Viterbi algorithm for state decoding in periodically inhomogeneous HMMs
The Viterbi algorithm allows one to decode the most probable state sequence of an HMM.
viterbi_p(delta, Gamma, allprobs, tod, trackID = NULL, mod = NULL)
delta: initial distribution of length N, or matrix of dimension c(k,N) for k independent tracks, if trackID is provided
This could e.g. be the periodically stationary distribution (for each track).
Gamma: array of transition probability matrices for each time point in the cycle of dimension c(N,N,L), where L is the length of the cycle
allprobs: matrix of state-dependent probabilities/ density values of dimension c(n, N)
tod: (Integer valued) variable for cycle indexing in 1, ..., L, mapping the data index to a generalised time of day (length n)
For half-hourly data L = 48. It could, however, also be day of year for daily data and L = 365.
trackID: optional vector of k track IDs, if multiple tracks need to be decoded separately
mod: optional model object containing initial distribution delta, transition probability matrix Gamma, matrix of state-dependent probabilities allprobs, and potentially a trackID variable
If you are using automatic differentiation either with RTMB::MakeADFun or qreml and include forward_p in your likelihood function, the objects needed for state decoding are automatically reported after model fitting. Hence, you can pass the model object obtained from running RTMB::report() or from qreml directly to this function.
vector of decoded states of length n
delta = c(0.5, 0.5) beta = matrix(c(-2, 1, -1, -2, -1, 1), nrow = 2, byrow = TRUE) Gamma = tpm_p(1:24, 24, beta) tod = rep(1:24, 10) n = length(tod) allprobs = matrix(runif(2*n), nrow = n, ncol = 2) states = viterbi_p(delta, Gamma, allprobs, tod)
Other decoding functions: stateprobs(), stateprobs_g(), stateprobs_p(), viterbi(), viterbi_g()