sim_markov_bridge: Simulate Markov chain bridge.
In a-parton/CTStepTurn: Fitting the continuous-time step-and-turn movement model

Description Usage Arguments Details Value See Also Examples

sim_markov_bridge returns a simulated realisation of a Markov chain between two known values and times.

1	sim_markov_bridge(num_states, fixed_values, behav_params)

num_states

Numeric, number of (behavioural) states in the Markov chain.

fixed_values

List with components:

inc_times: Vector of length two, start and end times of the simulation.
inc_behavs: Vector of length two, start and end known values (behaviours) of the simulation.

behav_params

List with components:

lambda: Vector of length num_states, switching rates out of each state.
q: Sqaure matrix size num_states, probability of switching from (row) each state to (column) another. Diagonal elements are NA.

Simulation is by rejection. Markov chain simulated forwards in time from the starting point, and then compared with the known end point. If the end point is correct, the simulation is accepted, otherwise it is rejected.

List with the components:

accept: Binary element that the rejection simulation has been accepted/rejected. If rejected, this is the only return value.
times: Vector, switching times of the simulation. Includes the fixed end points.
states: Vector, states at switching times of the simulation. Includes the fixed end points.

Other Markov chain simulations: calc_markov_steady_state, sim_markov_backward, sim_markov_forward

end_points <- list(inc_times = c(0,10),
                   inc_behavs = c(1,3))
param <- list(lambda = c(0.1,0.2,0.3),
              q = matrix(c(NA,0.5,0.3,0.35,NA,0.7,0.65,0.5,NA),nrow=3))

set.seed(123) # simulation does not meet correct end point and is rejected
sim_markov_bridge(3, end_points, param)
# $accept
# [1] FALSE

set.seed(2712) # simultion is accepted
sim_markov_bridge(3, end_points, param)
# $accept
# [1] TRUE
#
# $times
# [1]  0.000000  5.694254  6.831134  7.503054 10.000000
#
# $states
# [1] 1 3 1 3 3