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The accurate location of tectonic tremors helps improve understanding of their underlying physical processes. However, current location methods often do not statistically evaluate uncertainties to a satisfactory degree and do not account for potential biases due to subsurface structures not included in the model. To address these issues, we propose a novel three-step process for locating tectonic tremors. First, the measured time- and amplitude differences between station pairs are optimized to obtain station-specific relative time and amplitude measurements with uncertainty estimates. Secondly, the time– and amplitude–distance relationships in the optimized data are used to roughly estimate the propagation speed (i.e. shear wave velocity) and attenuation strength. Linear regression is applied to each event, and the resulting velocity and attenuation strength are used for quality control. Finally, the tremor location problem is formulated within a Bayesian framework where the model parameters include the source locations, local site delay/amplification factors, shear wave velocity and attenuation strength. The Markov chain Monte Carlo algorithm is used to sample the posterior probability and is augmented by a parallel tempering scheme for an efficient global search. We tested the proposed method on ocean-bottom data indicating an intense episode of tectonic tremors in Kumano-nada within the Nankai Trough subduction zone. The results show that the range of the 95 per cent confidence interval is typically <7 km horizontally and <10 km vertically. A series of experiments with different inversion settings reveals that adopting amplitude data and site correction factors help reduce random error and systematic bias, respectively. Probabilistic sampling allows us to spatially map the probability of a tremor occurring at a given location. The probability map is used to identify lineaments of tremor sources, which provides insights into structural factors that favour tremor activity. [ABSTRACT FROM AUTHOR]