{"id":193,"date":"2017-01-17T21:08:12","date_gmt":"2017-01-17T19:08:12","guid":{"rendered":"http:\/\/benediktehinger.de\/blog\/science\/?p=193"},"modified":"2017-01-17T21:08:12","modified_gmt":"2017-01-17T19:08:12","slug":"how-to-use-bimodal-priors-for-bayesian-data-analysis-in-stan","status":"publish","type":"post","link":"https:\/\/benediktehinger.de\/blog\/science\/how-to-use-bimodal-priors-for-bayesian-data-analysis-in-stan\/","title":{"rendered":"How to use bimodal priors for bayesian data analysis in STAN"},"content":{"rendered":"

I tried adding a bi-modal prior in STAN for a homework exercise on Bayesian Data Analysis. At first, I thought this could work:
\n“`STAN
\nmodel{
\n mu ~ normal(-0.5,0.3) + normal(0.5,0.3);
\n}
\n“`
\nBut it doesn’t. I had to dig deeper and I thought I could simply add multiple times to the log-posterior due to a sideremark of Bob Carpenter<\/a>:<\/p>\n

“`STAN
\ntarget += normal_lpdf(mu|.5,0.3);
\ntarget += normal_lpdf(mu|-.5,0.3);
\n“`
\nWhich also does not work. Finally, the solution is akin to the mixture model in the STAN manual:<\/p>\n

“`STAN
\n target += log_sum_exp(normal_lpdf(mu|.5,0.3),normal_lpdf(mu|-.5,0.3));
\n“`<\/p>\n

This results in beautiful bi-modal priors:
\n<\/a>\"\"<\/a><\/p>\n

I did not find anything on google or the manual of how to do this. If there is a smarter way to do it, please leave a comment.<\/p>\n

“`R<\/p>\n

library(rstan)<\/p>\n

model <- \"\ndata { \n}\nparameters {\nreal mu;\n} \ntransformed parameters {\n}\nmodel {\n\/\/mu ~ normal(10,1);\n\/\/mu ~ normal(-10,1);\ntarget += log_sum_exp(normal_lpdf(mu|-.5,.3),normal_lpdf(mu|.5,.3));\n\n}\"\n\n\n\nsamples <- stan(model_code=model, \n iter=2000, \n chains=4, \n thin=1,\n # seed=123 # Setting seed; Default is random seed\n)\n\nggmcmc::ggs_density(ggmcmc::ggs(samples))+theme_minimal()\n```\n<\/p>\n","protected":false},"excerpt":{"rendered":"

I tried adding a bi-modal prior in STAN for a homework exercise on Bayesian Data Analysis. At first, I thought this could work: “`STAN model{ mu ~ normal(-0.5,0.3) + normal(0.5,0.3); } “` But it doesn’t. I had to dig deeper and I thought I could simply add multiple times to the log-posterior due to a sideremark of Bob Carpenter: “`STAN target += normal_lpdf(mu|.5,0.3); target += normal_lpdf(mu|-.5,0.3); “` Which also does not work. Finally, the solution is akin to the mixture model in the STAN manual: “`STAN target += log_sum_exp(normal_lpdf(mu|.5,0.3),normal_lpdf(mu|-.5,0.3)); “` This results in beautiful bi-modal priors: I did not find…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-193","post","type-post","status-publish","format-standard","hentry","category-blog"],"_links":{"self":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/posts\/193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/comments?post=193"}],"version-history":[{"count":0,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/posts\/193\/revisions"}],"wp:attachment":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/media?parent=193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/categories?post=193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/tags?post=193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}