Finn Krogstad
Doctoral Candidate
Forest Engineering Program
College of Forest Resources
University of Washington

A simplified approach to Bayesian Metropolis-Hastings is hypothesized to
provide a simple, flexible tool for researchers who currently focus on
deterministic models. This approach allows researches to incorporate
existing models and data, incrementally move from simple to more complex,
address the range of parameter estimation and model testing and prediction
issues, and to use simulation experimentation to aid understanding of the
outputs. It is suggested that the approach outlined in this talk can provide
all the theory and tools necessary to get researchers started in using
Bayesian MCMC in their daily research.

The approach is as follows: Existing deterministic equations are
'directionalized', the uncertainty/variability is modeled for the input
variables, and observational error is modeled for all observed variables in
the existing WinBUGS software. Adding observed data to the resulting
'wrapped' model allows experimentation into how observation of some
variables alters uncertainty in others. The distinction between parameter
uncertainty and variability is discussed and modeled. Prior distributions
are not estimated, but modeled as posteriors with imperfect observations and
vague priors. Basic issues of convergence including burn-in and multi-modal
distributions are addressed. A more flexible approach is possible if
researchers can code their own MCMC simulations. Basic definitions of
probability, conditional probability, and marginal distributions are
necessary to turn questions into the integrals to be simulated. A brief
discussion of the Monte Carlo and Metropolis-Hastings algorithms is then
sufficient to allow coding and simulation of these problems.