Reconstructing the position of an interaction for any dual-phase time projection chamber (TPC) with the best precision is key to directly detecting Dark Matter. Using the likelihood-free framework, a new algorithm to reconstruct the 2-D (x; y) position and the size of the charge signal (e) of an interaction is presented. The algorithm uses the charge signal (S2) light distribution obtained by simulating events using a waveform generator. To deal with the computational effort required by the likelihood-free approach, we employ the Bayesian Optimization for Likelihood-Free Inference (BOLFI) algorithm. Together with BOLFI, prior distributions for the parameters of interest (x; y; e) and highly informative discrepancy measures to perform the analyses are introduced. We evaluate the quality of the proposed algorithm by a comparison against the currently existing alternative methods using a large-scale simulation study. BOLFI provides a natural probabilistic uncertainty measure for the reconstruction and it improved the accuracy of the reconstruction over the next best algorithm by up to 15% when focusing on events over a large radii (R > 30 cm, the outer 37% of the detector). In addition, BOLFI provides the smallest uncertainties among all the tested methods.
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