target: Class: target distribution

In PAWL: Implementation of the PAWL algorithm

Description

This class represents target distributions, that is, probability distributions from which we want to sample using MCMC or Wang-Landau.

Objects from the Class

Objects should created by calls of the function target. Examples are provided that should help implementing any continuous probability distributions.

Important slots

dimension:

Object of class "numeric": should be an integer specifying the dimension of the state space on which the target distribution is defined.

logdensity:

Object of class "function" : should be a function taking n points in the state space and parameters, and returning a vector of n real values. See the example below. This function is in most cases the most time-consuming part in a MCMC algorithm, so make sure it runs reasonably fast!

rinit:

Object of class "function" : this function should take an integer as argument, say n. Then the function should return a matrix of dimension n times d (where d is the dimension of the state space), representing n points in the state space. These n points will be used as starting points of a parallel MCMC algorithm.

Optional slots

parameters:

Object of class "list" : you can put anything in that list (and nothing, which is the defaults), the important thing is that calls to logdensity(x, parameters)

return sensible values. For example, for a gaussian target distribution, you can put the mean and the variance in the parameters list (see example below). If need be, you can put a whole data set in there.

type:

Object of class "character" : could be "continuous" or "discrete"; default is "continuous".

name:

Object of class "character" : ... if you want to name your distribution (default is "unspecified").

generate:

Object of class "function" : does not have to be specified, but if it is specified it should be a function to generate from the distribution (like rnorm is to the standard normal distribution).

Methods

show

signature(object = "target"): provides a little summary of a target object when called (or when print is called).

Author(s)

Luke Bornn <[e-mail]>, Pierre E. Jacob <[e-mail]>

Examples

  showClass("target")
  # starting points for MCMC algorithms
  rinit <- function(size) rnorm(size)
  # target log density function: a gaussian distribution N(mean = 2, sd = 3)
  parameters <- list(mean = 2, sd = 3)
  logdensity <- function(x, parameters) dnorm(x, parameters$mean, parameters$sd, log = TRUE)
  # creating the target object
  gaussiantarget <- target(name = "gaussian", dimension = 1,
                    rinit = rinit, logdensity = logdensity,
                    parameters = parameters)
  print(gaussiantarget)

PAWL documentation built on May 2, 2019, 5:58 a.m.