fitStateMR function

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

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.

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.

Returns

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.

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.

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)

See Also

rMR for simulation. fitMR for estimation of parameters.

Author(s)

Chaoran Hu