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different photon detection efficiencies of donor and acceptor channels.  A simple way to mitigate the dependence of the FRET distribution on   the burst size selection threshold is weighting bursts according proportionally  to their size (i.e. their information content) Fisher information)  so that the bursts with largest sizes will have the largest weights.  In statistics, weights proportional to the inverse of the variance are used   in the context of least-squares fitting to take into account samples  with different variances. In the case of a burst population with fixed FRET efficiency $E_p$,   bursts $n_a$ counts are commonly described by binomial random variable with $n_d + n_a$ trials and $E_p$ probability of success. While this model neglects the effect of background, it captures  the main features of a static FRET  population. Under the binomial assumption, the variance of each burst $E_i$ is inversely proportional to the burst size $n_{ti}$,  as reported in eq.~\ref{eq:var_e}.  $$\operatorname{Var}\left( \begin{equation}  \label{eq:var_e}  \operatorname{Var}\left(  E_i \right) =\operatorname{Var}\left( \frac{n_{ai}}{n_{ti}} \right)  = \frac{E_p(1-E_p)}{n_{ti}}$$ \frac{E_p(1-E_p)}{n_{ti}}  \end{equation}  The Therefore weights proportional to $n_{ti}$ are the natural choice (see SI XXX).  In general, this  weighting scheme is used for building efficient estimators for a population  parameter (e.g. $E_p$). But it  can be also  used to build weighted histograms or Kernel Density Estimation (KDE) plots. When plots which will exhibit FRET subpopulations with optimal width,  yielding more accurate fit of peaks positions and better resolving nearby peaks  (compared to corresponding non-weighted plots using the same burst-size threshold).  Traditionally, without  using weights, for optimal results,  the choice width  of a particular  burst FRET subpopulations peaks are manually optimized by finding an ad-hoc (high)   size-threshold which selects only bursts with the highest  size threshold affects (and thus lowest variance).  This procedure, needs to balance reduction in fitting error due to using bigger bursts  and the increase in fitting error due to  the shape lower number of bursts.  Conversely, the use of size weights allows a more efficient use  of burst information.  For example, by fixing  the burst distribution size threshold  to a lesser extent,  therefore lower threshold low value  (e.g. 20 photons) can be used in a wide variety of cases  without broadening the is possible   to obtain optimal-width FRET sub-populations  peaks of sub-populations, effectively removing the without any  need to an ad-hoc optimization of the burst size threshold search  for each measurement. an optimal burst-size threshold.  \paragraph{Python details}  FRETBursts has the option to weight bursts using γ-corrected 
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\verb|weights='size'| to histogram or KDE plot functions. The \verb|weights|  keyword can be also passed to fitting functions in order to fit  the weighted E or S distributions (see section~\ref{sec:fretfit}).  Several other Other  weighting functions (for example quadratical) depending quadratically onf the size)  are listed in the \verb|fret_fit.get_weights| documentation (\href{http://fretbursts.readthedocs.org/en/latest/fret_fit.html#fretbursts.fret_fit.get_weights}{link}).  However, using weights different from the size is not recommended   due to their less efficient use of burst information.  \subsection{Plotting \texttt{Data}}  \label{sec:plotting}