suffstat              package:spatstat              R Documentation

_S_u_f_f_i_c_i_e_n_t _S_t_a_t_i_s_t_i_c _o_f _P_o_i_n_t _P_r_o_c_e_s_s _M_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

       suffstat(model, X)

_A_r_g_u_m_e_n_t_s:

   model: A fitted point process model (object of class '"ppm"'). 

       X: A point pattern (object of class '"ppp"'). 

_D_e_t_a_i_l_s:

     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 * 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).

_V_a_l_u_e:

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

_A_u_t_h_o_r(_s):

     Adrian Baddeley adrian@maths.uwa.edu.au <URL:
     http://www.maths.uwa.edu.au/~adrian/> and Rolf Turner
     rolf@math.unb.ca <URL: http://www.math.unb.ca/~rolf>

_S_e_e _A_l_s_o:

     'ppm'

_E_x_a_m_p_l_e_s:

         data(swedishpines)
         fitS <- ppm(swedishpines, ~1, Strauss(7))
         X <- rpoispp(summary(swedishpines)$intensity, win=swedishpines$window)
         suffstat(fitS, X)

