Yes. Scientists frequently have to deal with data that have huge amounts of "noise". To find a pattern one has to filter out the noise. Many answers here point at raw data and say "See - randomness".
To design a "prayer filter" one has to understand some basics.
Would a God who hides in this "noise" want glaring examples of miracles in this day and age? Clearly he would not. So cut out all the obvious claims.
Why would God simply answer prayers because he is asked? This makes no sense, as atheists all point out. So cut out any prayer that God has no reason to answer. Make me rich for example, or I don't want to die now.
If God has a plan, why does not he not just let the Universe follow a simple deterministic path? There would be no "purpose" in such a universe. Just as people want "interactive" video games and movies, so the game of life is interactive. There are large parts that are predetermined, but there are times God chooses to intervene.
What kind of prayers would be answered, and why? Ones that would lead to changes in direction, and small changes can have huge implications. Most of the prayers I consider answered have been small request for assistance, and I believe the reason is to make me think.
{And I do not think I am unique in this at all. God needs to reinforce "goodness" (not necessarily religion). Satan works hard to cause chaos, and no doubt Satan influences religious leaders and clerics (politicians are ripe targets).}
Does one have to ask God in a particular way? This also makes no sense. If God is aware of things, he can intervene for the sake of helping good people.
Can one address a Saint, or an image, or an ancestor? Why not? God hears it anyway. But idol worship is considered akin to Satanic so one has to be careful. God would not answer a prayer to a jug of milk for more milk because it would be typical of a lazy idolatrous sod who should help himself.
Does one have to believe in God to get a prayer answered (even one that is not verbalized)? Again this does not make sense. The criteria is whether it serves the greater good, so I think even a moral atheist would get some assistance (even if they conitinue to believe such things are pure coincidence).
Does anyone know what God's plan is? Clearly no. But he may have been giving us some indication of the big picture in subtle ways. (Einstein stated that a mere mortal could not conceive of such a thing. Simple logic.)