SteffenZeidler

Hi Brian -- For a simple generic numerical solution could be used an additional function parameter mul.

static IObservable<IDictionary<S, Tuple<P, S>>> ViterbiRx<O, S, P>
(IObservable<Tuple<O, IEnumerable<S>>> obsStates, Func<S, P> startingProb, Func<S, S, P> transitionProb, Func<S, O, P> emissionProb, Func<P, P, P> mul)
{
    return obsStates.Scan((IDictionary<S, Tuple<P, S>>)null, (v, o) => o.Item2.ToDictionary(target => target, target =>
        v == null ? Tuple.Create(mul(startingProb(target), emissionProb(target, o.Item1)), target)
        : v.Select(source => Tuple.Create(mul(mul(source.Value.Item1, transitionProb(source.Key, target)), emissionProb(target, o.Item1)), source.Key)).Max()));
}

Test:

var obsResults = ViterbiRx<string,string,double>(mul: (x1, x2) => x1 * x2, ...);
var res = obsResults.ToListObservable();
Debug.Assert(Math.Round(res.Value[Rainy].Item1, 6) == 0.013440);
Debug.Assert(Math.Round(res.Value[Sunny].Item1, 6) == 0.002592);
Debug.Assert(res.Value.OrderBy(x => x.Value).Last().Key == Rainy);
Debug.Assert(res[2][Rainy].Item2 == Rainy);
Debug.Assert(res[1][Rainy].Item2 == Sunny);

Even with C# and LINQ a compact functional implementation is possible:

//using alias directive for P: using P = Double;
static IObservable<IDictionary<S, Tuple<P, S>>> ViterbiRx<O, S>
(IObservable<Tuple<O, IEnumerable<S>>> obsStates, Func<S, P> startingProb, Func<S, S, P> transitionProb, Func<S, O, P> emissionProb)
{
    return obsStates.Scan((IDictionary<S, Tuple<P, S>>)null, (v, o) => o.Item2.ToDictionary(target => target, target =>
        v == null ? Tuple.Create(startingProb(target) * emissionProb(target, o.Item1), target)
        : v.Select(source => Tuple.Create(source.Value.Item1 * transitionProb(source.Key, target) * emissionProb(target, o.Item1), source.Key)).Max()));
}