Book comment --2

(Sec 1.4):

Does the Bayesian analysis provide confidences or error bars?

-        Yes, I can show one plot in figure 4 with error bars.

It is more common for the variable of integration (d\theta) to be at the end of

the integral rather than first.

- Would be a lot of work, suggest not take this modification.

(Eqn 1.33):

If \gamma_j is the precision, should the inverse {\gamma_j}^{-1}, the variance,

appear in the Normal distribution in the equation.

-- Give me more time, I will respond soon.

More could be said about the Biology in the final paragraph in Section 1.4.3.

top of page 18:

spaces missing between A,B,C

(Eqn 1.47):

suggest move dX's after the function?

I'm confused by the text on page 17. Is C_{(s)} a column or ROW of C.

If it's a column, then doesn't C have K columns? and already denoted c_j?

C_(s)^T is the the s-th row of matrix and follows a Gaussian distribution.
Therefore, s = 1,…,p

Can \rho_s and \gamma be defined/introduced here, prior to their use in

diag(\rho_s,\gamma).

This section uses a lowercase k, whereas earlier section 1.2 began with

uppercase K, it would be good to be consistent.

(Sec 1.4.2.3, pg 21):

First line, mis-positioned bar should be above theta.

Eqn 1.75: small k

(Sec 1.4.2.4, first bullet):

Infer -> infer 

(Sec 1.4.2.5,  third bullet, equation):

What's Z'  (should there be a prime on the Z? (why Z'))

Change Z’ to Z (the symbol  in picture as well) 

Sec 1.5.1:

In section 1.5, you introduce a synthetic network with 54 players (illustrated in Fig 1.3), and generate expression levels for 10 mRNAs. When it comes to the evaluation and the construction of ROC curves, what is the ground truth to which you are comparing? 

12 edges:

A -> A, A -> B, A -> C,       , C -> D, C -> G, C -> K

D -> C, D -> E,       , F -> B, F -> D, G -> H, K -> J

Knowledge about the size of

the model that you are trying to recover (whilst acknowledging that there's a complex process actually generating the data) is useful, particularly its

topology. Possible structures on 10 nodes have between 0 and 100 edges.

Stating the network, gives an indication of how much information adding 

1, 2, or 3 prior interactions has.

Is it the network with the following 14 edges?

A -> A, A -> B, A -> C, B -> A, C -> D, C -> G, C -> K

D -> C, D -> E, E -> F, F -> B, F -> D, G -> H, K -> J

-No edges E -> F or B ->A

An image of this network would be a good figure to add.

I can draw it if you think necessary

How many edges are inferred by your methods? -i.e. if you had to choose a "best" point on the ROC curve? 

We tried to infer 12 edges, and performance is measured by AUC.

There are a number of related questions of interest, for

example, how many edges would you need to infer to get all the edges present in

the ground truth (mRNA 10 node) model correctly inferred?

Don’t test yet.

Book Comment 1

page 26, "0 corresponds to the baseline (no prior information) model",
what is the baseline?

--Baseline is ROC-A, with u=0 (no prior knowledge), described in step 1.

Is it always 0.68 without any variation? More information on the baseline(s) must
be given.

And why don't you plot the AUCs without baseline adjustment?

--Not understand Where 0.68 comes from. I can show mean value and std_error in
 one plot, rather than the 16-in-1 plot. If you want, I will send one to you.

page 26, "of of mu" <- "of mu"

page 27. what does "c" mean on the x-axis of Figure 1.4

c corresponds to the manually corrected arc, already in the text

Does the hidden state space dimensionality have any effect on the network
reconstruction accuracy? If it hasn't any influence,
then there seems to be no need for hidden states.
Why are 16 plots shown which all show exactly the same trends? The authors do not mention this finding in the text. They just mention that the "AUC performance can be seen to be linear with the number of prior arcs included" which is much less obvious from Figure 1.4.

It appears K has no influence for AUC. Should we show only one
plot with specific k and mu value, also variation will be plotted.  

page 28, Figure 1.5, why are there some bars missing in the histograms in Figure 1.5?

It means the replicates needed to achieve
the specific AUC is larger than 16, beyond the test setting.

Was there a threshold imposed on the maximal replicates (e.g. 16)?

Yes, we explored replicates with range 1,2,4,8,16

Wouldn't it be more intuitive to set those bars to this maximum
instead of leaving them out,

as higher bars indicate worse performances in Figure 1.5?

Bars would be more crowded 

There is no interpretation of the results. E.g. it is not mentioned
whether "mu" and "k" have an

effect on the inference results. 

mu and k have no obvious effect on results, we focus on replicates numbers.