On the 14th of July 2013, a methane peak was observed in the Gale crater. This methane peak has been investigated in a non-biological context before. This study applies exoplanet research strategies and knowledge about biological methane production on Earth to investigate the biological context. Bayes formula is the foundation of the Bayesian framework approach as proposed by Walker et al. [53]. This Bayesian framework allows for separate investigation of biotic and abiotic methane production pathways to assess the likelihood that one of these pathways is responsible for the methane observation. Before probability is investigated, the viability of biotic methane production is gauged by Thermodynamic calculations. These calculations use the Gibbs free energy and show methanogenesis and sulfate reduction as viable catabolic reactions under Martian temperature and chemical soil and atmosphere compositions. Mars analogue Experiments were conducted into the kinetics of methane and hydrogen sulfide gas production under the influence of Martian Regolith analogue and Martian atmospheric analogue. The seed organisms were gathered from the Belgian Boom clay layer in the HADES lab because the Boom clay layer has strong mineralogical similarities to the Martian regolith. The experiments show that both methane and hydrogen sulfide gas production is not significantly affected by the introduction of modified Phylosilicate Martian Regolith Analog (P-MRA) and Martian Atmosphere Analog (MAA). Comparison with the ADM1 kinetic model shows that only methane gas production is comparable within one standard deviation between all experiments and the model. Biomass growth and sulfur gas production are inconsistent between experiments and the kinetic model. To quantify the probability of biotic methane production, a modified ADM1 model was used for Monte Carlo (MC) analysis of the correlation between the Martian observed methane peak and the kinetic model output for varying initial chemical conditions and virtual reactor volumes. Based on this, 78% of the simulations showed a significant correlation. Using Bayes formula, the posterior probability of the methane peak being biological in origin is higher than the prior probability of an anaerobic community being active around the Gale crater. However, this misses the crucial information on the chance of this methane peak occurring in abiotic conditions.