6  Key stelfi functions

Summary of model fitting functions offered listing the key arguments for each.

Function Key arguments
fit_hawkes()
  • times - a vector of numeric occurrence times.

  • parameters - a vector of named starting values for \(\mu\) (mu), \(\alpha\) (alpha), and \(\beta\) (beta).

  • marks - optional, a vector of marks (\(m(t)\)).

fit_mhawkes()
  • times - a vector of numeric occurrence times.

  • stream - character vector specifying the stream ID of each observation in times.

  • parameters - a vector of named starting values for \(\mu\) (mu), \(\alpha\) (alpha), and \(\beta\) (beta).

fit_hawkes_cbf()

As fit_hawkes() plus

  • background - some assumed time dependent background function \(\mu(t)\).

  • background_integral - the integral of background.

  • background_parameters - parameter starting values for \(\mu(t)\).

( \(^*\)Note, \(\texttt{mu}\) in parameters will be ignored)

fit_lgcp()
  • locs - a named data frame of event locations, x, y, and t (optional).

  • sf - a polygon of the spatial domain.

  • smesh - a Delaunay triangulation of the spatial domain returned by INLA::inla.mesh.2d().

  • tmesh - optional, a temporal mesh returned by INLA::inla.mesh.1d()).

  • parameters - a vector of named starting values for \(\boldsymbol{\beta}\) (beta), | \(\text{log}(\tau)\) (log_tau), \(\text{log}(\kappa)\) (log_kappa), and \(\textrm{arctan}(\rho)\) (atanh_rho, optional).

fit_mlgcp()
  • locs, sf, and smesh - as fit_lgcp().

  • marks - a matrix of marks for each observation of the point pattern.

  • parameters - a list of named parameters, as fit_lgcp() plus (betamarks), (betapp), (marks_coefs_pp ).

  • methods - integer(s) specifying mark distribution: 0, Gaussian; 1, Poisson; 2, binomial; 3, gamma.

  • strfixed - fixed structural parameters, depends on mark distribution.

  • fields - a binary vector indicating whether there is a new random field for each mark.

fit_stelfi()
  • times - as fit_hawkes().

  • locs, sf, and smesh - as fit_lgcp().

  • parameters - a list of named parameter starting values for \(\mu\) (mu), \(\alpha\) (alpha), \(\beta\) (beta), \(\sigma_x\) (xsigma) \(\sigma_y\) (ysigma), and \(\rho\) (rho).

  • GMRF - logical, should a GMRF be included as a latent spatial effect if so \(\tau\) (tau) and \(\kappa\)(kappa) supplied to parameters.

Summary of utility and simulation functions listing the key arguments for each.

Function Key arguments Purpose
get_coefs()
  • obj - a fitted model object returned by any one of the functions in the Table above
Extract estimated parameter values from a fitted model.
get_fields()

As fit_lgcp() and

  • sd - logical, return standard deviation.
Extract estimated mean, or standard deviation, of GMRF(s).
get_weights()
  • mesh - a Delaunay triangulation of the spatial domain returned by INLA::inla.mesh. 2d().

  • sf - a polygon of the spatial domain.

Calculate mesh weights.
mesh_2_sf()
  • mesh - a Delaunay triangulation of the spatial domain returned by INLA::inla.mesh. 2d().
Transforms mesh into a sf object.
show_field()
  • x - a vector of values, one per each smesh node.

  • smesh - as fit_lgcp() .

  • sf - as fit_lgcp().

  • clip - logical, clip to domain

Plots spatial random field values.
show_hawkes()
  • obj - a fitted model object returned by fit_hawkes() or fit_hawkes_cbf().
Plot fitted Hawkes model.
show_hawkes_GOF()
  • obj - as show_hawkes().

  • plot - logical

  • return_values - logical, return compensator values

Plot goodness-of-fit metrics for a Hawkes model.
show_lambda()

As fit_lgcp() and

  • clip - logical, clip to domain
Plot estimated spatial intensity from a fitted log-Gaussian Cox process model.
sim_hawkes() As fit_hawkes() Simulate a Hawkes process.
sim_lgcp() As fit_lgcp() Simulate a realisation of a log-Gaussian Cox process.