# smooth.semi: Calculate the probability of being in a particular state for... In rarhsmm: Regularized Autoregressive Hidden Semi Markov Model

## Description

Calculate the probability of being in a particular state for each observation.

## Usage

 `1` ```smooth.semi(y, mod) ```

## Arguments

 `y` observed series `mod` list consisting the at least the following items: mod\$m = scalar number of states, mod\$delta = vector of initial values for prior probabilities, mod\$gamma = matrix of initial values for state transition probabilies. mod\$mu = list of initial values for means, mod\$sigma = list of initial values for covariance matrices. mod\$d = list of state duration probabilities. For autoregressive hidden markov models, we also need the additional items: mod\$arp = scalar order of autoregressive structure mod\$auto = list of initial values for autoregressive coefficient matrices

## Value

a matrix containing the state probabilities

## References

Rabiner, Lawrence R. "A tutorial on hidden Markov models and selected applications in speech recognition." Proceedings of the IEEE 77.2 (1989): 257-286.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```set.seed(15562) m <- 2 mu <- list(c(3,4,5),c(-2,-3,-4)) sigma <- list(diag(1.3,3), matrix(c(1,-0.3,0.2,-0.3,1.5,0.3,0.2,0.3,2),3,3,byrow=TRUE)) delta <- c(0.5,0.5) gamma <- matrix(c(0,1,1,0),2,2,byrow=TRUE) d <- list(c(0.4,0.2,0.1,0.1,0.1,0.1),c(0.5,0.3,0.2)) auto <- list(matrix(c(0.3,0.2,0.1,0.4,0.3,0.2, -0.3,-0.2,-0.1,0.3,0.2,0.1, 0,0,0,0,0,0),3,6,byrow=TRUE), matrix(c(0.2,0,0,0.4,0,0, 0,0.2,0,0,0.4,0, 0,0,0.2,0,0,0.4),3,6,byrow=TRUE)) mod <- list(m=m,mu=mu,sigma=sigma,delta=delta,gamma=gamma, auto=auto,arp=2,d=d) sim <- hsmm.sim(2000,mod) y <- sim\$series state <- sim\$state fit <- em.semi(y=y, mod=mod, arp=2) stateprob <- smooth.semi(y=y,mod=fit) head(cbind(state,stateprob),20) ```

### Example output

```iteration  1 ; loglik =  -10528.78
iteration  2 ; loglik =  -10503.73
state            1            2
[1,]     1 1.000000e+00 5.957608e-53
[2,]     1 1.000000e+00 5.356154e-34
[3,]     1 1.000000e+00 1.975280e-35
[4,]     1 1.000000e+00 6.290035e-48
[5,]     2 1.800191e-50 1.000000e+00
[6,]     1 1.000000e+00 1.327076e-19
[7,]     1 1.000000e+00 7.359963e-35
[8,]     1 1.000000e+00 1.077423e-27
[9,]     1 1.000000e+00 1.817945e-54
[10,]     2 7.185814e-39 1.000000e+00
[11,]     2 1.549371e-41 1.000000e+00
[12,]     1 1.000000e+00 1.482615e-22
[13,]     1 1.000000e+00 1.444602e-25
[14,]     2 9.598501e-28 1.000000e+00
[15,]     1 1.000000e+00 4.141223e-47
[16,]     2 1.255110e-32 1.000000e+00
[17,]     2 7.262155e-30 1.000000e+00
[18,]     2 7.083572e-52 1.000000e+00
[19,]     1 1.000000e+00 1.817082e-60
[20,]     2 5.073122e-41 1.000000e+00
```

rarhsmm documentation built on May 2, 2019, 9:33 a.m.