I imagine the efficiency of their algorithms depends on what they're looking for. If they're looking for patterns similar to those of historical terrorists, then their false positive rate is likely reasonably low considering the scale of their data set. If they're looking for patterns or traits of hypothetical terrorist behavior, that's another story. Systems-based trading in the financial sector comes to mind. Const…
what if its not just all about terrorist behaviour
Recent quotes concerning GCHQ provide an interesting insight in this regard:
http://www.guardian.co.uk/world/2013/jun/09/prism-gchq-willi...
> "If you are a law-abiding citizen ..."
This implies they go after criminals and not just terrorists.
> "... of all the things those agencies are doing to stop your identify being stolen ..."
I guess they're also in the identity protection business.
> "But if you are a would-be terrorist or the centre of a criminal network ..."
Again, targeting of criminals (albeit high level).
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IMHO, a top-secret dragnet surveillance program that's tightly restricted in scope to national security matters is a much easier pill to swallow than a completely legal, known program. The latter becomes nightmarish as soon as the data aggregates down the chain to law enforcement or other government agencies. Imagine local police departments having the same level of information about private citizens as NSA does. That's terrifying.