Using neural networks , Belokurov , Evans & Le Du ( 2003 , 2004 ) showed that 7 out of the 29 microlensing candidates towards the Large Magellanic Cloud ( LMC ) of the MACHO collaboration are consistent with blended microlensing and added Gaussian noise .
We then estimated the microlensing optical depth to the LMC to be 0.3 \times 10 ^ { -7 } \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2 % .0 pt \hbox { $ < $ } } \tau \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } % \raise 2.0 pt \hbox { $ < $ } } 0.5 \times 10 ^ { -7 } , lower than the value \tau = 1.2 ^ { +0.4 } _ { -0.3 } \times 10 ^ { -7 } claimed by the MACHO collaboration ( Alcock et al .
2000 ) .
There have been independent claims of a low optical depth to the LMC by the EROS collaboration , who have most recently reported \tau < 0.36 \times 10 ^ { -6 } ( Tisserand et al .
2006 ) .

Griest & Thomas ( 2005 ) have contested our calculations .
Unfortunately , their paper contains a number of scientific misrepresentations of our work , which we clarify here .
We stand by our application of the neural networks to microlensing searches , and believe it to be a technique of great promise .
Rather , the main cause of the disparity between Griest & Thomas ( 2005 ) and Belokurov et al .
( 2004 ) lies in the very different datasets through which these investigators look for microlensing events .
Whilst not everything is understood about the microlensing datasets towards the LMC , the latest downward revisions of the optical depth to ( 1.0 \pm 0.3 ) \times 10 ^ { -7 } ( Bennett 2005 ) is within \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } } 2 \sigma of the theoretical prediction from stellar populations alone .

Efficiency calculations can correct for the effects of false negatives , but they can not correct for the effects of false positives ( variable stars that are mistaken for microlensing ) .
In our opinion , the best strategy in a microlensing experiment is to eschew a decision boundary altogether and so sidestep the vagaries of candidate selection and efficiency calculations .
Rather , each lightcurve should be assigned a probability that it is a bona fide microlensing event and the microlensing rate calculated by summing over the probabilities of all such lightcurves .