We present a sample of 705 local giant stars observed using the New Mexico State University 1 m telescope with the Sloan Digital Sky Survey-III/Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograph, for which we estimate stellar ages and the local star formation history (SFH). The high-resolution (R ~ 22,500), near infrared (1.51–1.7 μm) APOGEE spectra provide measurements of stellar atmospheric parameters (temperature, surface gravity, [M/H], and [α/M]). Due to the smaller uncertainties in surface gravity possible with high-resolution spectra and accurate Hipparcos distance measurements, we are able to calculate the stellar masses to within 30%. For giants, the relatively rapid evolution up the red giant branch allows the age to be constrained by the mass. We examine methods of estimating age using both the mass–age relation directly and a Bayesian isochrone matching of measured parameters, assuming a constant SFH. To improve the SFH prior, we use a hierarchical modeling approach to constrain the parameters of the model SFH using the age probability distribution functions of the data. The results of an α-dependent Gaussian SFH model show a clear age–[α/M] relation at all ages. Using this SFH model as the prior for an empirical Bayesian analysis, we determine ages for individual stars. The resulting age–metallicity relation is flat, with a slight decrease in [M/H] at the oldest ages and a ~0.5 dex spread in metallicity across most ages. For stars with ages 1 Gyr we find a smaller spread, consistent with radial migration having a smaller effect on these young stars than on the older stars.
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