Final spelling checks.

appendices/lyttle21.tex

@@ -148,7 +148,7 @@ \subsection{Testing}\label{sec:test}
     \input{tables/test_random.tex}    
 \end{table}
 
-To represent the accuracy of the ANN, we present the median, $\mu_{1/2}$ and MAD estimator, $\sigma_\mathrm{MAD} = 1.4826\cdot\mathrm{median}(|E(x) - \mu_{1/2}|)$ of the error ($E(x)$) in Table \ref{tab:test}. The median is close to zero for all parameters, showing little systematic bias in the ANN. The MAD is also lower than observational uncertainties quoted in Section \ref{sec:data}. The spread in error for $\dnu$ of $\SI{0.06}{\mu\Hz}$ is comparable to that of observations with the best signal-to-noise. However, the error in $\dnu$ predictions is also comparable to other systematic uncertainties in $\dnu$ discussed in Section \ref{subsec:seismo_model}. Therefore, a robust model which takes account of systematic uncertainties pertaining to $\dnu$, including those from the ANN, will be explored in future work (Carboneau et al. in preparation).
+To represent the accuracy of the ANN, we present the median, $\mu_{1/2}$ and MAD estimator, $\sigma_\mathrm{MAD} = 1.4826\cdot\mathrm{median}(|E(x) - \mu_{1/2}|)$ of the error ($E(x)$) in Table \ref{tab:test}. The median is close to zero for all parameters, showing little systematic bias in the ANN. The MAD is also lower than observational uncertainties quoted in Section \ref{sec:data}. The spread in error for $\dnu$ of $\SI{0.06}{\mu\Hz}$ is comparable to that of observations with the best signal-to-noise. However, the error in $\dnu$ predictions is also comparable to other systematic uncertainties in $\dnu$ discussed in Section \ref{subsec:seismo_model}. Therefore, a robust model which takes account of systematic uncertainties pertaining to $\dnu$, including those from the ANN, will be explored in future work.
 
 \section{Prior Distributions}\label{sec:beta}
 

chapters/introduction.tex

@@ -119,7 +119,7 @@ \subsection{A Brief Theory of Solar-Like Oscillations}\label{sec:seismo-theory}
     \label{fig:seismo-echelle}
 \end{figure}
 
-The asymptotic expression helps us identify modes in a star. If the first term of Equation \ref{eq:asy} was exact, we would expect odd and even modes to be grouped together and separated by \(\dnu/2\). To show this, we revisit the power spectrum of 16 Cyg A and estimate a signal-to-noise ratio (SNR) by dividing out a moving median in log-frequency steps of \SI{0.005}{\dex}. We can see the regular pattern predicted by Equation \ref{eq:asy} in the left panel of Figure \ref{fig:seismo-echelle}. Every other mode is approximately separated by \(\dnu\). To see this effect over the wider spectrum, we created an \emph{echelle} plot in the right panel. Folding the spectrum by an estimate of \(\dnu\) reveals a sequence of ridges corresponding to modes of different angular degree. Odd and even angular degree are grouped together, although do not lie on top of each other. The small difference between modes of different \(l\) is described by the higher order terms neglected from Equation \ref{eq:asy}. A faint ridge corresponding to \(l=3\) modes is also visible next to the \(l=1\) ridge. However, 16 Cyg A represents one of the highest SNR dwarf stars observed by \emph{Kepler}, and the \(l=3\) ridge is otherwise not usually visible. 
+The asymptotic expression helps us identify modes in a star. If the first term of Equation \ref{eq:asy} was exact, we would expect odd and even modes to be grouped together and separated by \(\dnu/2\). To show this, we revisit the power spectrum of 16 Cyg A and estimate a signal-to-noise ratio (SNR) by dividing out a moving median in log-frequency steps of \SI{0.005}{\dex}. We can see the regular pattern predicted by Equation \ref{eq:asy} in the left panel of Figure \ref{fig:seismo-echelle}. Every other mode is approximately separated by \(\dnu\). To see this effect over the wider spectrum, we created an \emph{echelle} plot in the right panel. Folding the spectrum by an estimate of \(\dnu\) reveals a sequence of ridges corresponding to modes of different angular degree. Odd and even angular degree are grouped together, although they do not lie on top of each other. The small difference between modes of different \(l\) is described by the higher order terms neglected from Equation \ref{eq:asy}. A faint ridge corresponding to \(l=3\) modes is also visible next to the \(l=1\) ridge. However, 16 Cyg A represents one of the highest SNR dwarf stars observed by \emph{Kepler}, and the \(l=3\) ridge is otherwise not usually visible. 
 
 % Once we have identified a solar-like oscillator, what information is there to gain from asteroseismology? We have discussed how parameters \(\numax\) and \(\dnu\) scale with global stellar properties. Scaling these parameters with respect to the Sun, we can obtain relations for the radius and mass of the star,
 % %

chapters/lyttle21.tex

@@ -529,7 +529,7 @@ \subsection{Systematic Uncertainties}\label{sec:sys}
 
 We have already accounted for systematics due to the choice of helium enrichment and mixing-length parameter by marginalising over their uncertainties assuming their population distributions. However, there are other model physics which we have not freely varied, including diffusion and choice of solar mixture. Although our method can be adapted to different stellar evolutionary codes and choice of physics, an in-depth analysis of systematic uncertainties is left to future work. 
 
-In previous work studying stars in the APOKASC sample, several pipelines used a range of stellar evolutionary codes and model physics are employed to evaluate systematic uncertainties from the models \citep{Serenelli.Johnson.ea2017, SilvaAguirre.Lund.ea2017}. Using a hierarchical model in this work enabled us to reduce median statistical uncertainties to 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Howeber, the systematic uncertainty analysis of \citetalias{Serenelli.Johnson.ea2017} found median systematic uncertainties of 3, 1, and 13 per cent in mass, radius, and age respectively. These are comparable, highlighting the importance of including sources of systematic uncertainty in our model.
+In previous work studying stars in the APOKASC sample, several pipelines used a range of stellar evolutionary codes and model physics are employed to evaluate systematic uncertainties from the models \citep{Serenelli.Johnson.ea2017, SilvaAguirre.Lund.ea2017}. Using a hierarchical model in this work enabled us to reduce median statistical uncertainties to 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. However, the systematic uncertainty analysis of \citetalias{Serenelli.Johnson.ea2017} found median systematic uncertainties of 3, 1, and 13 per cent in mass, radius, and age respectively. These are comparable, highlighting the importance of including sources of systematic uncertainty in our model.
 
 Other systematics could arise from observational data. For example, we chose the ASPCAP DR14 $\teff$ scale which was systematically lower than the photometric scale of choice in \citetalias{Serenelli.Johnson.ea2017}. However, our method was still able to recover similar masses, radii, and ages. This could be explained by our choice of stellar model physics, as discussed previously.
 

chapters/software.tex

@@ -8,4 +8,4 @@ \chapter*{Data Availability \& Software}
 has been provided by national institutions, in particular the institutions
 participating in the \emph{Gaia} Multilateral Agreement. To query other published datasets, this research used the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in \citet{Ochsenbein.Bauer.ea2000}. Finally, this work used the \emph{Gaia}-\emph{Kepler} crossmatch database at \url{https://gaia-kepler.fun} created by Megan Bedell.
 
-I acknowledge use of the \textsc{Python} programming language (Python Software Foundation, \url{https://www.python.org}) for the majority of code written for this work. Specific Python packages used are referenced in-text with the exception of: \texttt{matplotlib} \citep[v3.6.2;][]{Caswell.Lee.ea2022,Hunter2007} and \texttt{seaborn} \citep{Waskom2021} for creating plots; \texttt{scipy} \citep{Virtanen.Gommers.ea2020} for general scientific computational methods; \texttt{astropy} \citep{AstropyCollaboration.Price-Whelan.ea2022} for reading and writing astronomical data; \texttt{astroquery} \citep{Ginsburg.Sipocz.ea2019} for querying astronomy databases; and \texttt{lightkurve} \citep{LightkurveCollaboration.Cardoso.ea2018} for processing \emph{Kepler} light curves. Finally, this thesis was compiled directly to PDF from \LaTeX~source code based on the \texttt{uob-thesis-template} template (\url{https://github.com/alexlyttle/uob-thesis-template}).
+I acknowledge use of the \textsc{Python} programming language (Python Software Foundation, \url{https://www.python.org}) for the majority of code written for this work. Specific Python packages used are referenced in-text, except for: \texttt{matplotlib} \citep[v3.6.2;][]{Caswell.Lee.ea2022,Hunter2007} and \texttt{seaborn} \citep{Waskom2021} for creating plots; \texttt{scipy} \citep{Virtanen.Gommers.ea2020} for general scientific computational methods; \texttt{astropy} \citep{AstropyCollaboration.Price-Whelan.ea2022} for reading and writing astronomical data; \texttt{astroquery} \citep{Ginsburg.Sipocz.ea2019} for querying astronomy databases; and \texttt{lightkurve} \citep{LightkurveCollaboration.Cardoso.ea2018} for processing \emph{Kepler} light curves. Finally, this thesis was compiled directly to PDF from \LaTeX~source code based on the \texttt{uob-thesis-template} template (\url{https://github.com/alexlyttle/uob-thesis-template}).

thesis.tex

@@ -105,7 +105,7 @@
 %% ACKNOWLEDGEMENTS -----------------------------------------------------------
 %
 \acknowledgements{%
-I am tremendously grateful to my PhD supervisor Guy R. Davies for his support and excellent mentorship throughout my postgraduate research. Additionally, I thank my first co-supervisor Andrea Miglio for his guidence before his move to the University of Bologna. I extend my thanks to Amaury Triaud, who took over from Andrea as my co-supervisor and has since been an inspiring mentor and leader of our research group. I would like to thank in advance my PhD examiners Daniel Reese and Chris Moore, and viva chairperson Annelies Mortier.
+I am tremendously grateful to my PhD supervisor Guy R. Davies for his support and excellent mentorship throughout my postgraduate research. Additionally, I thank my first co-supervisor Andrea Miglio for his guidance before his move to the University of Bologna. I extend my thanks to Amaury Triaud, who took over from Andrea as my co-supervisor and has since been an inspiring mentor and leader of our research group. I would like to thank in advance my PhD examiners Daniel Reese and Chris Moore, and viva chairperson Annelies Mortier.
 
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