``4th''. Problems with point-estimation for ``MMLD'' meant that this estimator could not be tested. The preliminary results of the following graphs were averaged over 100,000 iterations. Interestingly, the Expected Kullback-Leibler and Expected Root-Mean-Square distances can no longer be obtained from simply integrating under the graphs. Instead, they must be biased by multiplying it by the prior h(r). For the binomial distribution, this was not required because a uniform prior was used.

  

Figure: Expected Kullback-Leibler distance conditional upon r for the Poisson distribution

Figure shows that ``4th'' and ``WF87obs'' actually produces worse results than ``WF87''. At present, this cannot be explained. However, before dismissing the result as an implementation error, it is theoretically possible for the 4th-order extension to produce worse results than the 2nd-order extension [#!Dowe:private!#].

  

Figure: Expected Root-Mean-Square distance conditional upon r for the Poisson distribution

Figure also shows that ``4th'' and ``WF87obs'' produces worse results than ``WF87''. It is a possibility that a mistake has been made in the implementation. Therefore, it has been placed in the Appendices pending verification via another means.