Chi-square analog for context-dependent distributions Lets imagine that we have some experiments. Each experiment may result in one of the outcomes: A, B, C. So we have probabilities distribution for each experiment $P_A, P_B, P_C$ which is context-dependent.
E.g.:  


*

*$Context_1 \Rightarrow \{P_A^1, P_B^1, P_C^1\},$ experimental outcome is A

*$Context_2 \Rightarrow \{P_A^2, P_B^2, P_C^2\},$ experimental outcome is B

*$Context_3 \Rightarrow \{P_A^3, P_B^3, P_C^3\},$ experimental outcome is A

*$Context_4 \Rightarrow \{P_A^4, P_B^4, P_C^4\},$ experimental outcome is C


This probabilities are calculated by some function $F:Context\rightarrow \{P_A, P_B, P_C\}$  
I want to estimate an absolute trust rate of this function. In other words, I want to be able to say "we can trust this function on 86%" like we do when we deal with Pearson's chi-square test.  
Any suggestions?
 A: Sounds like you'll need a HMM to do that.
Have you read
Lawrence R. Rabiner (February 1989). "A tutorial on Hidden Markov Models and selected applications in speech recognition"
There are a few examples of models parameters discovery on page 259.
The question is how do you plan to update the probabilites? Maybe you can use a kind of success ratio? (if the player has not managed to win much recently using one of the 3 strategies, he may use it less and try more the two others...)
A: I may be misunderstanding your question (and falling into the same misunderstanding as fRed despite your explanation), in which case I apologize.  It seems to me like you are saying you already know the various P_A, P_B, and P_C values for each context.  I assume P_A + P_B + P_C = 1? Given those priors and the actual outcome you want to characterize the accuracy of the already established P values?
One approach might be simulation.  Given the various P_A, P_B, and P_C values for each context you could generate guesses from the model at the probabilities indicated by each P value and then compare that to the obtained data.  Averaging over many simulations you should get a sense of the average hit-rate of the model.
