fitStateMRH function

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

Estimate the state at each time point under the Moving-Resting-Handling process with Embedded Brownian Motion with animal movement data at discretely time points. See the difference between fitStateMRH

and fitViterbiMRH in detail part. Using fitPartialViterbiMRH

to estimate the state during a small piece of time interval.

fitStateMRH(data, theta, integrControl = integr.control())

fitViterbiMRH(data, theta, integrControl = integr.control())

fitPartialViterbiMRH(
  data,
  theta,
  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-Handling model, in the order of rate of moving, rate of resting, rate of handling, volatility and switching probability.
• 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, handling (p.m, p.r, p.h), which is $Pr(S(t = t_k) = s_k | X)$ for fitStateMRH; $log-Pr(s_0, ..., s_k | X_k)$ for fitViterbiMRH, where $X_k$ is $(X_0, ..., X_k)$; and $log-Pr(s_k, ..., s_{k+q-1}|X)$ for fitPartialViterbiMRH.
• estimated states with 0-moving, 1-resting, 2-handling.

Details

fitStateMRH 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 or handling).

fitViterbiMRH 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.

fitPartialViterbiMRH 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

## Not run:

## time consuming example
set.seed(06269)
tgrid <- seq(0, 400, by = 8)
dat <- rMRH(tgrid, 4, 0.5, 0.1, 5, 0.8, 'm')
fitStateMRH(dat, c(4, 0.5, 0.1, 5, 0.8))
fitViterbiMRH(dat, c(4, 0.5, 0.1, 5, 0.8))
fitPartialViterbiMRH(dat, c(4, 0.5, 0.1, 5, 0.8), 20, 10)
## End(Not run)

References

Pozdnyakov, V., Elbroch, L.M., Hu, C., Meyer, T., and Yan, J. (2018+) On estimation for Brownian motion governed by telegraph process with multiple off states. arXiv:1806.00849

See Also

rMRH for simulation. fitMRH for estimation of parameters.

Author(s)

Chaoran Hu