rMR {smam}

Sampling from a Moving-Resting Process with Embedded Brownian Motion

Description

A moving-resting process consists of two states: moving and resting. The transition between the two states is modeled by an alternating renewal process, with exponentially distributed duration. An animal stays at the same location while resting, and moves according to a Brownian motion while moving.

Usage

rMR(time, lamM, lamR, sigma, s0, dim = 2, state = FALSE)

rMovRes(time, lamM, lamR, sigma, s0, dim = 2)

rMRME(time, lamM, lamR, sigma, sig_err, s0, dim = 2, state = FALSE)

Arguments

time

time points at which observations are to be simulated

lamM

rate parameter of the exponential duration while moving

lamR

rate parameter of the exponential duration while resting

sigma

volatility parameter of the Brownian motion while moving

s0

the state at time 0, must be one of "m" or "r", for moving and resting, respectively

dim

(integer) dimension of the Brownian motion

state

indicates whether the simulation show the states at given time points.

sig_err

s.d. of Gaussian white noise

Value

A data.frame whose first column is the time points and whose other columns are coordinates of the locations.

References

Yan, J., Chen, Y., Lawrence-Apfel, K., Ortega, I. M., Pozdnyakov, V., Williams, S., and Meyer, T. (2014) A moving-resting process with an embedded Brownian motion for animal movements. Population Ecology. 56(2): 401–415.

Pozdnyakov, V., Elbroch, L., Labarga, A., Meyer, T., and Yan, J. (2017) Discretely observed Brownian motion governed by telegraph process: estimation. Methodology and Computing in Applied Probability. doi:10.1007/s11009-017-9547-6.

Examples

tgrid <- seq(0, 10, length=1001)
## make it irregularly spaced
tgrid <- sort(sample(tgrid, 800))
dat <- rMR(tgrid, 1, 1, 1, "m")
plot(dat[,1], dat[,2], xlab="t", ylab="X(t)", type='l')

dat2 <- rMR(tgrid, 1, 1, 1, "m", state = TRUE)
head(dat2)

dat3 <- rMRME(tgrid, 1, 1, 1, 0.01, "m", state = TRUE)
head(dat3)
plot(dat3[,1], dat3[,3], xlab="t", ylab="Z(t)=X(t)+GWN(0.01)", type="l")