Chapter 2 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.