  A Bayesian model to infer edge electron density profiles is developed for the
JET lithium beam emission spectroscopy system, measuring Li I line radiation
using 26 channels with ~1 cm spatial resolution and 10~20 ms temporal
resolution. The density profile is modelled using a Gaussian process prior, and
the uncertainty of the density profile is calculated by a Markov Chain Monte
Carlo (MCMC) scheme. From the spectra measured by the transmission grating
spectrometer, the Li line intensities are extracted, and modelled as a function
of the plasma density by a multi-state model which describes the relevant
processes between neutral lithium beam atoms and plasma particles. The spectral
model fully takes into account interference filter and instrument effects, that
are separately estimated, again using Gaussian processes. The line intensities
are inferred based on a spectral model consistent with the measured spectra
within their uncertainties, which includes photon statistics and electronic
noise. Our newly developed method to infer JET edge electron density profiles
has the following advantages in comparison to the conventional method: i)
providing full posterior distributions of edge density profiles, including
their associated uncertainties, ii) the available radial range for density
profiles is increased to the full observation range (~26 cm), iii) an
assumption of monotonic electron density profile is not necessary, iv) the
absolute calibration factor of the diagnostic system is automatically estimated
overcoming the limitation of the conventional technique and allowing us to
infer the electron density profiles for all pulses without preprocessing the
data or an additional boundary condition, and v) since the full spectrum is
modelled, the procedure of modulating the beam to measure the background signal
is only necessary for the case of overlapping of the Li line with impurity
lines.
