suffstat

0th

Percentile

Sufficient Statistic of Point Process Model

The canonical sufficient statistic of a point process model is evaluated for a given point pattern.

Keywords
spatial
Usage
suffstat(model, X)
Arguments
model
A fitted point process model (object of class "ppm").
X
A point pattern (object of class "ppp").
Details

The canonical sufficient statistic of model is evaluated for the point pattern X. This computation is useful for various Monte Carlo methods. Here model should be a point process model (object of class "ppm", see ppm.object), typically obtained from the model-fitting function ppm. The argument X should be a point pattern (object of class "ppp").

Every point process model fitted by ppm has a probability density of the form $$f(x) = Z(\theta) \exp(\theta^T S(x))$$ where $x$ denotes a typical realisation (i.e. a point pattern), $\theta$ is the vector of model coefficients, $Z(\theta)$ is a normalising constant, and $S(x)$ is a function of the realisation $x$, called the ``canonical sufficient statistic'' of the model.

For example, the stationary Poisson process has canonical sufficient statistic $S(x)=n(x)$, the number of points in $x$. The stationary Strauss process with interaction range $r$ (and no edge correction) has canonical sufficient statistic $S(x)=(n(x),d(x))$ where $d(x)$ is the number of pairs of points in $x$ which are closer than a distance $r$ to each other.

suffstat(model, X) returns the value of $S(x)$, where $S$ is the canonical sufficient statistic associated with model, evaluated when $x$ is the given point pattern X. The result is a numeric vector, with entries which correspond to the entries of the coefficient vector coef(model).

The sufficient statistic $S$ does not depend on the fitted coefficients of the model. However it does depend on the irregular parameters which are fixed in the original call to ppm, for example, the interaction range r of the Strauss process. The sufficient statistic also depends on the edge correction that was used to fit the model.

Non-finite values of the sufficient statistic (NA or -Inf) may be returned if the point pattern X is not a possible realisation of the model (i.e. if X has zero probability of occurring under model for all values of the canonical coefficients $\theta$).

Value

  • A numeric vector of sufficient statistics. The entries correspond to the model coefficients coef(model).

See Also

ppm

Aliases
  • suffstat
Examples
data(swedishpines)
    fitS <- ppm(swedishpines, ~1, Strauss(7))
    X <- rpoispp(summary(swedishpines)$intensity, win=swedishpines$window)
    suffstat(fitS, X)
Documentation reproduced from package spatstat, version 1.6-11, License: GPL version 2 or newer

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