  Accurate knowledge of the interstellar medium (ISM) at high Galactic
latitudes is crucial for future cosmic microwave background (CMB) polarization
experiments due to extinction, albeit low, remaining a foreground larger than
the anticipated signal in these regions. We develop a Bayesian model to
identify a region of the Hertzsprung-Russell (HR) diagram suited to constrain
the single-star extinction accurately at high Galactic latitudes. Using
photometry from Gaia, 2MASS and ALLWISE together with parallax from Gaia, we
employ nested sampling to fit the model to the data and analyse the posterior
over stellar parameters for both synthetic and real data. Charting low
variations in extinction is complex due to both systematic errors and
degeneracies between extinction and other stellar parameters. The systematic
errors can be minimised by restricting our data to a region of the HR diagram
where the stellar models are most accurate. Moreover, the degeneracies can be
significantly reduced by including astrophysical priors and spectroscopic
constraints. We show accounting for the measurement error of the data and the
assumed inaccuracies of the stellar models are critical in accurately
recovering small variations in extinction. We compare our posterior to stellar
parameters from the LAMOST and Gaia ESO spectroscopic surveys and demonstrate
that a full posterior solution is necessary to understand both the extinction
parameter and the effective temperature. We conclude by showing that under
reasonable prior assumptions and using the posterior mean extinction for each
star in a sample we can produce a dust map similar to other benchmark maps.
