Calculate conditional local state probabilities for periodically inhomogeneous HMMs

Computes $$\Pr(S_t = j \mid X_1, ..., X_T)$$ for periodically inhomogeneous HMMs

Usage

stateprobs_p(delta, Gamma, allprobs, tod, trackID = NULL, mod = NULL)

Arguments

delta

initial or stationary 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) as computed by stationary_p.

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.

Value

matrix of conditional state probabilities of dimension c(n,N)

See also

Other decoding functions: stateprobs(), stateprobs_g(), viterbi(), viterbi_g(), viterbi_p()

Examples

L = 24
beta = matrix(c(-1, 2, -1, -2, 1, -1), nrow = 2, byrow = TRUE)
Gamma = tpm_p(1:L, L, beta, degree = 1)
delta = stationary_p(Gamma, 1)
allprobs = matrix(runif(200), nrow = 100, ncol = 2)
tod = rep(1:24, 5)[1:100]

probs = stateprobs_p(delta, Gamma, allprobs, tod)