Forward filter a finite-state HMM

Run the HMM forward filter using log-emission densities and return observable predictive log-densities together with predicted and filtered state probabilities.

Usage

hmm_forward_filter(log_emission, transition_matrix, initial_probs)

Arguments

log_emission

Numeric matrix of log-emission densities with rows as observations and columns as states.

transition_matrix

Square transition probability matrix.

initial_probs

Initial state probability vector.

Value

A list with predicted_probs, filtered_probs, and log_predictive_density.

Examples

log_emission <- log(matrix(c(0.6, 0.4, 0.5, 0.5), nrow = 2, byrow = TRUE))
transition_matrix <- matrix(c(0.9, 0.1, 0.2, 0.8), nrow = 2, byrow = TRUE)
hmm_forward_filter(log_emission, transition_matrix, c(0.5, 0.5))
#> $predicted_probs
#>      [,1] [,2]
#> [1,] 0.50 0.50
#> [2,] 0.62 0.38
#> 
#> $filtered_probs
#>      [,1] [,2]
#> [1,] 0.60 0.40
#> [2,] 0.62 0.38
#> 
#> $log_predictive_density
#> [1] -0.6931472 -0.6931472
#>