Forward-Backward Algorithm to Calculate the Posterior Probabilities of Hidden States in Normal Model

Usage

posterior_prob_normal(data, pi, mat_T, means, sdev)

Arguments

data: (numeric) normal data
pi: (numeric) prior probability of states
mat_T: (matrix) transition probability matrix
means: (numeric) vector with prior means
sdev: (numeric) prior standard deviation

Value

List with the following elements:

F: auxiliary forward variables
B: auxiliary backward variables
s: weights

Details

Please see supplementary information at doi:10.1186/s12859-024-05751-4 for more details on the algorithm.

Examples

prior_mat <- rbind(c(1-0.05, 0.05, 0),
                  c(0.05, 1-0.1, 0.05),
                  c(0, 0.05, 1-0.05))

prior_means <- c(-0.1, 0.0, 0.1)
prior_sd  <- sqrt(0.1)
L <- 100

# Simulate HMM model based on normal data based on prior information
sim_data_normal <- hmm_simulate_normal_data(L = L,
                                            mat_T = prior_mat,
                                            means = prior_means,
                                            sigma = prior_sd)
pi <- sim_data_normal$pi
# pi <- get_pi(prior_mat)
hmm_norm_data <- sim_data_normal$data

# Calculate posterior probabilities of hidden states
post_prob <-  posterior_prob_normal(data = hmm_norm_data,
                                    pi = pi,
                                    mat_T = prior_mat,
                                    means = prior_means,
                                    sdev = prior_sd)
str(post_prob)
#> List of 3
#>  $ F: num [1:100, 1:3] 0.363 0.358 0.213 0.372 0.386 ...
#>  $ B: num [1:100, 1:3] 1.51 1.49 7.26 6.28 1.59 ...
#>  $ s: num [1:100] 1.157 1.221 0.433 0.307 1.207 ...