deletions | additions       diff --git a/section_Discussion_and_Conclusions_label__.tex b/section_Discussion_and_Conclusions_label__.tex  index 2c54b2e..1b3bf8b 100644  --- a/section_Discussion_and_Conclusions_label__.tex  +++ b/section_Discussion_and_Conclusions_label__.tex 
...
An improved understanding of the biases involved in a detection scheme is critical for relating the observed to the underlying population, and a simple way to assess a scheme's detection efficiency is to inject synthetic devil signals (with known parameters) into the real data streams. Then the detection scheme can be applied to recover the synthetic devils and the efficiency of detection assessed across a swath of devil parameters. Such an approach is common in exoplanet transit searches \citep[e.g.][]{Sanchis_Ojeda_2014}, where dips in photometric time series from planetary shadows closely resemble dust devil pressure signals. By injecting synthetic devils into real data, the often complex noise structure in the data is retained and simplifying assumptions (such as stationary white noise) are not required.   Among important limitations of our model, the advection velocity $\upsilon$ for devils remains an critical uncertainty for relating physical and statistical properties. This limitation points to the need for wind velocity measurements made simultaneously with pressure measurements in order to accurately estimate dust devil widths. In particular, correlations between $\upsilon$ and dust devil properties will skew the recovered parameters in ways not captured here. For example, the devils with the deepest pressure profiles seem to occur preferentially around mid-day local time both on Mars \cite{Ellehoj_2010} and the Earth \cite{Jackson_2015}. If winds at that time of day are preferentially fast or slow, then the profile widths recovered for the deepest devils will be skewed toward smaller or larger values. In addition, some field observations suggest devils with larger diameters may be advected more slowly than their smaller counterparts \cite{Greeley_2010}, which would tend to make their profiles look wider. The formulation described here could, in principle, account for this uncertainty by incorporating a distribution of $\upsilon$ determined observationally, $n(\upsilon)$. $\rho(\upsilon)$. The distribution $\rho(P_{\rm obs}, \tau_{\rm obs})$ can be converted to $\rho(P_{\rm obs}, \Gamma_{\rm obs})$ using $\rho(\upsilon)$ via the following integral:  Then the physical width of a devil profile could be represented using a probability density $\dfrac{dp}{d\Gamma_{\rm act}} \propto n(\upsilon)\ d\upsilon$. As highlighted in Section \ref{sec:comparison_to_observational_data} and discussed in \citet{Lorenz_2011}, the choice of the binning procedure (bin size, etc.) in constructing the distributions of physical properties shapes the result in non-trivial ways, and the approach used to describe the distributions will also depend on the procedure. Fortunately, the field of data science has provided several statistically robust and objective procedures for binning data that frequently use the data themselves to determine how they are binned \citep[e.g.][]{Feigelson_2009}. One simple way to ascertain the optimal binning procedure would be to generate synthetic populations according to prescribed distribution functions (power-laws, exponential, etc.) and then investigate which binning procedure allowed the most accurate recovery of the assumed distribution. As an alternative, \citet{Lorenz_2012} suggests plotting cumulative distributions to circumvent the ambiguities involved in binning choices altogether.