rmh                 package:spatstat                 R Documentation

_S_i_m_u_l_a_t_e _p_o_i_n_t _p_a_t_t_e_r_n_s _u_s_i_n_g _t_h_e _M_e_t_r_o_p_o_l_i_s-_H_a_s_t_i_n_g_s _a_l_g_o_r_i_t_h_m.

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

     Generic function for running the Metropolis-Hastings algorithm to
     produce simulated realisations of a point process model.

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

     rmh(model, ...)

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

   model: The point process model to be simulated. 

     ...: Further arguments controlling the simulation. 

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

     The Metropolis-Hastings algorithm can be used to generate
     simulated realisations from a wide range of spatial point
     processes. For caveats, see below.

     The function 'rmh' is generic; it has methods 'rmh.ppm' (for
     objects of class '"ppm"') and  'rmh.default' (the default). The
     actual implementation of the Metropolis-Hastings algorithm is
     contained in 'rmh.default'. For details of its use, see  'rmh.ppm'
     or 'rmh.default'.

     [If the model is a Poisson process, then Metropolis-Hastings is
     not used; the Poisson model is generated directly using 'rpoispp'
     or 'rmpoispp'.]

     In brief, the Metropolis-Hastings algorithm is a Markov Chain,
     whose states are spatial point patterns, and whose limiting
     distribution is the desired point process. After running the
     algorithm for a very large number of iterations, we may regard the
     state of the algorithm as a realisation from the desired point
     process.

     However, there are difficulties in deciding whether the algorithm
     has run for ``long enough''. The convergence of the algorithm may
     indeed be extremely slow. No guarantees of convergence are given!

     While it is fashionable to decry the Metropolis-Hastings algorithm
     for its poor convergence and other properties, it has the
     advantage of being easy to implement for a wide range of models.

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

     A point pattern, in the form of an object of class '"ppp"'. See
     'rmh.default' for details.

_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:

     'rmh.default'

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

         # See examples in rmh.default and rmh.ppm

