Array database systems are architected for scientific and engineering applications. In these applications, the value of a cell is often imprecise and uncertain. There are at least two reasons that a Monte Carlo query processing algorithm is usually required for such uncertain data. Firstly, a probabilistic graphical model must often be used to model correlation, which requires a Monte Carlo inference algorithm for the operations in our database. Secondly, mathematical operators required by science and engineering domains are much more complex than those of SQL. State-of-the-art query processing uses Monte Carlo approximation. We give an example of using Markov Random Fields combined with an array's chunking or tiling mechanism to model correlated data. We then propose solutions for two of the most challenging problems in this framework, namely the expensive array join operation, and the determination and optimization of stopping conditions of Monte Carlo query processing. Finally, we perform an extensive empirical study on a real world application.