© 2003 by Biometrika Trust
Bayesian inference for Markov processes with diffusion and discrete components
1 Department of Probability and Statistics, University of Sheffield, Sheffield S3 7RH, U.Kp.blackwell{at}sheffield.ac.uk
Data arising in certain radio-tracking experiments consist of both a continuous spatial component and a discrete component related to behaviour.This leads naturally to stochastic models with a state space which is a product of continuous and discrete components. We consider a class of such models in continuous time, which can be thought of as diffusions in random environments. They are related to switching diffusion or hidden Markov models, but observations are made on both components at discrete time points, so that neither component is completely ‘hidden’. We describe and illustrate an approach to fully Bayesian inference for these general models. The algorithm used is a hybrid Markov chain Monte Carlo method. The diffusion parameters, the environment parameters and the sample path of the environment process itself are updated separately, in sequence, and the individual steps are a mixture of Gibbs and random walk Metropolis–Hastings types. Some implementation and model checking issues are discussed, and an example using data arising from a radio-tracking experiment is described.
Key Words: Bayesian inference; Diffusion process; Hidden Markov model; Markov chain Monte Carlo; Ornstein–Uhlenbeck process; Posterior predictive model checking; Radio-tracking; Random environment
Received December 2000. Revised January 2003
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  J. M. Fryxell, M. Hazell, L. Borger, B. D. Dalziel, D. T. Haydon, J. M. Morales, T. McIntosh, and R. C. Rosatte Movement Ecology Special Feature: Multiple movement modes by large herbivores at multiple spatiotemporal scales PNAS, December 9, 2008; 105(49): 19114 - 19119. [Abstract] [Full Text] [PDF]
|
|