bandwidth | R Documentation |
This function calculates the optimal bandwidth matrix (kernel covariance) for a two-dimensional animal tracking dataset, given an autocorrelated movement model (Fleming et al, 2015). This optimal bandwidth can fully take into account all autocorrelation in the data, assuming it is captured by the movement model.
bandwidth(data,CTMM,VMM=NULL,weights=FALSE,fast=NULL,dt=NULL,PC="Markov",error=0.01,
precision=1/2,verbose=FALSE,trace=FALSE,dt.plot=TRUE,...)
data |
2D timeseries telemetry data represented as a |
CTMM |
A |
VMM |
An optional vertical |
weights |
By default, the weights are taken to be uniform, whereas |
fast |
Use FFT algorithms for weight optimization. |
dt |
Optional lag bin width for the FFT algorithm. |
PC |
Preconditioner to use: can be "Markov", "circulant", "IID", or "direct". |
error |
Maximum grid error for FFT algorithm, if |
precision |
Fraction of maximum possible digits of precision to target in weight optimization. |
verbose |
Optionally return the optimal |
trace |
Produce tracing information on the progress of weight optimization. |
dt.plot |
Execute a diagnostic |
... |
Arguments passed to |
The weights=TRUE
argument can be used to correct temporal sampling bias caused by autocorrelation.
weights=TRUE
will optimize n=length(data$t)
weights via constrained & preconditioned conjugate gradient algorithms.
These algorithms have a few options that should be considered if the data are very irregular.
fast=TRUE
is an approximation that discretizes the data with timestep dt
and applies FFT algorithms, for a computational cost as low as O(n \log n)
with only O(n)
function evaluations.
If no dt
is specified, then a choice of dt
will be automated with a message.
If the data contain some very tiny time intervals, say 1 second among hourly sampled data, then the default dt
setting can create an excessively high-resolution discretization of time, which will cause slowdown. In this case CTMM
should contain a location-error model and dt
should be increased to a larger fraction of the most-frequent sampling intervals.
If the data are irregular (permitting gaps), then dt
may need to be several times smaller than the median to avoid slow down.
In this case, try setting trace=TRUE
and decreasing dt
below the median until the interations speed up and the number of feasibility assessments becomes less than O(n)
.
fast=FALSE
uses exact time spacing and has a computational cost as low as O(n^2)
, including O(n^2)
function evaluations. With PC="direct"
this method will produce a result that is exact to within machine precision, but with a computational cost of O(n^3)
. fast=FALSE,PC='direct'
is often the fastest method with small datasets, where n \le O
(1,000), but scales terribly with larger datasets.
Returns a bandwidth matrix
object, which is to be the optimal covariance matrix of the individual kernels of the kernel density estimate.
To obtain a bandwidth scalar representing the variance of each kernel, a ctmm
object with isotropic=TRUE
is required. In this case, bandwidth
will return bandwidth matrix with identical variances along its diagonal. Note that forcing isotropic=TRUE
will provide an inaccurate estimate for very eccentric distributions.
In v1.0.1 the default fast
, dt
, PC
arguments depend on the sample size, with fast=FALSE
, PC="Direct"
for small sample sizes, fast=FALSE
, PC="Markov"
for moderate sample sizes, and fast=TRUE
, PC="Markov"
for large sample sizes, where dt
is taken to be the integer fraction of the median sampling interval closest to the minimum sampling interval.
In v0.6.2 the default dt
was increased form the minimum time difference to a small quantile no less than error
times the median.
C. H. Fleming.
T. F. Chan, “An Optimal Circulant Preconditioner for Toeplitz Systems”, SIAM Journal on Scientific and Statistical Computing, 9:4, 766-771 (1988) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/0909051")}.
D. Marcotte, “Fast variogram computation with FFT”, Computers and Geosciences 22:10, 1175-1186 (1996) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0098-3004(96)00026-X")}.
C. H. Fleming, W. F. Fagan, T. Mueller, K. A. Olson, P. Leimgruber, J. M. Calabrese, “Rigorous home-range estimation with movement data: A new autocorrelated kernel-density estimator”, Ecology, 96:5, 1182-1188 (2015) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1890/14-2010.1")}.
C. H. Fleming, D. Sheldon, W. F. Fagan, P. Leimgruber, T. Mueller, D. Nandintsetseg, M. J. Noonan, K. A. Olson, E. Setyawan, A. Sianipar, J. M. Calabrese, “Correcting for missing and irregular data in home-range estimation”, Ecological Applications, 28:4, 1003-1010 (2018) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/eap.1704")}.
akde
, ctmm.fit
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.