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Stellar dating using chemical clocks and Bayesian inference

Dating stars is a major challenge with a deep impact on many astrophysical fields. One of the most promising techniques for this is using chemical abundances. Recent space- and ground-based facilities have improved the quantity of stars with accurate observations. This has opened the door for using Bayesian inference tools to maximise the information we can extract from them. Our aim is to present accurate and reliable stellar age estimates of FGK stars using chemical abundances and stellar parameters. We used one of the most flexible Bayesian inference techniques (hierarchical Bayesian models) to exceed current possibilities in the use of chemical abundances for stellar dating. Our model is a data-driven model. We used a training set that has been presented in the literature with ages estimated with isochrones and accurate stellar abundances and general characteristics. The core of the model is a prescription of certain abundance ratios as linear combinations of stellar properties including age. We gathered four different testing sets to assess the accuracy, precision, and limits of our model. We also trained a model using chemical abundances alone. We found that our age estimates and those coming from asteroseismology, other accurate sources, and also with ten Gaia benchmark stars agree well. The mean absolute difference of our estimates compared with those used as reference is 0.9 Ga, with a mean difference of 0.01 Ga. When using open clusters, we reached a very good agreement for Hyades, NGC 2632, Ruprecht 147, and IC4651. We also found outliers that are a reflection of chemical peculiarities and/or stars at the limit of the validity ranges of the training set. The model that only uses chemical abundances shows slightly worse mean absolute difference (1.18 Ga) and mean difference (-0.12 Ga).