ddwell {LaMa} | R Documentation |
State dwell-time distributions of periodically inhomogeneous Markov chains
Description
Computes the dwell-time distribution of a periodically inhomogeneous Markov chain for a given transition probability matrix.
Usage
ddwell(x, Gamma, time = NULL, state = NULL)
Arguments
x |
vector of (non-negative) dwell times to compute the dwell-time distribution for |
Gamma |
array of |
time |
integer vector of time points in |
state |
integer vector of state indices for which to compute the dwell-time distribution. If |
Details
For Markov chains whose transition probabilities vary only periodically, which is achieved for example by
expressing the transition probability matrix as a periodic function of the time of day using tpm_p
or cosinor
, the probability distribution of time spent in a state can be computed analytically.
This function computes said distribution, either for a specific time point (conditioning on transitioning into the state at that time point) or for the overall distribution (conditioning on transitioning into the state at any time point).
Value
either time-varying dwell-time distribution(s) if time
is specified, or overall dwell-time distribution if time
is NULL
.
If more than one state
is specified, a named list over states is returned.
References
Koslik, J. O., Feldmann, C. C., Mews, S., Michels, R., & Langrock, R. (2023). Inference on the state process of periodically inhomogeneous hidden Markov models for animal behavior. arXiv preprint arXiv:2312.14583.
Examples
# setting parameters for trigonometric link
beta = matrix(c(-1, 2, -1, -2, 1, -1), nrow = 2, byrow = TRUE)
Gamma = tpm_p(beta = beta, degree = 1)
# at specific times and for specific state
ddwell(1:20, Gamma, time = 1:4, state = 1)
# results in 4x20 matrix
# or overall distribution for all states
ddwell(1:20, Gamma)
# results in list of length 2, each element is a vector of length 20