PHSMM (version 1.0)

tpmHMM: Tranistion probability matrix of the HMM representation

Description

Construction of the transition probability matrix corresponding to the HMM which exactly represents the HSMM. Not intended to be run by the user (internal function, called by the functions w2nHSMM and pmleHSMM).

Usage

tpmHMM(N, omega, d_r, R_vec, eps=1e-10)

Arguments

N

number of states of the HSMM, integer greater than 1.

omega

conditional transition probability matrix of the HSMM with N rows and N columns. The diagonal elements must be zero and the rows must sum to one.

d_r

list of vectors containing the dwell-time probabilities of the unstructured starts.

R_vec

vector of length N containing the lengths of the unstructured starts of the state dwell-time distributions.

eps

to avoid negative probabilities due to numerical underflow. Default is 1e-10.

Value

Returns the transition probability matrix of the HMM which exactly represents the HSMM.

References

For details on the code and construction of the matrix, see:

Langrock, R. and Zucchini W. (2011): Hidden Markov models with arbitrary state dwell-time distributions. Computational Statistics and Data Analysis, 55, p. 715--724.

Zucchini, W., MacDonald, I.L. and Langrock, R. (2016): Hidden Markov models for time series: An introduction using R. 2nd edition. Chapman & Hall/CRC, Boca Raton.

Examples

# NOT RUN {
# list of dwell-time probability vectors 
# (vector elements should not sum to one)
d_r<-list()
d_r[[1]]<-c(dgeom(0:9,0.2))
d_r[[2]]<-c(dgeom(0:9,0.1))
# tranistion probability matrix:
Gamma<-tpmHMM(N=2,omega=matrix(c(0,1,1,0),2,2),
  d_r=d_r,R_vec=sapply(d_r,length))
# }