rMRB function

Sampling from a Moving-Resting bridge

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. A moving-resting bridge is an extension of Brownian bridge that uses moving-resting process to bridge given starting point and ending point.

rMRB(time, start_pt, end_pt, lamM, lamR, sigma, s0)

Arguments

• time: time points at which observations are to be simulated
• start_pt: the start point location of Brownian bridge (numeric for one dimension, vector for multiple dimension)
• end_pt: the end point location of Brownian brige (numeric for one dimension, vector for multiple dimension)
• 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

Returns

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

Examples

tgrid <- seq(0, 10, length=1001)
## make it irregularly spaced
tgrid <- sort(sample(tgrid, 800))

## a 2-dim moving-resting bridge starting from c(0, 0)
## and ending at c(10, -10)
dat <- rMRB(tgrid, start_pt = c(0, 0), end_pt = c(10, -10),
            lamM = 1, lamR = 1, sigma = 1, "m")
par(mfrow = c(2, 1))
plot(dat[,1], dat[,2], xlab="t", ylab="X(t)", type='l')
plot(dat[,1], dat[,3], xlab="t", ylab="X(t)", type='l')
par(mfrow = c(1, 1))