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Inversion problems arises in many fields of science focusing on the process that explores the causal factors from which a set of measurements are observed. Statistical inversion is an alternative approach compared to deterministic methods with better capability to find optimal inverse values. Due to the increasing volume of data collections in the oil and gas industry, statistical approaches show its advantage on the implementation of large-scale inverse problems. In this paper, we address on the solution of big-data-scale inverse problems. After examining both conventional deterministic and statistical methods, we propose a statistical approach based on the Markov Chain Monte Carlo (MCMC) method and its implementation with the scalable dataset on the big data platform. The feasibility and methods to apply statistical inversion on the big data platform is evaluated by examining the use of parallelization and MapReduce technique. Numerical evidence from the simulation on our synthetic dataset suggests a significant improvement on the performance of inversion work. [ABSTRACT FROM AUTHOR]