  There exists an inordinate amount of spectral data in both public and private
astronomical archives which remain severely under-utilised. The lack of
reliable open-source tools for analysing large volumes of spectra contributes
to this situation, which is poised to worsen as large surveys successively
release orders of magnitude more spectra. In this Article I introduce sick, the
spectroscopic inference crank, a flexible and fast Bayesian tool for inferring
astrophysical parameters from spectra. sick can be used to provide a
nearest-neighbour estimate of model parameters, a numerically optimised point
estimate, or full Markov Chain Monte Carlo sampling of the posterior
probability distributions. This generality empowers any astronomer to
capitalise on the plethora of published synthetic and observed spectra, and
make precise inferences for a host of astrophysical (and nuisance) quantities.
Model intensities can be reliably approximated from existing grids of synthetic
or observed spectra using linear multi-dimensional interpolation, or a
Cannon-based model. Additional phenomena that transform the data (e.g.,
redshift, rotational broadening, continuum, spectral resolution) are
incorporated as free parameters and can be marginalised away. Outlier pixels
(e.g., cosmic rays or poorly modelled regimes) can be treated with a Gaussian
mixture model, and a noise model is included to account for systematically
underestimated variance. Combining these phenomena into a scalar-justified,
quantitative model permits precise inferences with credible uncertainties on
noisy data. Using a forward model on low-resolution, high S/N spectra of M67
stars reveals atomic diffusion processes on the order of 0.05 dex, previously
only measurable with differential analysis techniques in high-resolution
spectra. [abridged]
