BEDE: Bayesian estimates of dust evolution for nearby galaxies

We build a rigorous statistical framework to provide constraints on the chemical and dust evolution parameters for nearby late-type galaxies with a wide range of gas fractions ($3{{\ \rm per\ cent}}\lt f_g\lt 94{{\ \rm per\ cent}}$). A Bayesian Monte Carlo Markov Chain framework provides statistical constraints on the parameters used in chemical evolution models. Nearly a million one-zone chemical and dust evolution models were compared to 340 galaxies. Relative probabilities were calculated from the χ² between data and models, marginalized over the different time-steps, galaxy masses, and star formation histories. We applied this method to find 'best-fitting' model parameters related to metallicity, and subsequently fix these metal parameters to study the dust parameters. For the metal parameters, a degeneracy was found between the choice of initial mass function, supernova metal yield tables, and outflow prescription. For the dust parameters, the uncertainties on the best-fitting values are often large except for the fraction of metals available for grain growth, which is well constrained. We find a number of degeneracies between the dust parameters, limiting our ability to discriminate between chemical models using observations only. For example, we show that the low dust content of low-metallicity galaxies can be resolved by either reducing the supernova dust yields and/or including photofragmentation. We also show that supernova dust dominates the dust mass for low-metallicity galaxies and grain growth dominates for high-metallicity galaxies. The transition occurs around 12 + log (O/H) = 7.75, which is lower than found in most studies in the literature.