We studied the application of statistical reconstruction algorithms, namely maximum likelihood and least squares methods, to the problem of event reconstruction in a dual phase liquid xenon detector. An iterative method was developed for in-situ reconstruction of the PMT light response functions from calibration data taken with an uncollimated γ-ray source. Using the techniques described, the performance of the ZEPLIN-III dark matter detector was studied for 122 keV γ-rays. For the inner part of the detector (R<100 mm), spatial resolutions of 13 mm and 1.6 mm FWHM were measured in the horizontal plane for primary and secondary scintillation, respectively. An energy resolution of 8.1% FWHM was achieved at that energy. The possibility of using this technique for improving performance and reducing cost of scintillation cameras for medical applications is currently under study.