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We present a new method for inferring the metallicity (Z) and ionizationparameter (q) of HII regions and star-forming galaxies using strong nebularemission lines (SEL). We use Bayesian inference to derive the joint andmarginalized posterior probability density functions for Z and q given a set ofobserved line fluxes and an input photo-ionization model. Our approach allowsthe use of arbitrary sets of SELs and the inclusion of flux upper limits. Themethod provides a self-consistent way of determining the physical conditions ofionized nebulae that is not tied to the arbitrary choice of a particular SELdiagnostic and uses all the available information. Unlike theoreticallycalibrated SEL diagnostics the method is flexible and not tied to a particularphoto-ionization model. We describe our algorithm, validate it against othermethods, and present a tool that implements it called IZI. Using a sample ofnearby extra-galactic HII regions we assess the performance of commonly usedSEL abundance diagnostics. We also use a sample of 22 local HII regions havingboth direct and recombination line (RL) oxygen abundance measurements in theliterature to study discrepancies in the abundance scale between differentmethods. We find that oxygen abundances derived through Bayesian inferenceusing currently available photo-ionization models in the literature can be ingood (~30%) agreement with RL abundances, although some models performsignificantly better than others. We also confirm that abundances measuredusing the direct method are typically 0.2 dex lower than both RL andphoto-ionization model based abundances.

IZI: Inferring the Gas Phase Metallicity (Z) and Ionization Parameter (q) of Ionized Nebulae using Bayesian Statistics