fitStateMR {smam}

Estimation of states at each time point with Moving-Resting Process

Description

Estimate the state at each time point under the Moving-Resting process with Embedded Brownian Motion with animal movement data at discretely time points. See the difference between fitStateMR and fitViterbiMR in detail part. Using fitPartialViterbiMR to estimate the state within a small piece of time interval.

Usage

fitStateMR(data, theta, cutoff = 0.5, integrControl = integr.control())

fitViterbiMR(data, theta, cutoff = 0.5, integrControl = integr.control())

fitPartialViterbiMR(
  data,
  theta,
  cutoff = 0.5,
  startpoint,
  pathlength,
  integrControl = integr.control()
)

Arguments

data

a data.frame whose first column is the observation time, and other columns are location coordinates.

theta

the parameters for Moving-Resting model, in the order of rate of moving, rate of resting, volatility.

cutoff

the cut-off point for prediction.

integrControl

Integration control vector includes rel.tol, abs.tol, and subdivisions.

startpoint

Start time point of interested time interval.

pathlength

the length of interested time interval.

Details

fitStateMR estimates the most likely state by maximizing the probability of Pr(S(t = t_k) = s_k | X), where X is the whole data and s_k is the possible sates at t_k (moving, resting).

fitViterbiMR estimates the most likely state path by maximizing Pr(S(t = t_0) = s_0, S(t = t_1) = s_1, ..., S(t = t_n) = s_n | X), where X is the whole data and s_0, s_1, ..., s_n is the possible state path.

fitPartialViterbiMR estimates the most likely state path of a small peice of time interval, by maximizing the probability of Pr(S(t = t_k) = s_k, ..., S(t = t_{k+q-1}) = s_{k+q-1} | X), where k is the start time point and q is the length of interested time interval.

Value

A data.frame contains estimated results, with elements:

• original data be estimated.

• conditional probability of moving, resting (p.m, p.r), which is Pr(S(t = t_k) = s_k | X) for fitStateMR; log-Pr(s_0, ..., s_k | X_k) for fitViterbiMR, where X_k is (X_0, ..., X_k); and log-Pr(s_k, ..., s_{k+q-1}|X) for fitPartialViterbiMR.

• estimated states with 1-moving, 0-resting.

Author(s)

Chaoran Hu

See Also

rMR for simulation. fitMR for estimation of parameters.

Examples

set.seed(06269)
tgrid <- seq(0, 400, by = 8)
dat <- rMR(tgrid, 4, 3.8, 5, 'm')
fitStateMR(dat, c(4, 3.8, 5), cutoff = 0.5)
fitViterbiMR(dat, c(4, 3.8, 5), cutoff = 0.5)
fitPartialViterbiMR(dat, c(4, 3.8, 5), cutoff = 0.5, 20, 10)