  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.
