# detpointprocfamilyfun

##### Construct a New Determinantal Point Process Model Family Function

Function to ease the implementation of a new determinantal point process model family.

##### Usage

```
detpointprocfamilyfun(kernel = NULL,
specden = NULL, basis = "fourierbasis",
convkernel = NULL, Kfun = NULL, valid = NULL, intensity = NULL,
dim = 2, name = "User-defined", isotropic = TRUE, range = NULL,
parbounds = NULL, specdenrange = NULL, startpar = NULL, …)
```

##### Arguments

- kernel
function specifying the kernel. May be set to

`NULL`

. See Details.- specden
function specifying the spectral density. May be set to

`NULL`

. See Details.- basis
character string giving the name of the basis. Defaults to the Fourier basis. See Details.

- convkernel
function specifying the k-fold auto-convolution of the kernel. May be set to

`NULL`

. See Details.- Kfun
function specifying the K-function. May be set to

`NULL`

. See Details.- valid
function determining whether a given set of parameter values yields a valid model. May be set to

`NULL`

. See Examples.- intensity
character string specifying which parameter is the intensity in the model family. Should be

`NULL`

if the model family has no intensity parameter.- dim
character strig specifying which parameter is the dimension of the state space in this model family (if any). Alternatively a positive integer specifying the dimension.

- name
character string giving the name of the model family used for printing.

- isotropic
logical value indicating whether or not the model is isotropic.

- range
function determining the interaction range of the model. May be set to

`NULL`

. See Examples.- parbounds
function determining the bounds for each model parameter when all other parameters are fixed. May be set to

`NULL`

. See Examples.- specdenrange
function specifying the the range of the spectral density if it is finite (only the case for very few models). May be set to

`NULL`

.- startpar
function determining starting values for parameters in any estimation algorithm. May be set to

`NULL`

. See Examples.- …
Additional arguments for inclusion in the returned model object. These are not checked in any way.

##### Details

A determinantal point process family is specified either
in terms of a kernel (a positive semi-definite function, i.e. a
covariance function) or a spectral density, or preferably both.
One of these can be `NULL`

if it is unknown, but not both.
When both are supplied they must have the same arguments.
The first argument gives
the values at which the function should be evaluated. In general
the function should accept an \(n\) by \(d\) matrix or
`data.frame`

specifying \(n (>=0)\)
points in dimension \(d\). If the model is isotropic it only needs to
accept a non-negative valued numeric of length \(n\). (In fact
there is currently almost no support for non-isotropic models, so
it is recommended not to specify such a model.) The name
of this argument could be chosen freely, but \(x\) is
recommended. The remaining arguments are the parameters of the
model. If one of these is an intensity parameter the name should
be mentioned in the argument `intensity`

. If one of these
specifies the dimension of the model it should be mentioned in the
argument `dim`

.

The kernel and spectral density is with respect to a
specific set of basis functions, which is typically the Fourier
basis. However this can be changed to any user-supplied basis in
the argument `basis`

. If such an alternative is supplied it
must be the name of a function expecting the same arguments as
`fourierbasis`

and returning the results in the same
form as `fourierbasis`

.

If supplied, the arguments of convkernel must obey the
following: first argument should be like the first argument of
kernel and/or specden (see above). The second argument (preferably
called `k`

) should be the positive integer specifying how many times
the auto-convolution is done (i.e. the \(k\) in \(k\)-fold
auto-convolution). The remaining arguments must agree with the
arguments of `kernel`

and/or `specden`

(see above).

If supplied, the arguments of `Kfun`

should be like the
arguments of `kernel`

and `specden`

(see above).

##### Examples

```
# NOT RUN {
## Example of how to define the Gauss family
exGauss <- detpointprocfamilyfun(
name="Gaussian",
kernel=function(x, lambda, alpha, d){
lambda*exp(-(x/alpha)^2)
},
specden=function(x, lambda, alpha, d){
lambda * (sqrt(pi)*alpha)^d * exp(-(x*alpha*pi)^2)
},
convkernel=function(x, k, lambda, alpha, d){
logres <- k*log(lambda*pi*alpha^2) - log(pi*k*alpha^2) - x^2/(k*alpha^2)
return(exp(logres))
},
Kfun = function(x, lambda, alpha, d){
pi*x^2 - pi*alpha^2/2*(1-exp(-2*x^2/alpha^2))
},
valid=function(lambda, alpha, d){
lambda>0 && alpha>0 && d>=1 && lambda <= (sqrt(pi)*alpha)^(-d)
},
isotropic=TRUE,
intensity="lambda",
dim="d",
range=function(alpha, bound = .99){
if(missing(alpha))
stop("The parameter alpha is missing.")
if(!(is.numeric(bound)&&bound>0&&bound<1))
stop("Argument bound must be a numeric between 0 and 1.")
return(alpha*sqrt(-log(sqrt(1-bound))))
},
parbounds=function(name, lambda, alpha, d){
switch(name,
lambda = c(0, (sqrt(pi)*alpha)^(-d)),
alpha = c(0, lambda^(-1/d)/sqrt(pi)),
stop("Parameter name misspecified")
)
},
startpar=function(model, X){
rslt <- NULL
if("lambda" %in% model$freepar){
lambda <- intensity(X)
rslt <- c(rslt, "lambda" = lambda)
model <- update(model, lambda=lambda)
}
if("alpha" %in% model$freepar){
alpha <- .8*dppparbounds(model, "alpha")[2]
rslt <- c(rslt, "alpha" = alpha)
}
return(rslt)
}
)
exGauss
m <- exGauss(lambda=100, alpha=.05, d=2)
m
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*