Marble statues can change color for a few different reasons but mainly are all due to natural chemical reactions. Stone and marble are usually harder to discolor than metal but this can still happen and can be seen in art today.
One factor that can change the color or a marble statue over time is acid rain. In the case that a statue is left outside to be displayed there is the risk of acid rain affecting the work. For instance the faces can literally be worn away from acid rain erosion. This also happens a lot in cemeteries on headstones to the point where the headstone is no longer legible. These are cases where the statue has been outside in acid rain for an extended amount of time. Acid rain can also discolor the statue. If you have ever seen a statue with streaks of discoloration running through them this can also have been caused by being exposed to acid rain.
While researching this topic I also found out that discoloration to marble statues could be caused if the statues are moved around from place to place. If they started as an indoor sculpture and then are moved outdoors for display the elements can cause changes in the color of the statue. This can happen when iron is transported onto the stone by water and then stays there causing the color to change.
Another reason that the statues may change color is due to the internal structure that may have been built inside of the statue to give it more support. If the support structure is metal, over time it may begin to release metal ions into the stone. This release of metal ions into the stone will eventually change the color of the marble that the statues are made of over time.