# Probability of state sequences. Calculates the conditional probability of one or more state sequences, given the corresponding observations sequences (and the model parameters. ```r pr(s, y, model=NULL, tpm, Rho, ispd=NULL, warn=TRUE) ``` ## Arguments - `s`: A sequence of states of the underlying Markov chain, or a list of such sequences or a list of lists (!!!) of such sequences. - `y`: A data set to which a hidden Markov model might be fitted, or a collection of such data sets in the form of an object of class `"multipleHmmDataSets"` as returned by `rhmm()` if the argument `nsim` is greater than 1. In this latter case `s` must be a list of the same length as `y`, and `pr()` is applied recursively to each pair of entries of `s` and `y`. If `y` consists of a single observation sequence, it is used with each of the state sequences in `s` in turn. Otherwise the length of the list `y` must be the same as the length of the list `s`. (If not, then an error is given). If `y` is missing, it is extracted from `model` (whence it will **not** be of class `"multipleHmmDataSets"`!) provided that `model` and its `y` component are not `NULL`. Otherwise an error is given. - `model`: An object of class `hmm.discnp` as returned by `hmm()`. - `tpm`: The transition probability matrix of the chain. Ignored (and extracted from `model` instead) if `model` is not `NULL`. - `Rho`: An object specifying the emission probabilities of observations, given the underlying state. See `hmm()`. Ignored (and extracted from `model` instead) if `model` is not `NULL`. - `ispd`: The vector specifying the initial state probability distribution of the Markov chain. Ignored (and extracted from `model` instead) if `model` is not `NULL`. If both `ispd` and `model` are NULL then `ispd` is taken to be the stationary distribution of the chain, calculated from `tpm`. - `warn`: Logical scalar; should a warning be issued if `Rho` hasn't got relevant dimension names? (Note that if this is so, then the corresponding dimension names are formed from the sorted unique values of `y` or of the appropriate column(s) of `y`. And if **this** is so, then the user should be sure that the ordering of the entries of `Rho` corresponds properly to the the sorted unique values of `y`.) This argument is passed to the utility function `check.yval()` which actually issues the warning if `warn=TRUE`. ## Returns The probability of `s` given `y`, or a vector of such probabilities if `s` and `y` are lists, or a list of such vectors if `y` is of class `"multipleHmmDataSets"`. ## Author(s) Rolf Turner r.turner@auckland.ac.nz ## Warning The conditional probabilities will be tiny if the sequences involved are of any substantial length. Underflow may be a problem. The implementation of the calculations is not sophisticated. ## See Also `hmm()`, `mps()`, `viterbi()`, `sp()`, `fitted.hmm.discnp()` ## Examples ```r ## Not run: P <- matrix(c(0.7,0.3,0.1,0.9),2,2,byrow=TRUE) R <- matrix(c(0.5,0,0.1,0.1,0.3, 0.1,0.1,0,0.3,0.5),5,2) set.seed(42) lll <- sample(250:350,20,TRUE) set.seed(909) y.num <- rhmm(ylengths=lll,nsim=1,tpm=P,Rho=R,drop=TRUE) fit.num <- hmm(y.num,K=2,keep.y=TRUE,verb=TRUE) # Using fitted parmeters. s.vit.1 <- viterbi(y.num,fit.num) pr.vit.1 <- pr(s.vit.1,model=fit.num) # Using true parameters from which y.num was generated. s.vit.2 <- viterbi(y.num,tpm=P,Rho=R) pr.vit.2 <- pr(s.vit.2,y.num,tpm=P,Rho=R) set.seed(202) y.mult <- rhmm(fit.num,nsim=4) s.vit.3 <- viterbi(y.mult,tpm=fit.num$tpm,Rho=fit.num$Rho) pr.vit.3 <- pr(s.vit.3,y.mult,tpm=fit.num$tpm,Rho=fit.num$Rho) ## End(Not run) ```

pr function