Joint Bayesian Estimation of Quasar Continua and the Lyman-Alpha Forest
  Flux Probability Distribution Function
  We present a new Bayesian algorithm making use of Markov Chain Monte Carlo
sampling that allows us to simultaneously estimate the unknown continuum level
of each quasar in an ensemble of high-resolution spectra, as well as their
common probability distribution function (PDF) for the transmitted Ly$\alpha$
forest flux. This fully automated PDF regulated continuum fitting method models
the unknown quasar continuum with a linear Principal Component Analysis (PCA)
basis, with the PCA coefficients treated as nuisance parameters. The method
allows one to estimate parameters governing the thermal state of the
intergalactic medium (IGM), such as the slope of the temperature-density
relation $\gamma-1$, while marginalizing out continuum uncertainties in a fully
Bayesian way. Using realistic mock quasar spectra created from a simplified
semi-numerical model of the IGM, we show that this method recovers the
underlying quasar continua to a precision of $\simeq7\%$ and $\simeq10\%$ at
$z=3$ and $z=5$, respectively. Given the number of principal component spectra,
this is comparable to the underlying accuracy of the PCA model itself. Most
importantly, we show that we can achieve a nearly unbiased estimate of the
slope $\gamma-1$ of the IGM temperature-density relation with a precision of
$\pm8.6\%$ at $z=3$, $\pm6.1\%$ at $z=5$, for an ensemble of ten mock
high-resolution quasar spectra. Applying this method to real quasar spectra and
comparing to a more realistic IGM model from hydrodynamical simulations would
enable precise measurements of the thermal and cosmological parameters
governing the IGM, albeit with somewhat larger uncertainties given the
increased flexibility of the model.
