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\begin{document}

The following are my own comments on some things that need changing in
the thesis.



\subsection*{Throughout:}
\begin {description}
\item Standardize indicator function notation to $\mathcal{I}\{Y\in\mathcal{A}\}$,
for example.

\mustdone{}

\end{description}
\subsection*{Front Matter}
\begin {description}

\item[p. viii] Do the acknowledgments section.  Use outline in notebook.

\mustdo{}

\end {description}
\subsection*{Chapter 1. Introduction}
\begin {description}

\item[p.~9]  Whole locus Gibbs sampler and Heath and Thompson stuff]

\mustdo{}

\end{description}
\subsection*{Chapter 2. Importance Sampling}
\begin {description}

\item[p.~26]  ET wants a figure here that describes how the sampling is
done sequentially over alleles.

\item[End]  Add an Extensions and Caveats section that covers:
\begin{enumerate}
\item the logistic approximation for computational efficiency, (sort of)
\item accounting for extinction probabilities
\item the problem of allele order in the sequential method
\end{enumerate}

\mustdo{}


\end{description}
\subsection*{Chapter 3. P\'{o}lya Urn Model}
\begin {description}


\item[p.~59]  Note that the likelihood derived from the WF model may tend
to overestimate effective size (but this effect could be terribly slight).

\mustdo{}

\item[p.~61] Change the graph so it has the RB'd curve in there.

\mustdo{}

\item[Discussion and Extensions]  Add a brief discussion section in which the
following topics are addressed
\begin{enumerate}
\item Fluctuating $\lambda$  (mention models for detecting that or for seeing if
it depends on the actual number of breeding individuals)
\item Census sizes not known without error. 
\end{enumerate}

\mustdo{}


\end{description}
\subsection*{Chapter 4. Overlapping Year Classes}
\begin {description}

\item[Beginning]  Include Nielsenetal2000 in the motivation (supportive breeding
stuff).  Also include the other Nielsenetal paper on archived fish scales and DNA.

\mustdo{}

\item[p.~64]  Need some major clarification about why the model in which
``population sizes don't change" is crucial.

\mustdo{}

\item[Somewhere] Point out that sampling from juveniles to adults still assumes
H-W equilibrium.

\mustdo{}

\item[p.~92]  Come up with a different notation for $\dot{S}$

\mustdo{}

\item[p.~93] in 4.5, (25,60) is not less pointed than (60,125).

\mustdo{}

\item[Wrap-up]  Include a short concluding section that also notes that these
methods would be very appropriate to salmon hatchery situations (fecundity is
well known, census is well known, etc.)  Also that once again, $\lambda$ may vary
over time.  As in the previous chapter these methods could be extended to include
model comparison (those in which
$\lambda$ changes and those in which it doesn't)---particularly appropriate for
testing for changes in $\lambda$ over time---good example is before and after the
establishment of a supplemental breeding program, or coinciding with changes in
hatchery management style.   

\mustdo{}

\end{description}
\subsection*{Chapter 6. Direct Modeling of Hybridization}
\begin {description}

\item[Somewhere]  Note that the distinction between {\em a priori}, known, fixed
differences between species and frequency differences b/t species can both be
handled by the choice of prior.  

\mustdo{}

\item[p.~137]  Major tense overhaul required in writing about the four
analyses for demonstration.

\mustdo{}

\item[p.~148]  Add something about fewer problems with trapping states
because the component specific parameters are not greatly influenced by
sparsely-filled components.  

\mustdo{}

\end{description}
\subsection*{Bibliograply and 
Appendices}
\begin {description}

\item[Appendix~B]  This thing needs major cleaning up. Note in the beginning of it
that the notation departs a bit from the conventions in the main text---roman
lowercase now denotes a random vector so that the uppercase roman can be a matrix.

\mustdo{}
\end{description}


\newpage

The following are my paraphrases of Robin's comments on the dissertation.
\subsection*{Chapter 1. Introduction}
\begin {description}

\item[p.~6]   ``populations, however" should be ``populations; however,"
and that semi-colon should be used elsewhere before ``however."

\mustdo{Check this out in the Chicago Manual of Style}


\item[p.~8]  Define latent variables, say that the abbreviation for
Markov chain Monte Carlo is MCMC, and explain Monte Carlo before MCMC. 
Also, perhaps the section on Monte Carlo should precede the section on
Monte Carlo in genetics.

\mustdone{Did all the above, except left the sections in the same order as
they are now.  Did some re-working so that there is a mini-definition of
Monte Carlo before the MC in Genetics section, but point out that a more
in-depth introduction to MC will appear later in the first chapter.}

\item[p.~10] ``For example $X$ or $\theta$" is not a sentence.  ``The
two" means what?

\mustdone{Added a semi-colon. Deleted the sentence about the Bayesian
framework.}

\item[p.~12] Monte Carlo also useful for approximating distributions\ldots

\mustdone{Included a short paragraph explaining
how approximations of distributions are approximations of the
probability that the rv falls in an interval (for many
different intervals).  Each of these probabilities may be
expressed as an expectation.}

\item[p.~16] When is it not the case that $\frac{h(x)}{h(x)} = 1$?

\mustdone{Changed this around a bit, and clarified it.}

\end{description}
\subsection*{Chapter 2. Importance Sampling}
\begin {description}

\item[p.~21] The data are {\em random} genetic samples.

\mustdone{}

\item[p.~25]  Missing ``be."

\mustdone{}

\item[p.~27] ``The ability to estimate $N_e$ (add: {\em with adequate
precision}) requires data from many loci.

\mustdone{}


\item[p.~27] Regarding the assumption that the alleles are in linkage
disequilibrium at the beginning and remain in linkage equilibrium over
time---clearly there will be LD from finite population size. 
Explain\ldots.

\mustdo{Explain how it is that that assumption is implicit in the formulation.  Say that 
this will be violated in practice, but on expectation, the LD resulting from finite
population size should not greatly change the  result from the temporal method.  However, in
the discussion I should say that joint modeling of LD and temporal changes of frequencies
over time might be a fruitful area of research.  }

\item[p.~34] Note that the sample size is four times the effective
size---isn't that sort of odd, or at least it requires explanation.

\mustdo{Explain.}

\item[p.~36]  Note explicitly that the simulation is not a simulation
study with many different replicates---it is a single simulated data set
only.

\mustdo{Make this fact explicit.  Discuss the fact that this is not a simulation study to
determine the properties of the estimator---rather a set of simulated data to show that the
computational method yields a likelihood curve.}

\item[p.~37, Figure 2.3]  Features described in the caption are
not visible in the graph.

\mustdo{Include in caption that the features are almost impossible to see because the
error is quite small.}

\item[p.~38] Are the advantages of ML over $F$-statistics with respect to
bias, precision, or both?

\mustdo{Cite Williamson and Slatkin and also Wang saying it is both (though primarily in 
the presence of low freq alleles.  Also, though, greater flexibility in modelling changes in
population size, \etc}

\item[p.~39] Should be able to compute Pollak's estimator while excluding
the Pgm locus.

\mustdo{I did this---the new estimate via Pollak's method is close to the previous estimate
via Pollak's method (268 instead of 250).}

\item[p.~40] Needs a discussion of the underlying assumptions about $N_e$
over time.  And also more expansion upon the idea of $\lambda$ and how it
could change over time.

\mustdo{Include this discussion}

\end{description}
\subsection*{Chapter 3. P\'{o}lya Urn Model}
\begin {description}

\item[In general]  What does the method estimate when $\lambda$ fluctuates
over time?  Is it the harmonic mean $\lambda$, etc.?

\mustdo{This is really an interesting question that gets at the heart of the
issue that when combining data from many intervals to estimate a single
$N_e$ or  $\lambda$ one must weight the information from different intervals
in some way, either implicitly or explicitly.  Include a discussion section
to describe this sort of point.  }

\item[p.~41] The census size $C$ is easy to count as the number of
spawners in salmon populations, but what about other organisms? What gets
counted in $C$?]

\mustdo{Review Nunney's paper about this and describe.}

\item[p.~51]  Family size varies\ldots over time?  across families?  Be
more explicit.

\mustdo{Across families.  Also, this section needs substantial editorial assistance.}

\item[p.~51] ``It is possible to derive the inbreeding and variance
effective sizes of (should be ``in") the urn model."  (How can you have
te $N_e$ of a model?)

\mustdone{}

\item[p.~52, Bottom] Change ``previous generation" to generation~1.

\mustdone{}

\item[p.~53]  Define IBD.

\mustdone{}

\item[p~56]  Allele fixation stuff.  I must make clear that this is the
loss of an allele from the population in a single generation.

\mustdo{}

\item[p.~57, Bottom]  ``probably too low" should be ``probably too high"

\mustdone{}

\item[p.~58]  It is not clear why use of the Wright-Fisher model implies
the assumption that the distribution of family sizes are bimodal.

\mustdo{Explain this more fully, and describe better what I mean\ldots}

\item[p.~59]  Once again:  fixation probabilities within what time
frame?  One generation? Many generations?  \etc

\mustdo{}

\item[p.~59] ``Likelihood derived from WF model may overestimate the
effective size"\ldots which effective size am I talking about there?

\mustdo{Dramatically clarify.}

\item[p.~61]  Note in caption and text that this figure is based on the data from
Begon.

\mustdo{}


\end{description}
\subsection*{Chapter 4. Overlapping Year Classes}
\begin {description}

\item[p.~66] On determining the age of juveniles---can do with scales, but
also, in some spp. all the juveniles will be of a single age class.  

\mustdo{Point out the distinction between steelhead and some forms of
chinook, \etc  }

\item[p.~74] Juveniles and adults can be treated as independent binomial
draws from the previous generation.

\mustdo{Read over Nei \& Tajima and Waples and figure out if this would or would not 
apply to the present modeling scheme.}

\item[p.~74]  Determining age of the parent of a gene copy sampled
amongst juveniles could be done via pedigree analysis.

\mustdo{Point this out.  Cite ``family-printing."}

\item[p.~90]  Allele counts in the years 1950 to 1953 were simulated via
the urn model---describe more fully.

\mustdo{State explicitly how it follows the assumption in the prior}

\item[p.~90]  How do you know that 1954 to 1963 is long enough to
simulated to allow the allele frequencies to settle into a correlated
pattern?

\mustdo{Don't know for certain.  Cite Robin's manuscript that 20 years was enough for $F$'s
between generations to settle down---10 years may have not been quite enough, but, the
resulting allele counts probably represent a sample from the ``stationary" distribution
resulting from some series of census sizes back before 1949.}

\item[p.~90]  Juvenile survivorship figures---were those for stream or
ocean type fish?

\mustdo{Check Healey.  I think they were sort of aggregate measures.  Note that the absolute
values are not particularly important---the relative fecundities are the more important
figures there.}

\item[p.~90]  Cite the data source as Beamsderfer \etal

\mustdone{}

\item[p.~92] $\lambda$ may vary by age, but it is much more likely to
vary by year.  

\mustdo{Add a discussion, and discuss this, along with some other things.}

\item[p.~95] The fact that the 90\% credible interval overlaps .4 is nice,
but not very convincing by itself.

\mustdo{Point out again that this is a simulated dataset for demonstrating that the
computational method works.}


\end{description}
\subsection*{Chapter 5. Mixture and Admixture}
\begin {description}

\item[p.~110, Figure 5.2]  Correlation between $\alpha$ and
$\xi_\mathrm{P}$ are only apparent for $\alpha < 1.5$.

\mustdo{Note this in the caption, and also refer to it in the discussion when talking about
setting the upper limit on $\alpha$.}


\end{description}
\subsection*{Chapter 6. Direct Modeling of Hybridization}
\begin {description}

\item[p.~136]  Make it more explicit at this point that the sample of
juveniles was not a random sample---they were believed to be cutthroat.

\mustdo{}

\item[p.~141]  ``It is unlikely that any purebred individual will receive
high posterior probability of being in a non-purebred genotype frequency
category"  (assuming you know what pure SH and CUTT look like).

\mustdo{Figure out what he is getting at here, and expand.}

\end{description}
\subsection*{Bibliograply and 
Appendices}
\begin {description}

\item[p.~161] Thompson and Heath 1997 also says ``in press."  Straighten that out.

\mustdo{Will get straightened out when I figure out just which of that series of articles to
cite.}
\end{description}

\newpage

Following are some of Joe's comments on the dissertation:

\subsection*{Chapter 1. Introduction}
\begin {description}

\item[p.~12, section 1.5.1]   Was Monte Carlo actually used for development of
the A-bomb during the war?  My understanding is that it was used for
development of the H-bomb after the war.

\mustdo{Check out the book, Stanislaw Ulam 1909--1984,  Los Alamos, N.M. : Los
Alamos National Laboratory, 1987, QA7 .S79 1987}

\item[p.~12 line 5 from bottom]  I understand that Monte Carlo methods are
most often used to approximate expectations, but they also serve to
approximate variances.

\mustdone{Explain in the text that many things can be expressed
as expectations, including variances and distributions, \etc}

\item[p.~17]  Again a quibble.  Yes, to do what you describe,  $h(x)$ should be
easy to compute.  In our MCMC method for inferring ML estimates of
$4N\mu = \Theta$, we actually have a case where $h(x)$ is known only up to
a constant.  In that case instead of the integral  $g_n$ we only get it
as $g_n/(\int h)$, but that is good enough to give us the likelihood
ratios and permit ML inference.

\mustdo{Include another paragraph describing what happens when $h(x)$ is known only
up to a normalizing constant.  Check out Adrian's chapter
in MCMC in Practice---I believe that has a lot about different variations on importance sampling.
Or maybe Gelman et al's section on importance sampling.  Also include a description of the
method as applied in Joe's paper too. }

\item[pp.~18--19]   I am not sure after reading all this that I still know what
Rao-Blackwellization is.  I think it needs a bit more intuitive
explanation.  I couldn't winkle it out of the notation, though I am sure
it is there.

\mustdone{I tried to give a preliminary, intuitive explanation in a new paragraph.}

\end{description}
\subsection*{Chapter 2. Importance Sampling}
\begin {description}


\item[p.~22]  Explain a little -- the reader may not get it that the assumption
is that there a great many more juveniles than adults, and hence that
one can indeed (almost) sample with replacement from the adults.

\item[p.~22]  The uniform prior on $P_{N_e}({\bf X}_0)$ is tossed in without much
comment as to the reasonableness of doing this.

\mustdo{Recall that Ellen and Monty looked at the differences this made and found that it didn't make
much difference if they used a beta prior.  Primarily because, I believe, if you have a sample of 200
alleles at the first sample, that information completely overwhelms the weight in the prior.  With very
many alleles, then it might be better to use a unit-information prior---\ie the Jeffreys prior. But it
should make very little difference, since it really will not change the posterior distribution of the
latent allele counts in that first generation greatly. } 

\item[p.~27]  The unbiased estimators of variances on this page, and the
confidence interval estimates sound like they are in effect assuming
that the $P_{N_e}(Y, X^{(i)})$ are i.i.d.  Of course they aren't, but
are these estimates somehow reliant on having large enough  m  that
they may be regarded as i.i.d.  Might say so if so.

\mustdo{In fact, the $P_{N_e}(Y, X^{(i)})$ are i.i.d.!  This is an importance sampling exercise.  What I
don't mention, though I suppose I could, is that the same block of random numbers is used for each value
of $N_e$ so that, in fact, there is some correlation that way which makes the curve smoother---it
doesn't improve the estimation of the absolute value of the likelihood, but it does improve the
estimation of the relative likelihoods between values of $N_e$.} 

\item[pp.~31--34]  The reflection stuff loses me.  I think readers may have the
same problem.  It is too much, too densely, without any intuitive
explanation.

\mustdo{Give an intuitive introduction to the section}

\end{description}
\subsection*{Chapter 3. P\'{o}lya Urn Model}
\begin {description}

\item[p.~41, 7 lines from bottom]  ``leads to unattractive computational
situations".  The reader will find this to whiz by too fast with no
explanation.  In fact, section 3.2 does explain it.  Needs some
signposting here that this will be covered in that section.

\mustdo{Signpost it!}

\item[p.~47, line 12]   When it is said that  X  follows the compound
multinomial Dirichlet distribution, presumably that is true conditionally
given the $n_i$, not marginally.  This should be made clear.

\mustdo{The whole section could be cleaned and cleared up a little bit.}

\item[p.~55  (3.16)]   $N$ is described above it, but then in this equation $C$ is
used instead.

\mustdo{This was a typo that I should check to make sure I have already fixed.}

\item[pp.~55--59]  I must be missing something here.  Surely with an initial
frequency 0.025 of an allele, in all these models the fixation
probability of that allele (long-term) must be the same for all copies of
the gene and thus be exactly 0.025.  Or am I not getting it?  (In
which case readers might not either). {\em And again:}   I think I have expressed
earlier my confusion about the fixation probability material here:  the fixation
probability in all these models is just
the initial frequency of the allele, so you obviously mean fixation under some
conditioning, but I can't tell what.  I think you said at your Final Exam it
was
probability of fixation within some limited time (one generation, I guess)
which
makes it more like a fixation time than a fixation probability.  Obviously this
needs clearing up.


\mustdone{I restructured things so that I talked about eigenvalue effective size
first, then I describe the calculation of probability of fixation in a single
generation as an indicator, of sorts, of the rate of loss of rare alleles, and
making it very clear what is meant by probability of fixation of allele (i.e. 
in one generation}

\item[p.~62]   ``significantly"  (typo)

\mustdo{Better fix it.}

\end{description}
\subsection*{Chapter 5. Mixture and Admixture}
\begin {description}
\item[]
\item[p. 99]  It is not clear whether "`multilocus genotype' tyically implies
knowledge
of the gametic phase".  I would say that this varies.

\mustdone{Changed it to ``sometimes" implies knowledge of gametic phase\ldots}

\item[p. 102]  The assumption here seems to be that the admixture is old, so that
the admixed individuals are at linkage equilibrium.  This needs to be explained
more.  Of course you later (Chapter 6) have a model in which they aren't at
equilibrium.

\mustdo{Well, in fact,  they are not in equilibrium---the disequilibrium is part
of the information that one actually exploits to be able to separate the sample
into two clusters.  However, the model used for the admixing process is an
heuristic one, rather than one that explicitly models the admixture.  In fact, it
is really a model that could account for recent admixture, or, as Pritchard et al.
use it, for population {\em structure}. I will make that more clear.      }

\item[p. 104]   $1\{X = a\}$  would be expressed usually by either having the { ...
} material in subscript or by using $\delta$ instead of 1, with the { ... }
material
either as subscript or argument ( ... ).

\mustdone{Ah, yes.  I was not terribly satisfied with my notation for the
indicator function.  Not only that, but it wasn't standardized throughout the
thesis.  I like the idea of using $1_{\{X=a\}}$, for example, but I actually have
some indicator functions imbedded within others, and that would over-subscript
things.  $\delta$ already has a different use in Chapter 2.  Instead, I have now
settled on $\mathcal{I}\{X=a\}$ as the notation for the indicator function
throughout the thesis, (and I do introduce it as such in each chapter in which I
use it). }

\item[p. 107]  line 6    runs past the margin.

\mustdone{Thanks.  For the final run I will seek and remove all those overfull
hboxes.}


\item[p. 109]  Explain more clearly that the ``proportion of purebred cats" means
proportion that includes both pre F. sylvestris and housecats.



\end{description}
\subsection*{Chapter 6. Hybrids}
\begin {description}
\item[p. 128]   You might also note that this analysis allows for the linkage
disequilibrium that arises in hybridization, at least partly.  However ...
You do note that (p. 131) you are assuming unlinked markers.  You might
emphasize this a bit more and point out that a modified analysis would be
needed for linked markers.

\end{description}
\end{document}