mcmc.fmove {ctmcmove}

Fit continuous-time functional movement model to telemetry data.

Description

Fits a functional movement model to telemetry data following Buderman et al., 2015.

Usage

mcmc.fmove(xy,t,fdabasis,tpred=t,QQ="CAR2",a=1,b=1,r=1,q=1,
           n.mcmc=100,num.paths.save=10,sigma.fixed=NA)

Arguments

xy

A two-column matrix with each row corresponding to the x,y locations of a telemetry location.

t

A numeric vector of length = nrow(xy), with the i-th entry corresponding to the time of the i-th telemetry location in xy.

fdabasis

A "basisfd" object, typically resulting from a call to "create.bspline.basis" in the fda package. Other basis functions can be used.

tpred

Numeric vector of times to impute the quasi-continuous path.

QQ

The precision matrix of the fda basis coefficients. This can either be a string, taking on values of "CAR1" or "CAR2", or can be a user specified matrix (or sparse matrix using the Matrix package) of dimension equal to the number of basis functions in fdabasis. Defaults to "CAR2". "CAR1" will result in less-smooth paths.

a

The shape parameter of the inverse gamma prior on the observation variance.

b

The scale parameter of the inverse gamma prior on the observation variance.

r

The shape parameter of the inverse gamma prior on the partial sill parameter of the spline basis coefficients.

q

The scale parameter of the inverse gamma prior on the partial sill parameter of the spline basis coefficients.

n.mcmc

Number of mcmc iterations to run.

num.paths.save

Number of quasi-continuous path realizations to save. Defaults to 10.

sigma.fixed

Numeric value (or the default NA). If NA, then the observation variance sigma^2 is estimated using MCMC. If a numeric value, this is the fixed standard deviation of the observation error.

Details

Fits the functional movement model of Buderman et al., 2015, and outputs quasi-continuous paths that stochastically interpolate between telemetry locations. The model fit is as follows (written out for 1-D):

y_t = observed location at time t

z_t = Sum_k beta_k*phi_k(t) = true location at time t, expressed using a linear combination of spline basis functions phi_k(t).

y_t ~ N( z_t , sigma^2 )

beta ~ N( 0 , tau^2 * QQ^-1 )

sigma^2 ~ IG(a,b)

tau^2 ~ IG(r,q)

Value

s2.save

Numeric vector of the values of sigma^2 at each mcmc iteration

tau2.save

Numeric vector of the values of tau^2 at each mcmc iteration

pathlist

A list of length num.paths.save, with each item itself being a list with two entries:

xy = a matrix with rows corresponding to x,y locations of the quasi-continuous path imputation

t = a vector with entries corresponding to the times at which the quasi-continuous path was imputed

Author(s)

Ephraim M. Hanks

References

Buderman, F.E.; Hooten, M. B.; Ivan, J. S. and Shenk, T. M. A functional model for characterizing long-distance movement behavior. Methods in Ecology and Evolution, 2016, 7, 264-273.

Examples

## For example code, do
##
## > help(ctmcMove)