## 1 Introduction  
Ground subsidence induced by underground coal mining activities is a very complicated process, which depends on mining thickness, mining depth, production methods, overlying strata properties and many other factors [1]. Because coal mining-induced land subsidence prediction plays an important role in underground mining under buildings, water bodies, railways and other important structures [2], a number of subsidence prediction methods have been proposed since the middle of the last century. Based on the differences between modeling approaches, these existing methods could be divided into three categories, including empirical methods, influence function methods and theoretical simulation methods. By making use of a larger number of in-situ subsidence observations, empirical methods could be used to develop prediction models (e.g., typical curves or profile functions) for ground movement and deformation, and the empirical formula which is used to calculate prediction parameters via the mining and geological parameters of the mining area [3; 4; 5; 6; 7]. Empirical methods are simple to use and yield fairly satisfactory results; however, the application of the methods is restricted to areas where the geological and mining conditions are identical, and can only be used to predict subsidence for simple two-dimensional problems of rectangular extraction. Theoretical simulating methods (e.g., the finite element method, boundary element simulation method and discrete element method) consider the material of the overlying strata, such as the cohesion less stochastic or elastic theoretical models [8; 9; 10; 11; 12; 13]. Based on the model, mining-induced strata or ground movement and deformation could be calculated. Although the methods could be treated as very useful tools for investigating the mechanism of underground coal mining-induced ground subsidence, their effectivity in the accuracy of their subsidence prediction has not been established. Influence function methods (e.g., Konthe theory, [PERSON]'s method, [PERSON]'s method or [PERSON]'s method) fall somewhere between empirical methods and theoretical simulating methods [14; 15; 16; 17]. The methods typically divide the extraction area into a series of infinitesimal areas (or elementary cubes) [18; 19; 20]. Based on theoretical investigation, the methods could develop influence functions to describe the influence of the extraction of infinitesimal areas. The subsidence induced by the extraction of a whole mining area is equivalent to the amount of subsidence induced by the extraction of an infinitesimal area. The parameters of influence functions could be obtained by making use of in-situ subsidence observations in general. Influence methods can be mathematically validated and are applicable in various mining conditions. While the methods would become more complicated in the case of, for example, extensive irregular area mining-induced subsidence prediction, they predict symmetrical subsidence profiles about the trough center, which is not always the case. In addition, artificial neural network-based methods have also recently been used for the prediction of mining-induced subsidence [21; 22; 23; 24; 25; 26]. Artificial neural network-based subsidence prediction seems to be a promising method for predicting coal mining-induced subsidence, although there are still many problems, such as the unexplained behavior of the network, the difficulty of determining the proper network structure, and the unknown reliability. The Probability Integration Method (PIM), the theory of which was developed by [PERSON] and functions via [PERSON]'s theory, is one of the influential function methods [27; 28; 29; 30]. The method makes use of the probability integration function as its main function.