Low-metallicity, compact starburst galaxies referred to as Green Peas (GPs) provide a unique window to study galactic evolution across cosmic epochs. In this work, we present new deep optical spectra for three GPs from OSIRIS at the 10m Gran Telescopio Canarias (GTC), which are studied using a state-of-the-art methodology. A stellar population synthesis is conducted with 1098 spectral templates. The methodology succeeds at characterising stellar populations from 0.5 Myrs to 10 Gyrs. The light distribution shows a large red excess from a single population with 𝑙𝑜𝑔 (𝑎𝑔𝑒) > 8.5𝑦𝑟 in the GP sample analysed. This points towards an incomplete characterisation of the gas luminosity, whose continuum already accounts between 7.4% and 27.6% in the galaxy sample. The emission spectra are fitted with the largest Bayesian chemical model consisting of a electron temperature, a electron density, the logarithmic extinction coefficient and eleven ionic species under the direct method paradigm. Additionally, building on previous work, we propose a neural networks sampler to constrain the effective temperature and ionization parameter of each source from photoionization model grids. Finally, we combine both methodologies into a 16-dimensional model, which for the first time, simultaneously explores the direct method and photoionization parameter spaces. Both techniques consistently indicate a low metallicity gas, 7.76 < 12 + 𝑙𝑜𝑔 ( 𝑂 /𝐻) < 8.04, ionized by strong radiation fields, in agreement with previous works.