Exploiting informative priors for Bayesian classification and regression trees

A general method for defining informative priors on statistical models is presented and applied specifically to the space of classification and regression trees. A Bayesian approach to learning such models from data is taken, with the Metropolis- Hastings algorithm being used to approximately sample from the posterior. By only using proposal distributions closely tied to the prior, acceptance probabilities are easily computable via marginal likelihood ratios, whatever the prior used. Our approach is empirically tested by varying (i) the data, (ii) the prior and (iii) the proposal distribution. A comparison with related work is given

Markov Chain Monte Carlo using tree-based priors on model structure

We present a general framework for defining priors on model structure and sampling from the posterior using the Metropolis-Hastings algorithm. The key idea is that structure priors are defined via a probability tree and that the proposal mechanism for the Metropolis-Hastings algorithm operates by traversing this tree, thereby defining a cheaply computable acceptance probability. We have applied this approach to Bayesian net structure learning using a number of priors and tree traversal strategies. Our results show that these must be chosen appropriately for this approach to be successful

Markov Chain Monte Carlo using Tree-Based Priors on Model Structure

We present a general framework for defining priors on model structure and sampling from the posterior using the Metropolis-Hastings algorithm. The key idea is that structure priors are defined via a probability tree and that the proposal mechanism for the Metropolis-Hastings algorithm operates by traversing this tree, thereby defining a cheaply computable acceptance probability. We have applied this approach to Bayesian net structure learning using a number of priors and tree traversal strategies. Our results show that these must be chosen appropriately for this approach to be successful

Markov chain Monte Carlo using tree-based priors on model structure.

We present a general framework for defining priors on model structure and sampling from the posterior using the Metropolis-Hastings algorithm. The key ideas are that structure priors are defined via a probability tree and that the proposal distribution for the Metropolis-Hastings algorithm is defined using the prior, thereby defining a cheaply computable acceptance probability. We have applied this approach to Bayesian net structure learning using a number of priors and proposal distributions. Our results show that these must be chosen appropriately for this approach to be successful