Simulations Using Markov Chain Monte Carlo Methods
Markov chain Monte Carlo is a powerful method to estimate parameters that involve a mathematically intractable normalization constant. We discuss the Metropolis-Hastings algorithm in problems with one unknown and two unknown parameters. In the one-parameter case, we discuss the Beta-Binomial model. Due to conjugate prior distribution, the actual posterior distribution is known, providing an opportunity to compare our sampler output to the actual posterior distribution. We illustrate the two-parameter case with an example of the normal distribution with unknown mean and variance. In the last section, we carry out simulations of Straussian spatial point patterns, conditioning on the number of points in the pattern.