Fit the fBM model.

Fit the fBM model.

fbm_fit(
  Xt,
  dt,
  drift = c("linear", "none", "quadratic"),
  vcov = TRUE,
  ad_only = TRUE
)

Arguments

Xt

Matrix of trajectory positions, where each row is an observation and each column is a measurement coordinate. The trajectory is assumed to be sampled at a constant frequency.

dt

Interobservation time \(\Delta t\) = 1/fps (positive scalar).

drift

Character string specifying one of the preset drift types "linear", "none", or "quadratic". Custom drift functions are not supported through this simplified interface. See csi_model for details.

vcov

Logical; if TRUE, also estimate the variance matrix.

ad_only

Whether to return estimates of (alpha, log(D)) only, or the entire parameter vector omega in the computational basis.

Value

A vector of estimated parameters on the transformed scale. If vcov == TRUE, a list with components:

coef

A vector of estimated parameters on transformed scale.

vcov

A matrix of estimated covariance of parameters on transformed scale.

If ad_only == TRUE, instead of the transformed scale parameters, returns an estimate (and possibly the estimated convariance) of (alpha, D).

See also

fbm_model, the class definition for the fBM model.

Examples

# simulate data from the fbm model
alpha <- .8

dt <- 1/60
N <- 1800
ndim <- 2

Xt <- csi_sim(drift = matrix(0, N-1, ndim),
              acf = fbm_acf(alpha, dt, N-1),
              Sigma = diag(ndim),
              X0 = rep(0, ndim))


# Fit the fbm model
fbm_fit(Xt, dt = dt, drift = "linear")
#> $coef
#>      alpha       logD 
#>  0.7604718 -0.8502970 
#> 
#> $vcov
#>              alpha        logD
#> alpha 0.0003726923 0.001424218
#> logD  0.0014242183 0.005998638
#>