Josue P. 4-6

Summary:  

The author first takes us through Bayes theorem and indicates the steps to find our posterior distribution of the stimulus given the response.  Of importance, a 95% credible interval is derived using a known distribution.

In the next section, we find a way to find an estimate to find a frequentist distribution and corresponding confidence interval.

In the next section, we compare the Bayesian and frequentist estimate.  The estimates are equal in a special case, but have different CIs.  We find that the estimates are generally equal and that the confidence interval is much bigger than the credible interval.

General Comments:  Overall, I think the author does a nice job of explaining the estimates.  What is not clear from pages 4-6 is what exactly the author is estimating and how it makes sense in context to neurons.  This is apparent, especially, in the Bayesian Inference section, where neurons are not even mentioned.

I like Equations 4 and 8, in particular.  In 8, do you need to add given the data?  I think it would be helpful to have a parallel structure in the Population Vector with respect to the estimate and CI.  If you had two equations to mirror the ones in the Bayes section, it would be more immediately apparent that you are interested in comparing these two quantities.

The graphic is sort of confusing and I'm not sure how it shows the difference between the estimates.  It looks like the distributions are the same to me.

How do you repeatedly compute the ratio?  Are you bootstrapping?  Leaving an observation out?  I think this could be further addressed.

Specific comments:

Right after Equation (4).  

This is large information dump!  Double check to make sure everything is defined.  For instance, I'm not sure where N comes in to play in Eq. 7.  Also, it would be good to recap what the responses and what the stimuli are.  In "Hence equation 6 is simply...," I would take out the word 'simply.'

Population Vector section.  

It would be nice to have a transition into this paragraph such as "In contrast to Bayesian inference to derive an estimate and CI, population vector is..."

It would be useful to highlight the mean and CI as these are the most important parts of the section.  It seems the author is switching to polar coordinates here, and perhaps that should be made clear.

Comparing Population Estimates.  

I like the topic sentence, and it makes it very explicit that the above two sections are competing methods.  I like that you give the punch line of the equation (the estimates are equal) and then derive it.   This goes with the Gopen paper about stressing objects of importance.

As stated above, more detail should be given about repeatedly computing the ratio.  I think it also should be spelled out that the confidence interval seems larger than the credible interval.

The Figure.

I find this to be a very confusing graphic.  What does the inset mean?  How does it relate to the curve?  It looks like the two estimates give the same results in the right.