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• The HMR model can accurately predict the methane production of the individual cows studied. • It models population-level shape parameters while allowing individual variation in scale. • The partially pooled approach made more accurate predictions than the fully pooled one. Monitoring methane production from individual cows is required for evaluating the success of greenhouse gas reduction strategies. However, converting non-continuous measurements of methane production into daily methane production rates (MPR) remains challenging due to the general non-linearity of the methane production curve. In this paper, we propose a Bayesian hierarchical stochastic kinetic equation approach to address this challenge, enabling the sharing of information across cows for improved modelling. We fit a non-linear curve on climate respiration chamber (CRC) data of 28 dairy cows before computing an area under the curve, thereby providing an estimate of MPR from individual cows, yielding a monitored and predicted population mean of 416.7 ± 36.2 g/d and 407.2 ± 35.0 g/d respectively. The shape parameters of this model were pooled across cows (population-level), while the scale parameter varied between individuals. This allowed for the characterization of variation in MPR within and between cows. Model fit was thoroughly investigated through posterior predictive checking, which showed that the model could reproduce this CRC data accurately. Comparison with a fully pooled model (all parameters constant across cows) was evaluated through cross-validation, where the Hierarchical Methane Rate (HMR) model performed better (difference in expected log predictive density of 1653). Concordance between the values observed in the CRC and those predicted by HMR was assessed with R2 (0.995), root mean square error (10.0 g/d), and Lin's concordance correlation coefficient (0.961). Overall, the predictions made by the HMR model appeared to reflect individual MPR levels and variation between cows as well as the standard analytical approach taken by scientists with CRC data. [ABSTRACT FROM AUTHOR]