{"id":159,"date":"2013-09-10T15:55:00","date_gmt":"2013-09-10T19:55:00","guid":{"rendered":"http:\/\/www.matthewpratola.com\/?p=159"},"modified":"2018-02-13T18:53:07","modified_gmt":"2018-02-13T23:53:07","slug":"159","status":"publish","type":"post","link":"https:\/\/matthewpratola.com\/2013\/09\/10\/159\/","title":{"rendered":""},"content":{"rendered":"<p>I&#8217;m just about to submit some of our newest research involving Bayesian regression trees!&nbsp; A really exciting project on MCMC samplers that has enabled us to use this flexible and scaleable regression model approach in challenging uncertainty quantification problems.&nbsp; <strong>Update<\/strong>: appears in Bayesian Analysis 11(3) (2016): 885-911.&nbsp; Abstract follows.<\/p>\n<blockquote>\n<p style=\"text-align: justify;\"><em>Bayesian regression trees are flexible non-parametric models that are well suited to many modern statistical regression problems.&nbsp; Many such tree models have been proposed, from the simple single-tree model to more complex tree ensembles.&nbsp; Their non-parametric formulation allows for&nbsp; effective and efficient modeling of datasets exhibiting complex non-linear relationships between the model predictors and observations.&nbsp; However, the mixing behaviour of the MCMC sampler is sometimes poor.&nbsp; This is because the proposals in the sampler are typically local alterations of the tree structure, such as the birth\/death of leaf nodes, which does not allow for efficient traversal of the model space.&nbsp; This poor mixing can lead to inferential problems, such as under-representing uncertainty.&nbsp; In this paper, we develop novel proposal mechanisms for efficient sampling.&nbsp; The first is a rule perturbation proposal while the second we call tree rotation.&nbsp; The perturbation proposal can be seen as an efficient variation of the change proposal&nbsp; found in existing literature.&nbsp; The novel tree rotation proposal is simple to implement&nbsp; as it only requires local changes to the regression tree structure, yet it efficiently traverses disparate regions of the model space along contours of equal probability.&nbsp; When combined with the classical birth\/death proposal, the resulting MCMC sampler exhibits good acceptance rates and properly represents model uncertainty in the posterior samples.&nbsp; We implement this sampling algorithm in the Bayesian Additive Regression Tree (BART) model and demonstrate its effectiveness on a prediction problem from computer experiments and a test function where structural tree variability is needed to fully explore the posterior.<\/em><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m just about to submit some of our newest research involving Bayesian regression trees!&nbsp; A really exciting project on MCMC samplers that has enabled us to use this flexible and scaleable regression model approach in challenging uncertainty quantification problems.&nbsp; Update: appears in Bayesian Analysis 11(3) (2016): 885-911.&nbsp; Abstract follows. Bayesian regression trees are flexible non-parametric &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/matthewpratola.com\/2013\/09\/10\/159\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","footnotes":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[8],"tags":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/s2GB44-159","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/posts\/159"}],"collection":[{"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/comments?post=159"}],"version-history":[{"count":14,"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/posts\/159\/revisions"}],"predecessor-version":[{"id":217,"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/posts\/159\/revisions\/217"}],"wp:attachment":[{"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/media?parent=159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/categories?post=159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matthewpratola.com\/wp-json\/wp\/v2\/tags?post=159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}