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The goal of this paper is to apply statistical methods to determine electronsdensities and their errors from measurements of density-sensitive lineintensities in the quiet Sun. Three methods are employed. The first is the useof L-function plots to provide a quick visual assessment of the likelihood thata set of line intensities can provide a robust estimate of these quantities. Asecond methods involves a chi-squared minimization together with a prescriptionfor determining the regions of statistical confidence in addition to thebest-fitting value. A third method uses a Bayesian inference technique thatemploys a Monte-Carlo Markov-chain (MCMC) calculation from which an analysis ofthe posterior distributions provide estimates of the mean and regions of highprobability density. Using these three methods, observations ofextreme-ultraviolet spectral lines originating from regions of the quiet Sunhave been analyzed. The quantitative chi-squared minimization and MCMC samplingprovide results that are generally in good agreement, especially for sets oflines of ions that have L-function plots that suggest that a robust analysismight be possible.

Quiet Sun electron densities and their uncertainties derived from spectral emission line intensities