Bayesian Parameter Estimation in Ising and Potts Models: A Comparative Study with Applications to Protein Modeling

Ising and Potts models are discrete Gibbs random field models originating in statistical physics, which are now widely used in statistics for applications in spatial modeling, image processing, computational biology, and computational neuroscience. However, parameter estimation in these models remains challenging due to the appearance of intractable normalizing constants in the likelihood. Here we compare several proposed approximation schemes for Bayesian parameter estimation, including multiple Monte Carlo methods for approximating ratios of normalizing constants based on importance sampling, bridge sampling, and recently proposed perfect simulation methods. On small lattices where exact recursions can be used for comparison, we evaluate the accuracy and rate of convergence for these methods, and compare to a pseudo-likelihood based method. We conclude that a pseudo-likelihood approximation to the posterior performs surprisingly well, and is the only method that scales to realistic-size problems. We demonstrate this approach for statistical protein modeling, and compare the results on a protein fold recognition experiment, where it significantly outperforms knowledge-based statistical potentials based on the ‘quasi-chemical approximation’ commonly used in structural bioinformatics. ∗Corresponding author: Scott C. Schmidler, Department of Statistical Science, Duke University, Durham, NC 27708-0251. Tel: (919) 684-8064; Fax: (919) 684-8594; Email: [email protected]