General Comments:

I think the section explains the exact model you are using pretty
well.  I was a little confused by some of the notation, but by the end
I understood the model pretty well.


Summary of Section:

The section seems to be focusing on the state space equations for the
interaction between neuron firing rates and "center-out" type
movement.  I'm not actually sure what center-out movement is, but
maybe you defined it in the introduction?


Specific Comments:


Section 2.1:

Parapgraph 2:  You use $z_t^i$ to represent the firing rate of neuron
$i$, but you also use $z_t$ to represent one of the dimensions of
space.  This double use confused me for a few paragraphs.  I would
suggest changing the firing rates to something else, maybe $r_t^i$?
You could also change the spacial dimensions to be x_1, x_2, x_3, but
that might be confusing with the time subscripts.

Paragraph 3, sentence 2:  I think you can remove this
sentence.  You repeat yourself later when you label the two equations
(1a) and (1b).  If you change the paragraph before the equations to:

"For decoding neural activity neuroscientists use the state space
model.  The state space model can be expressed using the following two
equations"

Paragraph 3, last sentence:  I think it would be useful to link this
section to the next section better.  You could do this by adding
another sentence that says how you are going to describe these
assumptions and the solution in the next section.  Something like:
"In the next section we state these assumptions and describe the
Kalman filter solution."


Section 2.2:

Pararaph 1:

1st Sentence:  I wasn't sure what M1 is, maybe you could remind the
reader?

2nd Sentence:  I was confused when $z_t$ was not indexed by $i$ like
it was in equation (1).  I think it would distract the reader less and
add to consistency of notation if you keep the index and use $z_t^i$.
I also think $\alpha_p$ should also be indexed by $i$, since it refers
to a single neuron's preferred direction.  I was not sure if $h_0$ or
$h_p$ depended on the neuron in question either.

Equation 5:  I was wondering if it should be p(z_t | v_t, Z_{t-1}), it
seems like conditioning on $Z_t$ would also condition on $z_t$, and
thus remove the randomness.

Equation 8:  I found this equation a little bit confusing.  You stated
you were going to use Bayes Theorem, but then you go straight to an
equation with an integral that does not look quite like Bayes
Theorem.  I think it might add clarity if you add an intermediate step
of
$$
p(v_t | Z_t) = \frac{p(z_t | v_t Z_{t-1}) p(v_t | Z_{t-1})}{p(z_t)}
$$
Then the next step is a pretty direct step.  If you want to save
space, I think you can keep the equation the way it is, but maybe then
you don't need to mention Bayes Theorem.  I think this will help give
the reader what they expect.