  We present a statistical inference approach to estimate the frequency noise
characteristics of ultra-narrow linewidth lasers from delayed self-heterodyne
beat note measurements using Bayesian inference. Particular emphasis is on
estimation of the intrinsic (Lorentzian) laser linewidth. The approach is based
on a statistical model of the measurement process, taking into account the
effects of the interferometer as well as the detector noise. Our method
therefore yields accurate results even when the intrinsic linewidth plateau is
obscured by detector noise. The regression is performed on periodogram data in
the frequency domain using a Markov-chain Monte Carlo method. By using explicit
knowledge about the statistical distribution of the observed data, the method
yields good results already from a single time series and does not rely on
averaging over many realizations, since the information in the available data
is evaluated very thoroughly. The approach is demonstrated for simulated time
series data from a stochastic laser rate equation model with 1/f-type
non-Markovian noise.
