Sick, the spectroscopic inference crank

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]