USING HIDDEN MARKOV-CHAINS AND EMPIRICAL BAYES CHANGE-POINT ESTIMATION FOR TRANSECT DATA

Consider a lattice of locations in one dimension at which data are obs erved. We model the data as a random hierarchical process. The hidden process is assumed to have a (prior) distribution that is derived from a two-state Markov chain. The states correspond to the mean values (h igh and low) of the observed data. Conditional on the states, the obse rvations are modelled, for example, as independent Gaussian random var iables with identical variances. In this model, there are four free pa rameters: the Gaussian variance, the high and low mean values, and the transition probability in the Markov chain. A parametric empirical Ba yes approach requires estimation of these four parameters from the mar ginal (unconditional) distribution of the data and we use the EM algor ithm to do this. From the posterior of the hidden process, we use simu lated annealing to find the maximum a posteriori (MAP) estimate. Using a Gibbs sampler, we also obtain the maximum marginal posterior probab ility (MMPP) estimate of the hidden process. We use these methods to d etermine where change-points occur in spatial transects through grassl and vegetation, a problem of considerable interest to plant ecologists .