Great, there goes the neighborhood. Who let the finance guys in? Seriously, I've been known to do a few things in quant finance, so I guess I can give an opinion.
Yes, F#/ML is well suited to all three disciplines that you mention.
- Statistics - there aren't a lot of libraries out to do this type of work, but implementation is cheap for many of the basics. There are also a few good libraries (dnAnalytics, QuantLIB, etc.) that have great code bases (not in F#) that can either be used directly (interop with F#), or as a model for building your own. Obviously those libraries are also focused on aspects in Quant Finance and not just the statistics aspect. I still use 'R' for some of my statistics works, but I'm trying to get as much built in F# as necessary to cover that functionality.
- High Frequency - Give me your view on "high-frequency". Are you talking real time tick data off of standard finance feeds? I keep about 2TB of daily data from the markets and find F# as one of the best manipulation tools. I think that SQL Server Service Broker and/or WF present useful models of infrastructure although neither is a feature rich as BizTalk. F# plays well with all of these and adds suitable advantage.
- AI - I currently have models within JJB Research to perform Genetic Algorithms, Genetic Programming, Emergent Computation, Swarm Computation and ACO (Ant Colony Optimization) all in F#. I'm just starting to do work in Bayesian Networks, SVMs and a few other disciplines. I have not done any significant work in Neural Nets in F# although that would be trivial to implement. While I can't share those code bases, I can tell you that F# adds value in each of these areas.
I tend not to think of "vs." when doing this type of work. F#, C#, C++ and others are nothing more than tools. Used well, each is capable of yielding great results. For me the key is the interop, i.e. I want an environment where I can do F#, C#, SQL Server, BizTalk, WF, WCF, XML, etc. without regard to costs of interop. I get that with the .NET runtime. All of those other tools make things easy to build. F# is the key to my infrastructure for compute intensive tasks. In representation, it is less verbose and much easier to represent many of my works, models in particular, when compared with any other language out there, even outside of .NET.
What you should consider is the cost in time to learn. Be certain that you have enough time/effort to learn these languages to a level of competence that will give you the leverage that you need. If you already have ML in your background, I would think the cost to learn F# would be cheap.
My works made many a ring. I had an ideal setting at Berlin with Karl and Leopold.