This chapter deals with likelihood inference for spatial point processes using the methods of Moyeed and Baddeley (1991), Geyer and Thompson (1992), Gelfand and Carlin (1993), Geyer (1994), and Geyer and Møller (1994) using Markov chain Monte Carlo (MCMC). The basic message is
If you can write down a model, I can do likelihood inference for it, not only maximum likelihood estimation, but also likelihood ratio tests, likelihood based confidence regions, profile likelihoods, whatever. That includes conditional likelihood inference and inference with missing data.This is overstated, of course. There is no question that one can write down a model so complicated that Monte Carlo will take so much time that no one would wait for an answer. But analyses that can be done are far beyond what is generally recognized.
This does not mean that MCMC likelihood analyses are easy. They usually require writing of computer code or at least modification of someone else's code, and they require hours of computer time. Each analysis is more a mini research project than a routine calculation. But if an analysis is worth doing, it generally can be done.
The code used to do the analyses in this chapter is available by anonymous ftp from the server at the School of Statistics, University of Minnesota ftp://stat.umn.edu/pub/points/points.tar.gz
Most of the code is written in the S language except for the samplers, which are written in C to be dynamically loaded into S or S-plus. One bit of code uses the S-plus function acf. The reader who has S-plus can reproduce the results in this section using this code. The reader who has S can reproduce all but the optimal spacing calculation in Section 1.13.2.
Samplers are provided only for three models. To do a new model, it would be necessary to write new code or modify my code. If there is a way to make samplers both efficient and easy to modify, I do not know it.
Computer code traditionally comes with such a disclaimer, scientific papers traditionally do not. MCMC is a complex mixture of computer programming, statistical theory, and practical experience. When it works, it does things that cannot be done any other way, but it is good to remember that it is not foolproof.