Brendan McVeigh - Sections 4 & 5

Summary: 4.1 Your ABC algorithm works on simplified, simulated data.
There are some differences as you use only an approximate method.  The
ABC algorithm makes a wider posterior than the true posterior.  Thus,
credible intervals would be wider but would contain that of the true
posterior.

4.2 Your ABC algorithm is run on metal rich and metal poor stars.  A
previously calculated value for the energy does not lie in your 95\%
CI.

5 You calculated values consistent with previous findings in the case
of one parameter.  However, that this estimate is conditional on other
parameter values.

Future work will include estimating the parameters separately and
together.  You would like a more accurate model of the galaxy.

General Comments: I like your paper, but I think your sections are a
bit disjointed.  If I understand correctly, you first tested your
algorithm on the simulated data to confirm it worked and then used it
on the Sculptor estimates.  This does not quite come through in the
results section, and perhaps would be useful to explicitly state that
line of reasoning before the two subsections.

I think one of the results of your algorithm is computational
complexity, and I think more can be said about it.  It would be
helpful to explain why each step takes longer and longer.  What would
be the ideal place to stop?

For Sculptor estimates, I am a little confused.  Perhaps you should
put E_c somewhere in the table heading?  It's not immediately clear
that the Strigari Value is the E_c parameter.  You also talk about
metal poor then metal rich but you introduce them in reverse order
earlier.  You should flip one or the other.

For the discussion, it would be useful to include more specifics about
the parameters.  What parameters do you think would lead to changes in
the posterior?  Also the sentence "The simplest explanation may
be...," I think the "of likely" needs to be removed.

Figures: I don't know if the left part of Figure 6 is ever referred
to.  I think Table 3 could be better represented by a graph or in the
text.  It would be useful to see the Strigari estimates on Figure 7.

Specific Comments:  

4.1 Is the last sentence of this paragraph an empirical or theoretical
result?

4.2 It would be helpful to remind the reader of what PMC is and also
what \phi_lim is.  Is E_c the Strigari value?  I am not sure how you
fix the other parameters.

5.  The sentence "The test performed, a chi-squared test..." could be
explained better in the first paragraph.

The same with "Modeling both population simulataneously" needs fixing
to remove "random"?