Viterbi.hmm0norm {HMMextra0s}

Viterbi Path of a 1-D HMM with Extra Zeros

Description

Finds the most probable sequence of hidden states of an observed process.

Usage

Viterbi.hmm0norm(R, Z, HMMest)

Arguments

R

is the observed data. R is a T * 1 matrix, where T is the number of observations.

Z

is the binary data with the value 1 indicating that an event was observed and 0 otherwise. Z is a vector of length T.

HMMest

is a list which contains pie, gamma, sig, mu, and delta (the HMM parameter estimates).

Value

y

is the estimated Viterbi path.

v

is the estimated probability of each time point being in each state.

Author(s)

Ting Wang

References

Wang, T., Zhuang, J., Obara, K. and Tsuruoka, H. (2016) Hidden Markov Modeling of Sparse Time Series from Non-volcanic Tremor Observations. Journal of the Royal Statistical Society, Series C, Applied Statistics, 66, Part 4, 691-715.

Examples

pie <- c(0.002,0.2,0.4)
gamma <- matrix(c(0.99,0.007,0.003,
                  0.02,0.97,0.01,
                  0.04,0.01,0.95),byrow=TRUE, nrow=3)
mu <- matrix(c(0.3,0.7,0.2),nrow=1)
sig <- matrix(c(0.2,0.1,0.1),nrow=1)
delta <- c(1,0,0)
y <- sim.hmm0norm(mu,sig,pie,gamma,delta, nsim=5000)
R <- as.matrix(y$x,ncol=1)
Z <- y$z
HMMEST <- hmm0norm(R, Z, pie, gamma, mu, sig, delta)
Viterbi3 <- Viterbi.hmm0norm(R,Z,HMMEST)