deletions | additions       diff --git a/subsection_Bad_fit_and_pathological__.tex b/subsection_Bad_fit_and_pathological__.tex  index d0fc8f0..2e140a3 100644  --- a/subsection_Bad_fit_and_pathological__.tex  +++ b/subsection_Bad_fit_and_pathological__.tex 
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I identify three kinds of undesirable behaviors in the Gp fits obtaines through the procedure outlined above.   \subsubsection{Early time instability}  The earliest epochs are separated by large gap by design, since we are fiting the magnitude against the logarithm of time. This creates instabilities: the behavior of the lightcurves between the first and second datapoint varies hugely. This generally cause very large uncertainty bands between the first and second observed epoch, and on occasion between the first few epochs. This is not necessarily undesirable: the uncertainty at early times in a way reflects the fact that the early behavior is in fact diverse, and the large uncertainty arising from our choice to fit in log space reflects that.  However, issues arise in a few cases, where early spikes in brightness are not compensated by brigthness deficits, with a mean rise brightness, and an uncertainty not sufficient to compensate for it. In most cases we can correct that by simply substituting the mean GP interpolation between the first and second datapoint with a linear interpolation, preserving the uncertainty band as determined by the GPs. After all, the time interval between the first nd second datapoint is generally small (~1 ($\sim~1$  day for modern surveys, but mostly not more that a few days even for SNe discovered before the advent of synoptic surveys). This comes at the occasional cost of some small discontinuities between the second and third datapoint, which we deem non-critical.